Artificial intelligence resources in control and automation engineering 9781608055890, 1608055892

Citation preview

Artificial Intelligence Resources in Control and Automation Engineering

Edited By

Evelio J. González University of La Laguna Spain

Co-Editors:

Leopoldo Acosta Sánchez University of La Laguna Spain

Alberto F. Hamilton Castro University of La Laguna Spain

eBooks End User License Agreement Please read this license agreement carefully before using this eBook. Your use of this eBook/chapter constitutes your agreement to the terms and conditions set forth in this License Agreement. Bentham Science Publishers agrees to grant the user of this eBook/chapter, a non-exclusive, nontransferable license to download and use this eBook/chapter under the following terms and conditions: 1. This eBook/chapter may be downloaded and used by one user on one computer. The user may make one back-up copy of this publication to avoid losing it. The user may not give copies of this publication to others, or make it available for others to copy or download. For a multi-user license contact [email protected] 2. All rights reserved: All content in this publication is copyrighted and Bentham Science Publishers own the copyright. You may not copy, reproduce, modify, remove, delete, augment, add to, publish, transmit, sell, resell, create derivative works from, or in any way exploit any of this publication’s content, in any form by any means, in whole or in part, without the prior written permission from Bentham Science Publishers. 3. The user may print one or more copies/pages of this eBook/chapter for their personal use. The user may not print pages from this eBook/chapter or the entire printed eBook/chapter for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained from the publisher for such requirements. Requests must be sent to the permissions department at E-mail: [email protected] 4. The unauthorized use or distribution of copyrighted or other proprietary content is illegal and could subject the purchaser to substantial money damages. The purchaser will be liable for any damage resulting from misuse of this publication or any violation of this License Agreement, including any infringement of copyrights or proprietary rights. Warranty Disclaimer: The publisher does not guarantee that the information in this publication is error-free, or warrants that it will meet the users’ requirements or that the operation of the publication will be uninterrupted or error-free. This publication is provided "as is" without warranty of any kind, either express or implied or statutory, including, without limitation, implied warranties of merchantability and fitness for a particular purpose. The entire risk as to the results and performance of this publication is assumed by the user. In no event will the publisher be liable for any damages, including, without limitation, incidental and consequential damages and damages for lost data or profits arising out of the use or inability to use the publication. The entire liability of the publisher shall be limited to the amount actually paid by the user for the eBook or eBook license agreement. Limitation of Liability: Under no circumstances shall Bentham Science Publishers, its staff, editors and authors, be liable for any special or consequential damages that result from the use of, or the inability to use, the materials in this site. eBook Product Disclaimer: No responsibility is assumed by Bentham Science Publishers, its staff or members of the editorial board for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products instruction, advertisements or ideas contained in the publication purchased or read by the user(s). Any dispute will be governed exclusively by the laws of the U.A.E. and will be settled exclusively by the competent Court at the city of Dubai, U.A.E. You (the user) acknowledge that you have read this Agreement, and agree to be bound by its terms and conditions. Permission for Use of Material and Reproduction Photocopying Information for Users Outside the USA: Bentham Science Publishers grants authorization for individuals to photocopy copyright material for private research use, on the sole basis that requests for such use are referred directly to the requestor's local Reproduction Rights Organization (RRO). The copyright fee is US $25.00 per copy per article exclusive of any charge or fee levied. In order to contact your local RRO, please contact the International Federation of Reproduction Rights Organisations (IFRRO), Rue du Prince Royal 87, B-I050 Brussels, Belgium; Tel: +32 2 551 08 99; Fax: +32 2 551 08 95; E-mail: [email protected]; url: www.ifrro.org This authorization does not extend to any other kind of copying by any means, in any form, and for any purpose other than private research use. Photocopying Information for Users in the USA: Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by Bentham Science Publishers for libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Services, provided that the appropriate fee of US $25.00 per copy per chapter is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers MA 01923, USA. Refer also to www.copyright.com

DEDICATION

To Laura

CONTENTS Foreword

i

Preface

ii

List of Contributors

iii

CHAPTERS 1. Intelligent PID DC Motor Speed Control Alteration Parameters Using Particle Swarm Optimization Boumediène Allaoua and Brahim Mebarki

3

2. Systems Theoretic Techniques for Modeling, Control and Decision Support in Complex Dynamic Systems Armen Bagdasaryan

15

3. Fuzzy Controllers Design for the Inertia Wheel Inverted Pendulum Fatah Chetouane

73

4. Engineering Congestion Control of Internet Video Streaming with Fuzzy Logic Martin Fleury, Emanuel A. Jammeh and Mohammed Ghanbari

92

5. Artificial Intelligence and Electrical Drives Ben Hamed Mouna and Sbita Lassaâd 6. Mobile Manipulator with Resolved Acceleration and Knowledge-Based Fuzzy Active Force Control M. Mailah, E. Pitowarno and A. Noshadi 7. Intelligent Systems Used in Continuous Casting Process Gelu Ovidiu Tirian

135

159

8. A Novel Electric Load Demand Forecaster Using Taguchi’s Method and Artificial Neural Network Albert W.L. Yao, J.H. Sun, H.T. Liao, C.Y. Liu and C.T. Yin

180

9. An Application of a Dynamic Matrix Control Algorithm: Path Tracking Using Predictive Control J. Espelosín, A. Hamilton, L. Acosta, J. Toledo and E.J. González

193

Index

 

108

198

i

FOREWORD It brings me immense satisfaction to have been asked to write the prologue for this book, the content of which is dedicated to presenting a variety of research that has been carried out in the areas of Control and Automation, and one shared by us all, that of Artificial Intelligence. Personally, I have had the pleasure of working with the editors of this book for many years here at the University of La Laguna, years in which many personal, educational and research based discoveries have been made. I began working alongside Leopoldo Acosta from the moment I joined the University of La Laguna, more than 20 years ago. Those first few years were intense years, but ones in which I was lucky enough to count on his support from day one. His doctoral thesis (1991) focused on Control, but more specifically on Dynamic Programming in Continuous/Discreet Deterministic and Stochastic Systems; it was work that dealt with finding the heuristic properties that would reduce the spatial and temporal complexity of Dynamic Programming. Later, Alberto Hamilton joined the group, and together, we continued to pursue and develop this line of investigation, including, under the same approach, Neuronal Networks; our aim is to substitute the stages of Dynamic Programming with Neuronal Network Systems. His doctoral thesis defence, lead by Leopoldo and myself, was conducted in 1995. Evelio González’s incorporation reinforced the role of Artificial Intelligence. His doctoral thesis, which was led by Alberto Hamilton, tackled the subject matter of Multipurpose Structures based on Intelligent Agents, as well as the systemisation of the use of Multistage Neuronal Networks in Control. His doctoral thesis defence was conducted in 2004. Since then we have dedicated ourselves to different tasks related to Control, Robotics and Education, even though our shared background is in Artificial Intelligence. It has been of great pleasure to work with all of them over these many years. Now, in 2011, they have gone on to edit this book, one in which researchers from all over the world have presented their own particular research relating to the practical application of Artificial Intelligence to the problems found in Control and Robotics. It is always good news when a new book is released, and for this reason sincere congratulations go to the authors and editors of this book.

Lorenzo Moreno Director of Systems Engineering and Automation and Computer Architecture Department University of La Laguna Spain

ii

PREFACE This book series focuses on the application of Artificial Intelligence resources in fields related to Control and Automation Engineering. These resources (involving techniques such as neural networks, fuzzy logic, expert systems and others) have become a key tool for those researchers and engineers who need powerful answers to a wide range of problems. The book series pretends to be a survey guide for those people, presenting them with practical examples of real cases where those techniques have been successfully applied. This way, it is hoped that researchers will find new ideas to apply in their own systems. The focus of this book, then, lies in practical applications and real systems, where the combination of AI and Control and Automation Engineering techniques have been shown to be a powerful tool. Some significant research on the application of these techniques has been included in this book. Allaoua and Mebarki describe the design of an intelligent controller for a DC motor drive using the Particle Swarm Optimization (PSO) method for create the optimal Proportional-Integral-Derivative (PID) controller alteration parameters. Chetouane introduces the problem of controlling a wheel inverted pendulum (IWIP) system using fuzzy logic techniques. Fleurym Jammeh and Ghanbari introduce the control problem faced when designing a fuzzy logic congestion controller in terms of the restrictions of a compressed video bitstream and the uncertainties that affect congestion control. Ben Hamed Mouna and Sbita Lassaâd present the application of fuzzy logic and neural networks in motor drive systems, in particular, artificial neural network speed sensorless fuzzy control both in scalar and vector control of induction motors. The research by Mailah and Pitowarno concerns the application of a novel and robust intelligent Active Force Control (AFC) based strategy to control a differentially-driven wheeled Mobile Manipulator (MM) system with nonholonomic constraint. Tirian describes a new control method, based on fuzzy logic, for avoiding cracks inside the crystallizing apparatus in continuous casting of steel. Yao et al. develop a demand-control system with an intelligent predictor to manage the electric facility online using Taguchi’s and rolling modeling methods of artificial neural networks. Finally, Espelosín et al. have developed an application for a dynamic matrix control algorithm: path tracking using predictive control. As editors, we would like to thank these authors for their valuable contributions to the field of Control and Automation Engineering.

Evelio J. González, Leopoldo Acosta and Alberto F. Hamilton University of La Laguna Spain

iii

List of Contributors ACOSTA, L. Dep. de Ingeniería de Sistemas y Automática y Arquitectura y Tecnología de Computadores. Universidad de La Laguna. Avd. Francisco Sánchez S/N La Laguna, CP: 38206. Spain. ALLAOUA, B. Faculty of the Sciences and the Technology, Department of the Technology, Bechar University, B.P 417 BECHAR (08000), Algeria. BAGDASARYAN, A. Russian Academy of Sciences, Trapeznikov Institute for Control Sciences, 65 Profsoyuznaya, 117997, Moscow, Russia. BEN HAMED, M. High Institute of Industrial Systems of Gabès, University of Gabès, Tunisia. CHETOUANE, F. Electrical and Industrial Engineering Department, Université de Moncton, New Brunswick, E1A3E9 Canada. ESPELOSÍN, J. Dep. de Ingeniería de Sistemas y Automática y Arquitectura y Tecnología de Computadores. Universidad de La Laguna. Avd. Francisco Sánchez S/N La Laguna, CP: 38206. Spain. FLEURY, M. University of Essex, School of Computer Science and Electronic Engineering, Multimedia Network Laboratory, Colchester, CO4 3SQ, United Kingdom. GHANBARI. M. University of Essex, School of Computer Science and Electronic Engineering, Multimedia Network Laboratory, Colchester, CO4 3SQ, United Kingdom. GONZÁLEZ, E.J. Dep. de Ingeniería de Sistemas y Automática y Arquitectura y Tecnología de Computadores. Universidad de La Laguna. Avd. Francisco Sánchez S/N La Laguna, CP: 38206, Spain. HAMILTON, A. Dep. de Ingeniería de Sistemas y Automática y Arquitectura y Tecnología de Computadores. Universidad de La Laguna. Avd. Francisco Sánchez S/N La Laguna, CP: 38206, Spain. JAMMEH. E.A. University of Essex, School of Computer Science and Electronic Engineering, Multimedia Network Laboratory, Colchester, CO4 3SQ, United Kingdom. LIAO, H.T. Ming Hsing University of Science and Technology, Taiwan. LIU, C.Y. Southern Taiwan University, Taiwan.

iv

MAILAH, M. Department of System Dynamics and Control, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia. MEBARKI. B. Faculty of the Sciences and the Technology, Department of the Technology, Bechar University, B.P 417 BECHAR (08000), Algeria. NOSHADI, A. Department of System Dynamics and Control, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia. PITOWARNO. E. Electronic Engineering Polytechnic Institute of Surabaya, ITS Sukolilo, Surabaya 60111, Indonesia. SBITA, L Engineering School of Gabès (ENIG), University of Gabès, Tunisia. SUN, J.H. National Kaohsiung First University of Science and Technology, Taiwan. TIRIAN, G.O. “Politehnica” University of Timisoara, Faculty of Engineering Hunedoara, Romania. TOLEDO, J. Dep. de Ingeniería de Sistemas y Automática y Arquitectura y Tecnología de Computadores, Universidad de La Laguna, Avd. Francisco Sánchez S/N La Laguna, CP: 38206, Spain. YAO, A.W.L. National Kaohsiung First University of Science and Technology, Taiwan. YIN,C.T. Machine & Tool Co. Ltd., Taiwan.

 

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 3-14

3

CHAPTER 1 Intelligent PID DC Motor Speed Control Alteration Parameters Using Particle Swarm Optimization Boumediène Allaoua* and Brahim Mebarki Faculty of the Sciences and the Technology, Department of the Technology, BECHAR University, B.P 417 BECHAR (08000), Algeria Abstract: In this paper, an intelligent controller of DC Motor drive is designed using Particle Swarm Optimization (PSO) method for formation of optimal Proportional-Integral-Derivative (PID) controller alteration parameters. The proposed approach has superior feature, including easy implementation, stable convergence characteristics and very good computational performances efficiency. The DC Motor Scheduling PID-PSO controller is modeled in MATLAB environment. Comparing with fuzzy logic controller using PSO intelligent algorithms, the planned method is more proficient in improving the speed loop response stability, the steady state error is reduced, the rising time is made suitable and the disturbances do not affect the performances of driving motor with no overtaking.

Keywords: Intelligent controller, DC motor, particle swam optimization, PID controller, fuzzy logic. 1. INTRODUCTION In spite of the development of power electronics resources, the direct current machines are becoming more and more useful insofar as they have found wide application, i.e. automobile industry (electric vehicle), weak power using battery system (motor of toy), the electric traction in the multi-machine systems, etc. The speed of DC motor can be adjusted to a great extent so as to provide easy control and high performance [1, 2]. There are several conventional and numeric controller types intended for controling the DC motor speed at its executing various tasks: PID Controller, Fuzzy Logic Controller; or the combination between them: PID-Particle Swarm Optimization, PID-Neural Networks, PID-Genetic Algorithm, PID-Ants Colony Optimization and the optimal Fuzzy Logic controller using the different strategy. PID controllers are widely used in industrial plants because they are simple and robust. Industrial processes are subjected to variation in parameters and parameter perturbations, which when significant make the system unstable. So the control engineers are on look for automatic tuning procedures. From the control point of view, dc motor exhibits excellent control characteristics because of the decoupled nature of the field [2]. Recently, many modern control methodologies such as nonlinear control [3], optimal control [4], variable structure control [5] and adaptive control [6] have been extensively proposed for DC motor. However, these approaches are either complex in theoretical bases or difficult to implement [7]. PID control with its three term functionality covering treatment to both transient and steady-states response, offers the simplest and yet most efficient solution to many real world control problems [8]. In spite of the simple structure and robustness of this method, optimally tuning gains of PID controllers have been quite difficult. The PSO methods have been employed successfully to solve complex optimization problems. PSO first introduced by Kennedy and Eberhart [9] is one of the modern heuristic algorithms; it has been motivated by the behavior of organisms, such as fish schooling and bird flocking [10, 11]. Generally, PSO is characterized as a simple concept, easy to implement, and computationally efficient. Unlike the other heuristic techniques, PSO has a flexible and well-balanced mechanism to enhance the global and local exploration abilities [12]. *Address correspondence to Boumediene Allaoua: Faculty of the Sciences and the Technology, Department of the Technology, BECHAR University, B.P 417 BECHAR (08000), Algeria; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

4 Artificial Intelligence Resources in Control and Automation Engineering

Allaoua and Mebarki

In this paper, scheduling PID tuning parameters using particle swarm optimization strategy for a DC motor speed control is proposed. This paper has been organized as follows: in section 2 the DC motor is described and the model of it is shown. In section 3, the particle swarm optimization method is reviewed. Section 4, describes how PSO is used to design the PID controller values optimally for a DC motor speed control. A comparison between the results obtained by the proposed method and Fuzzy-PSO method [13] via simulation of the DC motor speed control is presented in section 5. The paper is concluded in section 6. 2. MODEL OF DC MOTOR DC machines are characterized by their versatility. By means of various combinations of shunt series and separately-excited field windings they can be designed to display a wide variety of volt-ampere or speedtorque characteristics for both dynamic and steady-state operation. Because of the ease with which they can be controlled systems of DC machines have been frequently used in many applications requiring a wide range of motor speeds and a precise output motor control [14, 15]. In this paper, the separated excitation DC motor model is chosen according to its good electrical and mechanical performances more than other DC motor models. The DC motor is driven by applied voltage. Table 1 shows used symbols and Fig. (1) shows the equivalent circuit of DC motor with separate excitation. The characteristic equations of the DC motor are represented as:

d iex dt

Rex .iex Lex

d iind dt

Rind .iind Lind

d wr dt

Lindex .iex .iind J

1 .Vex Lex

(1)

Lindex .wr .iex Lind Cr J

1 .Vind Lind

(2)

fc .wr J

(3)

The equivalent circuit of DC motor with separate excitation is illustrated in Fig. (1). Table 1: Used symbols Symbols

Designations

Units

iex and iind

Excitation current and Induced current.

[A]

wr

Rotational speed of the DC Motor.

[Rad/Sec]

Vex and Vind

Excitation voltage and Induced voltage

[Volt]

Rex and Rind

Excitation Resistance and Induced Resistance.

[ ]

Lex , Lind and Lindex

Excitation, Induced and Mutual Inductance.

[mH]

J

Moment of Inertia.

[Kg.m2]

Cr

Couple resisting.

[N.m]

fc

Coefficient of Friction.

[N.m.Sec/Rad]

From the state equations (1), (2), (3) previous, we can construct the model with the environment MATLAB 7.6 (R2008a) in Simulink version 7.1. The model of the DC motor in Simulink is shown in Fig. (2). The various parameters of the DC motor are shown in Table 2.

Intelligent PID DC Motor Speed Control

Artificial Intelligence Resources in Control and Automation Engineering 5

Lindex

R ex

iex

Lind Rind

Lex

Vex

i in d

wr

E

Vind

Induce

Excitation

Figure 1: Equivalent circuit of DC motor with Separate Excitation.

1 Vind

1/Lind

1 s

Rind

Lindex 1 /Lind 240

1 /Lex

1 s

Rex

Vex 1 /Lex 1 Wr 1 s

fc

Lindex Cr 1 /J

Figure 2: Model of the DC Motor in Simulink. Table 2: Parameters of the DC Motor

Vex = 240 [V] Vind = 240 [V] Rex = 240 [ ]

Rind = 0.6 [ ] Lex = 120 [mH] Lind = 0.012 [mH] Lindex = 1.8 [mH] J = 1 [Kg.m2]

Cr = 29.2 [N.m]

fc = 0.0005[N.m.Sec/Rad]

6 Artificial Intelligence Resources in Control and Automation Engineering

Allaoua and Mebarki

3. OVERVIEW PARTICLE SWARM OPTIMIZATION

PSO is a population based optimization method first proposed by Eberhart and Colleagues [9-11]. Some of the attractive features of PSO include the ease of implementation and the fact that no gradient information is required. It can be used to solve a wide array of different optimization problems. Like evolutionary algorithms, PSO technique conducts search using a population of particles, corresponding to individuals. Each particle represents a candidate solution to the problem at hand. In a PSO system, particles change their positions by flying around in a multidimensional search space until computational limitations are exceeded. Concept of modification of a searching point by PSO is shown in Fig. (3). Xk : current position, Xk+1 : modified position, Vk : current velocity, Vk+1 : modified velocity, VPbest : velocity based on Pbest, Vgbest : velocity based on gbest.

X ik

1

Vi k Vi k X ik

1

gbest i

Vi Gbest

Vi Pbest

Pbest i

Figure 3: Concept of modification of a searching point by PSO.

The PSO technique is an evolutionary computation technique, but it differs from other well-known evolutionary computation algorithms such as the genetic algorithms. Although a population is used for searching the search space, there are no operators inspired by the human DNA procedures applied on the population. Instead, in PSO, the population dynamics simulates a ‘bird flock’s’ behavior, where social sharing of information takes place and individuals can profit from the discoveries and previous experience of all the other companions during the search for food. Thus, each companion, called particle, in the population, which is called swarm, is assumed to ‘fly’ over the search space in order to find promising regions of the landscape. For example, in the minimization case, such regions possess lower function values than others, visited previously. In this context, each particle is treated as a point in a d-dimensional space, which adjusts its own ‘flying’ according to its flying experience as well as the flying experience of other particles (companions). In PSO, a particle is defined as a moving point in hyperspace. For each particle, at the current time step, a record is kept of the position, velocity, and the best position found in the search space so far. Particle swarm optimization, developed by Kennedy and Eberhart [9-11], is one of the modern heuristic algorithms. It was inspired by the social behavior of bird and fish schooling, and has been found to be robust in solving continuous nonlinear optimization problems. This algorithm is based on the following scenario: a group of birds is randomly searching food in an area and there is only one piece of food. All birds are unaware where the food is, but they do know how far the food is at each time instance. The best and most effective strategy to find the food would be to follow the

Intelligent PID DC Motor Speed Control

Artificial Intelligence Resources in Control and Automation Engineering 7

bird which is nearest to the food. Based on such scenario, the PSO algorithm is used to solve the optimization problem. PSO algorithm procedure is shown in Fig. (4).

  START Initialize particles with random position and velocity

Evaluate particles Compare and update Pbest Compare and update gbest Update velocity and position Test

  END Figure 4: The PSO algorithm procedure.

In PSO, each single solution is a “bird” in the search space; this is referred to as a particle. The swarm is modeled as particles in a multidimensional space, which have positions and velocities. These particles have two essential capabilities: their memory of their own best position and knowledge of the global best. Members of a swarm communicate good positions to each other and adjust their own position and velocity based on good positions according to (4) and (5). vi(,tm 1)

w.vi(,tm)

xi(,tm 1)

xi(,tm)

c1 r1 ( gbest i , m

xi(,tm) ) c2 r2 (pbest m

vi(,tm 1) ; i=1,2,…,n ; m=1,2,…,d

xi(,tm) )

(4) (5)

Where: n

Number of particles in the group,

d

dimension,

t

Pointer of iterations(generations),

vi(,tm)

Velocity of particle I at iteration t,

Vdmin

vi(,td)

Vdmax

(6)

8 Artificial Intelligence Resources in Control and Automation Engineering

Allaoua and Mebarki

w

Inertia weight factor,

c1,c2

Acceleration constant,

r1,r2

Random numbers between 0 and 1,

xi(,td)

Current position of particle i at iterations, pbest Best position of a specific particle,

gbest

Best particle of the group.

1.

Initialize a group of particles including the random positions, velocities and accelerations of particles.

2.

Evaluate the fitness of each particle.

3.

Compare the individual fitness of each particle to its previous pbest. If the fitness is better, update the fitness as pbest.

4.

Compare the individual fitness of each particle to its previous gbest. If the fitness is better, update the fitness as gbest.

5.

Update velocity and position of each particle according to (4) and (5).

6.

Go back to step 2 of the process and keep repeating until some stopping condition is met.

4. PID-PSO CONTROLLER ALTERATION OPTIMAL PARAMETERS REALIZATION 4.1. Fitness Function

The general equation of PID controller is [8]: U (t )

K p e(t )

1 de(t ) e(t )dt Td Ti dt

(7)

Where: Kp = proportional gain; Ti = integral time; Td= derivative time.

The variable e(t) represents the tracking error which is the difference between the desired input value and the actual output. This error signal will be sent to the PID controller and the controller computes both the derivative and the integral of this error signal. The signal U(t) from the controller is now equal to the proportional gain (Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the error plus the derivative gain (Kd) times the derivative of the error [8, 18]. In PID controller design methods, the most common performance criterias are Integrated Absolute Error (IAE), the integrated of Time Weight Square Error (ITSE) and Integrated Of Squared Error (ISE) that can be evaluated analytically in the frequency domain [16, 18]. These three integral performance criterias in the frequency domain have their own advantages and disadvantages. For example, disadvantage of the IAE and ISE criteria is that its minimization can result in a response with relatively small overshoot but a long settling time because the ISE performance criterion weights all errors equally independent of time. Although the ITSE performance criterion can overcome the disadvantage of the ISE criterion, the derivation processes of the analytical formula are complex and time-consuming [16, 17]. The IAE, ISE, and ITSE performance criterion formulas are as follows:

Intelligent PID DC Motor Speed Control

IAE

r (t ) y (t )dt 0

Artificial Intelligence Resources in Control and Automation Engineering 9

e(t ) dt

(8)

0

e 2 (t )dt

ISE

(9)

0

t e 2 (t )dt

ITSE

(10)

0

In this paper a time domain criterion is used for evaluating the PID controller. A set of good control parameters P, I and D can yield a good step response that will result in performance criteria minimization in the time domain. The values of Kp, Ki and Kd in our research are calculated after to give the study state error equal to 0% and the used criteria to decide which are the best parameters in the intervals of space research 10 ≤ Kp ≤ 18 ; 0 < Ki ≤ 60 ; 10 ≤ Kd ≤ 50. These performance criterias in the time domain include the overshoot, rise time, settling time, and steady-state error. 4.2. Adjustment PSO for PID Controller Parameters

In this paper, a PID controller used PSO Algorithms to find the optimal parameters of DC Motor speed control system. The structure of the PID controller with PSO algorithms is shown in Fig. (5). 000 Objective function PSO Reference Speed

algor ithms

+ _

PID

Kp Ki Kd

DC Motor

Output Speed

PID Controller

Figure 5: The block diagram of proposed PID Controller with PSO algorithms.

The control system shows poor characteristics and even it becomes unstable, if improper values of the controller tuning constants are used. So it becomes necessary to tune the controller parameters to achieve good control performance with the proper choice of tuning constants [19, 20]. Unlike the conventional techniques, wherein the particles having unfavorable costs are discarded and those with favorable costs are reproduced, the unification of particle clusters allows us to use the same position in the optimal solution space. The i-th particle other than the best one is made to assume different positions on the surface of the virtual sphere centered at the i-th particle position, whose radius is the Euclidean distance between this and the best particle. Every time, as the particle assume new positions, it is ensured to update the best particle by comparing the costs corresponding to these positions with the previously selected best particle cost [21]. Simultaneously, the best particle in a given instant is assumed to reference speed towards the rest of the particles in the cluster, which leads to establishment of steady state error with axes connecting the best particle and the rest in the population. Subject to the condition that the angle subtended by the vector joining the i-th particle to the best one and the vector joining the present and the next positions of the i th particle lies within new degrees. In the proposed PSO method each particle contains three members P, I and D. It means that the search space has three dimensions and particles must converge in a three dimensional space. The flowchart of the

10 Artificial Intelligence Resources in Control and Automation Engineering

Allaoua and Mebarki

PSO-PID control system is shown in Fig. (6). The reference speed in this work is 127.93 Rad/sec and the parameters of PSO algorithms used in simulation are mentioned in Table 3. Start GenerateInitial Populations

Run the DC Motor speed control model for each set of Parameters Calculate parameters [ Kp, Ki, Kd ] of PID Controller Calculate the fitness function Calculate the Pbestof each particle and gbest of population Update the velocity, position, gbestand pbest of particles

No

Maximum iteration number reached? Yes Stop

Figure 6: The flowchart of the PSO-PID control system.

Objectives:

Our objective here is to minimize the error. We calculate the step response of the system out of which we calculate the error. The Iterations are run till the error minimizes. 5. COMPUTER SIMULATION & RESULTS 5.1. Optimal PID-PSO Controller Response

To control the speed of the DC motor at 127.93 Rad/Sec, according to the trials, the following PSO parameters (Table 3) are used to verify the performance of the PID-PSO controller parameters: Table 3: Parameters of PSO algorithms Population Size

50

Number of Iterations

300

wmax

0.589

wmin

0.106

c1

1.474

c2

1.503

Intelligent PID DC Motor Speed Control

Artificial Intelligence Resources in Control and Automation Engineering 11

The simulation results are obtained for 0.01 second range time. The best population may be plotted to give an insight into how the PSO Algorithm converged to its final values as illustrated in Fig. (7). The speed response of PID Controller tuning parameters using particle swarm optimization strategy is shown in Fig. (8). Table 4 lists the performance of PID-PSO controller.

Kp Value 18

G a in

16 14 12 10

0

50

100

150

200

250

300

200

250

300

200

250

300

Ki Value 60

G a in

40

20

0

0

50

100

150 Kd Value

50

G a in

40 30 20 10

0

50

100

150 Generations

Figure 7: Illustration of PSO Algorithms converging through Particle swarm optimization Algorithm values : Kp = 11.890 ; Ki = 4.118 ; Kd = 17.757.

140 120

Speed Wr [Rad/Sec]

100 80 60 40 20 0

0

0.001

0.002

0.003

0.004

0.005 0.006 Time [Sec]

0.007

0.008

Figure 8: The speed response of PID Controller tuning parameters using PSO strategy.

0.009

0.01

12 Artificial Intelligence Resources in Control and Automation Engineering

Allaoua and Mebarki

Table 4: Performance of PID-PSO controller [ Kp, Ki, Kd ]

[11.890 ; 4.118 ; 17.757]

Rising time [Sec]

0.0027

Overtaking [%]

0

Steady state error [%]

0

5.2. Results Comparison of PID-PSO Controller with Fuzzy-PSO Controller

To show the effectiveness of the proposed approach, a comparison is made with the designed PID controller using PSO and Fuzzy controller optimized via PSO [13]. The performances of the Fuzzy-PSO controller are listed in Table 5. Table 5: Performance of Fuzzy-PSO controller Results

Fuzzy-PSO Controller [13]

Rising time [Sec]

0.0087

Overtaking [%]

0

Steady state error [%]

0

The speed response of PID-PSO Controller comparing with the speed response of FLC (Fuzzy Logic Controller) with PSO algorithms is shown in Fig. (9). Table 6 lists the performances of the two controllers. Table 6: Performances of the two controllers Results

Fuzzy-PSO Controller [13]

PID-PSO Controller

Rising time [Sec]

0.0087

0.00271

Overtaking [%]

0

0

Steady state error [%]

0

0

140

120

Speed Wr [Rad/Sec]

100

80

60

40

20

0

0

0.01

0.02

0.03

0.04

0.05 Time [Sec]

0.06

0.07

0.08

0.09

0.1

Intelligent PID DC Motor Speed Control

Artificial Intelligence Resources in Control and Automation Engineering 13

140

S peed [Rad/S ec]

120 100 80 60 40 20 0

0

0.01

0.02

0.03

0.04

0.05 Time [Sec]

0.06

0.07

0.08

0.09

0.1

Figure 9: The speed response of PID-PSO Controller and Fuzzy-PSO Controller.

6. CONCLUSIONS

In this paper a new design method to determine optimal PID controller parameters using the PSO method is presented. The speed of a DC Motor drive is controlled by PID-PSO controller. Obtained through simulation of DC motor; the results show that the proposed controller can perform an efficient search for the optimal PID controller. By comparison with Fuzzy-PSO controller, it shows that this method can improve the dynamic performance of the system in a better way. The PID-PSO controller is the best which presented satisfactory performances and possesses good robustness (No overshoot, minimal rise time, Steady state error = 0). 7. DISCLOSURE

Part of information included in this chapter has been previously published in for example: "Trends in Biotechnology Volume 27, Issue 4, April 2009, Pages 199-209. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

H. Hénao, G.A. Capolino : "Méthodologie et application du diagnostic pour les systèmes électriques", Revue de l'Electricité et de l'Electronique (REE), no. 6, (in French), pp. 79-86, Jun. 2002. S. Raghavan : "Digital Control for Speed and Position of a DC Motor", MS Thesis, Texas A&M University, Kingsville, Aug. 2005. S. Weerasooriya, M.A. El-Sharkawi : "Identification and control of a DC motor using back propagation neural networks", IEEE Trans. Energy Conversion, vol. 6, pp. 663-669, 1991. J.A. Reyer and P.Y. Papalambros, "An Investigation into Modeling and Solution Strategies for Optimal Design and Control", ASME Design Engineering Technical Conferences, Las Vegas, Nevada, pp. 10-13, Sep. 2000. F. J. Lin, K. K. Shyu and Y. S. Lin, "Variable structure adaptive control for PM synchronous servo motor drive", IEE Proc. IEE B: Elect. Power Applicat., vol. 146, pp. 173-185, Mar. 1999. A. Rubaai, R. Kotaru : "Online identification and control of a DC motor using learning adaptation of neural networks", IEEE Trans. Industry Application, vol. 36, pp. 935-942, 2000. C.L. Lin, H.Y. Jan: "Evolutionarily multi-objective PID control for linear brushless DC motor", in Proc, IEEE Int. Conf .Industrial Elect. Society, pp. 39-45, Nov. 2002. K. Ang, G. Chong, Y. Li: "PID control system analysis, design, and technology", IEEE Trans. Control System Technology, vol. 13, pp. 559-576, Jul. 2005. J. Kennedy, R. Eberhart : "Particle Swarm optimization", Proc. IEEE Int. Conf. on Neural Network, vol. 4, pp. 1942-1948, 1995.

14 Artificial Intelligence Resources in Control and Automation Engineering

[10] [11] [12] [13]

[14] [15]

[16] [17] [18]

[19] [20] [21]

Allaoua and Mebarki

Y. Shi, R. Eberhart : "A modified particle swarm optimizer", Proc. 1998 Int. Conf. on Evolutionary Computation, The IEEE World Congress on Computational Intelligence, Anchorage, pp. 69-73, May 1998. M. Clerc, J. Kennedy: "The particle swarm-explosion, stability, and convergence in a multidimensional complex space", IEEE Trans. Evolutionary Computation, vol. 6, pp. 58-73, 2002. M. A. Abido : "Optimal design of power-system stabilizers using particle swarm optimization", IEEE Trans. Energy Conversion, vol. 17, pp. 406-413, Sep. 2002. B. Allaoua, A. Abderrahmani, B. Gasbaoui, A. Nasri : "The Efficiency of Particle Swarm Optimization Applied on Fuzzy Logic DC Motor Speed Control", Serbian Journal of Electrical Engineering, vol. 5, no. 2, pp. 247-262, Nov. 2008. A. Halila : "Étude des machines à courant continu", MS Thesis, University of LAVAL, (in French), May 2001. G.A. Capolino, G. Cirrincione, M. Cirrincione, H. Henao, R. Grisel : "Digital Signal Processing for Electrical Machines", Proceedings of ACEMP'01 (Aegan International Conference on Electrical Machines and Power Electronics), Kusadasi, Turkey, pp. 211-219, June 2001. J. Lieslehto : "PID controller tuning using Evolutionary programming", American Control Conference, pp. 2527, Jun. 2001. Y. Mitsukura, T. Yamamoto, M. Kaneda : "A design of self-tuning PID controllers using a genetic algorithm", in Proc. Amer. Contr. Conf., San Diego, CA, pp. 1361-1365, June 1999. A. Popov, A. Farag, H. Werner: "Tuning of a PID controller Using a Multi-objective Optimization Technique Applied to A Neutralization Plant", 44th IEEE Conference on Decision and Control, and the European Control Conference 2005. Z.L. Gaing : "A particle swarm optimization approach for optimum design of PID controller in AVR system", IEEE Trans. Energy Conversion, vol. 19, pp. 384-391, June 2004. T.H. Kim, I. Maruta, T. Sugie : "Robust PID controller tuning based on the constrained particle swarm optimization", Automatica, vol. 44, Issue 4, pp. 1104-1110, Apr. 2008. V. Mukherjee, S.P. Ghoshal: "Intelligent particle swarm optimized fuzzy PID controller for AVR system", Electric Power Systems Research, Vol. 77, Issue 12, pp. 1689-1698, Oct. 2007.

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 15-72

15

CHAPTER 2 Systems Theoretic Techniques for Modeling, Control and Decision Support in Complex Dynamic Systems Armen Bagdasaryan* Russian Academy of Sciences, Trapeznikov Institute for Control Sciences, 65 Profsoyuznaya, 117997, Moscow, Russia Abstract: Nowadays, modern complex systems of any interdisciplinary nature can hardly be analyzed and/or modeled without comprehensive usage of system theoretic approach. The complexity and uncertainty of the nature of modern systems, and the heterogeneity of related information, require a complex approach for their study, based on systems theory and systems analysis and consisting of information and expert knowledge management, initial pre-processing, modeling, simulation, and decision making support. As the complexity of systems increases, system theoretic methods become more crucial. Often they provide the only effective tools of obtaining the information about the elements in a system, connections between those elements, and the means for getting the adequate representation of system in a whole. The variety of complex systems can be described by deterministic or stochastic differential equations, statistical mechanics equations, neural network models, cellular automata, finite state machines, multi-agent systems, etc. Most of the complex real world objects are modeled as dynamic systems enriched by artificial intelligence resources. Equipped with artificial intelligence techniques, these models offer a wide variety of advantages such as coping with incomplete information and uncertainty, predicting system’s behavior, reasoning on qualitative level, knowledge representation and modeling, where computer simulations and information systems play an important and active role, and facilitate the process of decision making. This chapter aims to discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view, with special emphasis on methodological aspects. We consider the main characteristics of complex systems and of system approach to complex system study. Then the chapter continues with the general dynamic modeling and simulation technique for complex hierarchical systems functioning in control loop. The proposed technique is based on the information-mathematical models and described in terms of the hierarchical state transition diagrams. The methodology is sufficiently abstract to allow both qualitative and quantitative analysis of system state dynamics and control through hierarchical scenario calculus. The evaluation of different scenarios is defined by the multiple criteria vector-functions related to the efficiency of control strategies and time required for system goals achievement. We also offer general architectural and structural models of computer information system intended for simulation and decision support in complex systems.

Keywords: Modeling, control, decision, complex dynamic systems, complex hierarchical systems. 1. INTRODUCTION Complex System Science, as a field of research, has emerged in the past two decades. It is a multidisciplinary field aiming at understanding the complex phenomena of the real world that surrounds us. It studies how parts of a system give rise to the collective behaviors of the system and how the system interacts with its environment [1, 2]. The field of complex systems cuts across all traditional disciplines of science as well as physics, mathematics, biology, engineering, management, and medicine. It focuses on certain questions about parts, wholes and relationships. These questions are relevant to all traditional fields. Examples of complex *Address correspondence to Armen Bagdasaryan: Russian Academy of Sciences, Trapeznikov Institute for Control Sciences, 65 Profsoyuznaya, 117997, Moscow, Russia; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

16 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

systems are neural networks in the brain that produce intelligence and consciousness, artificial intelligence systems, swarm of software agents, social insect (animal) colonies, ecological and biological systems, traffic patterns, robotic systems, social and economic systems and many other scientific areas can be considered to fall into the realm of complex systems. Complex systems are usually understood intuitively as a phenomenon consisting of a large number of elements organized in a multilevel hierarchical structure [3, 4], where elements themselves could represent systems (the concept “system of systems”) [1]. The term complex is used to point out the fact that the problem treated here cannot be expressed only in quantitative relations but instead the most relevant values are qualitative. So, the first and main characteristic of complex systems is that they contain a large number of mutually interacting entities (components, agents, processes, etc.) whose aggregate activity is nonlinear, cannot be derived from the direct summations of the activity of individual entities, and typically exhibit a some sort of self-organization (for example, hierarchical) [5-9]. Another important characteristic of complex systems is that the description of complex systems requires the notion of purpose, since the systems are generally purposive [2]. This means that the dynamics of the system has a definable objective or function. Each element of a complex system interacts with other elements, directly or indirectly. The actions of or changes in one element affect other elements. This makes the overall behavior of the system very hard to deduce from and/or to track in terms of the behavior of its parts. This occurs when there are many parts, and/or when there are many interactions between the parts. Since the behavior of the system depends on the elements interactions, an integrative system theoretic (top-down) approach seems more promising, as opposed to a reductionist (bottom-up) one. Any scientific method (approach, technique) of studying complex real world systems relies on modeling (analytical, numerical) and computer simulation [10]. The study of complex systems begins from a set of models that capture aspects of the dynamics of simple or complex system. Most of the complex real world objects are modeled as dynamic systems [11]. These systems can be described by deterministic or stochastic differential equations, neural network models, cellular automata, finite state machines, multiagent systems, etc. Most of the complex systems can be studied by using nonlinear mathematical models, statistical methods and computer modeling approaches. These models should be sufficiently general to encompass a wide range of possibilities but have sufficient structure to capture interesting features [12]. There are three interrelated approaches to the modern study of complex systems: (1) how interactions give rise to patterns of behavior, (2) understanding the ways of describing complex systems, and (3) the process of formation of complex systems through pattern formation and evolution. But the final intention in the study of complex systems is to understand the real nature of the processes, their dynamics, their influence and interconnections, and the possible outcomes in order to make preventive actions and to make correct decisions. It also facilitates taking composite decisions, which are often the only possible ones in case of complex systems. Moreover, as a rule, modern complex systems are large-scale. Large-scale systems are typically imposed a hierarchical structure in order to manage complexity. In hierarchical models, the notion of consistency is much important, as it ensures the implementation of high-level objectives by the lower level systems [3, 4, 8, 9, 12]. Such a description of system depends largely on the problem domain, specific goals and the point of view of the researcher. Although the problem of a researcher as an active element of the system has been considered in the literature to date, there is no unique opinion on the influence of the observer in the process of modeling. Although many efforts have been made, there is no commonly accepted definition of a complex system. Heuristic approaches basically focus on the interaction between (microscopic) subsystems and the emergence of new qualities at the (macroscopic) system level, e.g. Complex systems are systems with multiple interacting components whose behavior cannot be simply inferred from the behavior of the components. - New England Complex Systems Institute.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 17

By complex system, it is meant a system comprised of a (usually large) number of (usually strongly) interacting entities, processes, or agents, the understanding of which requires the development, or the use of, new scientific tools, nonlinear models, out of equilibrium descriptions and computer simulations. - Journal Advances in Complex Systems. Nevertheless, whatever definition one relies on, any complex system is a system with numerous components and interconnections, interactions or interdependencies which are difficult to describe, understand, predict, manage, design, and/or change [2, 12]. For this reason, computer simulations play a crucial role in studying complex systems and in understanding of how these systems function and work, and how they could be efficiently controlled. Nowadays, information technologies and computer simulations have evolved into an essential tool for modeling, assessment and support in any domain requiring decision making. The complexity and uncertainty of the nature of complex systems, and the heterogeneity of related information, require a complex approach for their study, based on and consisting of data and knowledge management, modeling, simulation and, lastly, decision making support [13-15]. So, the search for the ways of formalization and automation of processes of modeling, control, and decision support in complex systems continues to attract much attention. This chapter aims to discuss the problems of modeling, control, and decision support in complex dynamic systems from a general system theoretic point of view, with special emphasis on methodological aspects. We consider the main characteristics of complex systems and of system approach to complex systems study. The chapter continues with the general dynamic modeling and simulation technique for complex hierarchical systems consisting of many objects and functioning in control loop. The proposed technique is based on the information-mathematical models and is described in terms of the hierarchical state transition diagrams. The methodology is sufficiently abstract to allow both qualitative and quantitative analysis of system functioning and state dynamics through hierarchical scenario calculus. The evaluation of different scenarios is defined by the multiple criteria vector-functions related to the efficiency of control strategies and time required for system goals achievement. We also offer a general structure of computer information system intended for simulation and analysis of dynamic processes, control strategies and development scenarios in complex systems, and a structural scheme of decision support process. The chapter is organized as follows. The next section presents the principles of system approach to complex systems study and the basic features of complex systems. The problem of modeling and control within the context of complexity of modern systems is addressed in section 3. The section 4 is devoted to the analysis of known existing paradigms and methods of mathematical modeling and simulation of complex systems, which support the processes of control and decision making. In section 5 we present the method of hierarchical state diagrams as a tool of dynamic modeling and simulation of complex hierarchical systems; we give conceptual principles of agent-based parametric modeling and then we describe the method in much detail. Then we outline some possible directions of further development of the proposed technique. The architecture of information system that supports simulation and analysis of dynamic processes and control scenarios, and decision making in complex hierarchical systems is proposed in section 6. In conclusion we make some final remarks on the topic of this chapter, and outline the areas of application of the presented technique. 2. SYSTEM THEORETIC APPROACH FOR COMPLEX SYSTEMS STUDY The majority of real-life problems can be classified as complex ones, and, as a result, they inhabit some particular characteristics, which require interdisciplinary approaches for their study. Every complex system is an integration of interconnected parts and components (through informational, physical, mechanical, energetic exchange, etc.), which result in emerging of new properties and interaction with the environment as a whole entity. If some part is extracted from the system, it loses its particular characteristics and

18 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

converts into an array of components or assemblies. An effective approach to complex system study has to follow the principles of system analysis [16-20], which are: 1.

Description of the system. Identification of its main properties and parameters;

2.

Study of interconnections amongst parts of the system, which include informational, physical, dynamical, temporal interactions, as well as the functionality of the parts within the system;

3.

Study of the system interactions with the environment, in other words, with other systems, nature, etc.;

4.

System decomposition and partitioning. Decomposition supposes the extraction of series of system parts, and partitioning suggests the extraction of parallel system parts. These methods can be based on cluster analysis (iterative process of integration of system elements into groups) or content analysis (system division into parts, based on physical partitioning or function analysis);

5.

Study of each subsystem or system part, utilizing optimal corresponding tools (multidisciplinary approaches, problem-solving methods, expert advice, knowledge discovery tools, etc.);

6.

Integration of the results received from the previous stage, and obtaining a pooled fused knowledge about the system. The synthesis of knowledge and composition of a whole model of the system can include formal methods for design, multi-criteria methods of optimization, decision-based and hierarchical design, artificial intelligence approaches, case-based reasoning, and others such as hybrid methods.

Basic reasons that make it difficult for complex systems to be described by formalized methods are the following ones: Information incompleteness on the state and the behavior of a complex system; Presence of a human (observer, researcher) as an intelligent subsystem that forms requirements and makes decisions in complex systems; Uncertainty (inconsistency, antagonism) and multiplicity of the purposes of a complex system, which are not given in a precise formulation; Restrictions imposed on the purposes (controls, behavior, final results) externally and/or internally in relation to a system are often unknown; Weak structuredness, uniqueness, combination of individual behaviors with collective ones are the intrinsic features of complex systems. Complex systems are different from simple systems by their capabilities of: Self-organization - the ability of a complex system to autonomously change own behavior and structure in response to events and to environmental changes that affect the behavior. For systems with a network structure, including hierarchical one, self-organization can amount to: (1) disconnecting certain constituent nodes from the system, (2) connecting previously disconnected nodes to the same or to other nodes, (3) acquiring new nodes, (4) discarding existing nodes, (5) acquiring new links, (6) discarding existing links, (7) removing or modifying existing links.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 19

Co-evolution - the ability of a complex system to autonomously change its behavior and structure in response to changes in the system environment and in turn to cause changes in the environment by its new (corrected) behavior. Complex systems co-evolve with their environments: they are affected by the environment and they affect their environment. Emergence - the property that emerge from the interaction of constituent components of a complex system. The emergent properties do not exist in the components and because they emerge from the unpredictable interaction of components they cannot be planned or designed. Adaptation - the ability of a complex system to autonomously adjust its behavior in response to the occurrence of events that affect its operation. Complex systems should adapt quickly to unforeseen changes and/or unexpected events in the environment. Adaptation enables the system to modify itself and to revive in changing environment. Anticipation - the ability of a system to predict changes in the environment to cope with them, and adjust accordingly. Anticipation prepares the system for changes before these occur and helps the system to adapt without it being perturbed. Robustness - the ability of a system to continue its functions in the face of perturbations. Robustness allows the system to withstand perturbations and to keep its function and/or follow purposes, giving the system the possibility to adapt. Being oriented on the analysis of complex object as a whole, the system approach does include the methods of decomposition of complex system on separate subsystems. But the main purpose is the subsequent synthesis of subsystems, which provides the priority of a whole. However, reaching this priority is not simple. For a number of complex systems, optimum of the whole system cannot be obtained from optimums of its subsystems. It should be noted, that complex systems that possess the property of integrity do not have constituent elements and act as one whole object. In this kind of systems, the connections and relations are so complicated and strong (all-to-all) that they cannot be considered as an interaction between the localized parts of system. In physical systems the integrity corresponds to locality that is to such an influence of one part of system to another which cannot be explained by interaction between them. As a rule, connections in integrative systems are often based on structural principles, but not on the cause/effect principle. 3. COMPLEXITY, MODELING, AND CONTROL IN COMPLEX SYSTEMS Complex systems are more often understood as dynamical systems with complex, unpredictable behavior. Multidimensional systems, nonlinear systems or systems with chaotic behavior, adaptive systems, modern control systems, and also the systems, which dynamics depends on or is determined by human being(s), are the formal examples of complex systems [21-27]. In connection with modeling and control complexity, complex systems have specific characteristics, among which are: Uniqueness; Weak structuredness of knowledge about the system;

20 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

The composite nature of system; Heterogeneity of elements composing the system; The ambiguity of factors affecting the system; Multivariation of system behavior; Multicriteria nature of estimations of system’s properties; and, as a rule; High dimensionality of the system. Under such conditions, the key problem of complex systems theory and control theory consists in the development of methods of qualitative analysis of the dynamics of such systems and in the construction of efficient control techniques. In a general case, the purpose of control is to bring the system to a point of its phase space which corresponds to maximal or minimal value of the chosen efficiency criterion. Another main and actual problems in the theory of complex systems and control sciences is a solution of “ill-posed, weakly- and poorly-structured and weakly-formalized complex problems” associated with complex technical, organizational, social, economic, cognitive and many other objects, and with the perspectives of their evolution. Since the analysis and efficient control are impossible without a formal model of the system, the technologies for building the models of complex systems have to be used. Complexity of a system is a property stipulated by an internal law of the system that defines some important parameters, including spatial structure and properties of the processes in this structure. This definition of complexity is understood as certain physical characteristic of nature. Since it is a nonlinearity of internal regularities (laws) that underlies the complexity of real world systems, complexity and nonlinearity are sometimes considered as synonyms. And the more complex a process or geometrical form of a system (or object) is, the more it is nonlinear. Complexity is a many-faceted concept. Today we can distinguish several basic forms of complexity: structural, geometrical, topological, dynamical, hierarchical, and algorithmic. However, other possible forms of complexity can be found as well. For example, one that comes from large scales. Large-scale control systems typically possess a hierarchical architecture in order to manage complexity. Higher levels of the hierarchy utilize coarser model of the system, resulting from aggregating the detailed lower level models. In this layered control paradigm, the notion of hierarchical consistency is important, as it ensures the implementation of high-level objectives by the lower level systems [28-30]. Large-scale systems are systems of very high complexity. Complexity is typically reduced by imposing a hierarchical structure on the system architecture [3, 4, 6-9, 12]. Hierarchical structures for discrete event systems have been considered in multiple works [30-33]. In such a structure, systems of higher functionality reside at higher levels of the hierarchy and are therefore unaware of unnecessary lower-level details. One of the main challenges in hierarchical systems is the extraction of a hierarchy of models at various levels of abstraction which are compatible with the functionality and objectives of each layer. The notions of abstraction or aggregation refer to grouping the system states or control objects into equivalence classes [30]. Algorithmic complexity finds itself in many software systems. These are the most complex systems developed by human being, although their structure and dynamics are comparatively simple. Structural, dynamical, algorithmic, hierarchical and large-scale complexities of systems attract much of attention because we face them, manifestations of nonlinearity of nature, in our everyday life. Interplay between intellectualized mathematical and information technologies of control and decision support plays an important role in modeling of processes of evolution and functioning of complex systems. Intellectualization of complex control systems has actively been developing in recent decade. In order to intellectualize modern control systems, the artificial intelligence methods or intelligent subsystems

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 21

embedded in control system are more often applied [34, 35, 46, 104]. The intellectualization of complex systems seems to be a positive and very perspective direction of control systems development. It significantly eases control decision making, as the underlying mechanisms are similar to those used by human intellect. Control processes in intellectualized systems are based on the experience, skills and knowledge, that is, they are mostly based on the “understanding” of complex situations of purposeful behavior. An elementary intellect in control systems is constructed by using feedback loops and information flows, which give a system the capability of “understanding” of current situations. To “understand” the more complex situations, an adaptive subsystem should be added to the main feedback loop. However, if the object/system performs multiple functions (multipurpose object) then each function makes the system more complex and, as a consequence, the more sophisticated intelligent subsystems have to be used. But many questions remain: how to differ control systems by the level of intelligence; at what level of evolution of control systems they can be considered as artificial intelligence systems; what is the relation between adaptive properties and intelligent systems. For modeling and analysis of complex control systems in the presence of principally non-formalizable problems and impossibility of strict mathematical formulation of problems, expert knowledge and information databases are used. Construction of models of complex systems is accompanied by extensive use of expert knowledge and information about the system stored in data- and information systems. This knowledge should be integrated in a unified way. Qualitative character of most of parameters of complex systems results in knowledge fuzziness and uncertainty and, as a consequence, in problem of its formalization. The analysis above supports the fact that complex systems are usually difficult to model, design, and control. There are several particular methods for coping with complexity and building complex systems. At the beginning, a conceptual model of system is developed, which reflects the most important, in the context of the problem under study, material and energy and information processes taking place between different elements of system (or, subsystems), internal states of which can be considered as independent. This kind of model determines the general structure of system and it should be complemented by algorithmic and, more often, by mathematical models of each of the subsystems. These models can be represented by graph models, Petri nets models, system dynamics models or by their combination. The obtained models are aggregative that reflect the dynamics of the most important, for the current investigation, variables. Then, the next step consists in checking the mathematical models for their behavioral adequacy to real system, and in identification of parameters of the models over the sets of admissible external actions and initial/boundary conditions. The difficulties of solution of these problems increase as the system becomes more complex. For this reason, another important step is the structuring of problem domain (or situations), control domain, and simulation scenarios. For these purposes, stratified models, state (or flow) diagram models, system dynamics models, aggregative models and robust identification can be used. However, the developed model should be subjected to intense analysis and possible changes after its testing for structural controllability, observability, identifiability, and sensitivity. These properties guarantee the model rigidity in a given class of variations of the problem conditions and, as a consequence, the reliability and accuracy of system simulation. Besides that, the rigidity enables one to reduce the model to canonical (more simple) forms, which leads to significant simplification of modeling, control synthesis, and analysis of the system. Thus, when constructing a model of complex dynamical system, three forms of its description arise: (1) conceptual model, (2) formalized model, (3) mathematical model, and (4) computer model. 4. MATHEMATICAL AND SIMULATION MODELING OF COMPLEX DYNAMIC SYSTEMS: EXISTING FRAMEWORKS AND PARADIGMS The system approach assumes that any object under study is considered as a single complex system together with the control subsystems. To ensure high quality management one should be familiar with the properties of controlled subsystems. In order to identify the properties of controlled subsystems, as well as to evaluate the quality of decisions, their responses to applied decisions and activities, and the results of automated modeling of the subsystems in different predictable conditions should be used in the process of functioning of the object.

22 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

In systems simulation there are several paradigms, formulations of problems, and approaches to their solution, which are used as a “framework” for building and analyzing models [36, 37]. There are several quite different viewpoints on system modeling: dynamical systems, system dynamics, discrete event systems, cellular automata models, neural network models, finite state machines, cognitive modeling (cognitive maps), and multi-agent models.These paradigms differ, rather, by concepts and views on the problems and approaches to solving them, than the applications areas. Often, the adherents of a paradigm believe that the right formulation and solution of problems of modeling and simulation can only be possible within the framework of concepts and techniques of this particular paradigm. For example, the advocates of modeling and analysis of dynamical systems believe that other approaches are “not entirely” scientific, or they are just special cases of system representation and analysis as systems of algebraic differential and/or integral equations. In fact, each of the paradigms has their own right for a life, and use of one or another paradigm is determined only by the aims of modeling and is associated with those aims by means of the chosen level of abstraction for solving (control) problems. 4.1. Aggregative Models of Systems Aggregative model describes the control object as a multilevel structure of dynamical systems of given types, or as aggregates [38]. In this description, the system is viewed as a synthesis (the most general and most complex) of a generalizing class of complex systems, and is called aggregative system [38-40]. The aggregate is used to model the elementary blocks of complex system. So, aggregative system is a system composed of any set of aggregates, if the transmission of information between them is assumed to be instantaneous and without distortion. Let be a subset of real numbers, , , , be sets of any nature. The elements of these sets are interpreted as follows: is a time instant, is an input signal, is a control symbol (signal), is an output signal, is a state. States, input, control, and output signals are considered as functions of time, , , , and . Formally, aggregate is a mathematical model represented by the tuple , , , , , , where and are operators (in general case, random ones); is a transition operator which defines the current state on the basis of previous states (history); is an output operator. These operators realize the functions and . In general, all sequences of events in the aggregate are realizations of random sequences with the given distribution laws. The structure of these operators distinguishes the aggregates amongst any other systems. As a rule, it is always possible to distinguish two types of states: (1) ordinary states in which the system remains almost all the time, (2) special states, specific to the system in some isolated time instants, coinciding with the receipt of input and control signals or with the issuance of the output signal; at these moments the aggregate may change its state discontinuously, but between the special states the change of the coordinates occurs smoothly and continuously. The aggregate is a mathematical scheme of quite a general type, special cases of which are Boolean algebras, contact relay networks, finite automata, dynamical systems, described by ordinary differential equations, and some other mathematical objects. The model of aggregate can be used as a model for a discrete-continuous system (hybrid system) in a whole or as a basic model for its components. In the latter case, the system is represented as a network of aggregates with fixed communication channels. As an example of system of this kind, a complex system of aircraft flight control of a large airport can be considered; it is as the automated control system with extensive and large distributed information system and with very complex information processing algorithms.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 23

4.2. Discrete Event Models and Hybrid Systems Discrete event approach [41] to modeling of complex systems can be used for formal description of both discrete and discrete-continuous (hybrid) systems. The description formalism includes mathematical model of system, specification language, as well as a set of procedures and functions that implement the simulation algorithm [42]. In contrast to the aggregative approach, the simulation algorithm is based on the discrete event dynamic modeling of complex systems [43-46]. The discrete-continuous system is a mathematical model of the form , , , , , where

,

0 is a discrete model of time;

is a set of process classes; is a set of event classes (the causes of instantaneous change of behavior and structure of the system); is a set of algorithms for the event classes (preparatory discrete actions on the transition to new behavior of the system); is a calendar of event planning; is a set of equations that describe the local behavior of system processes at time intervals between the events. The calendar of event planning contains the information about the events in different objects; the dynamics of system is described with the help of the calendar. The model of calendar of event planning can be given as the tuple ,

,

where is a condition for occurrence of the event (planning of event by condition, it can be given in the form of logical formula, predicate). The structure and behavior of a process is described by the mathematical model , , ,

where ,

,

are input and output channels;

is a set of static process variables that are defined by algebraic expressions and can be changed only upon the implementation of event algorithms; is a set of functions, dynamic variables, that are defined by differential equations from ; is a main body of the process that consists of the descriptions of its various behaviors. Modeling the behavior of discrete-continuous system means building of a set of event sequences leading to the change of system’s behavior and structure, assuming the initial state to be an event. The global behavior is modeled using a special monitor process which shifts the system time in accordance with the calendar of event planning, or in accordance with the analysis of the occurrence time of the event, which is scheduled by the condition. The simulation process ends when the event calendar is empty.

24 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

As we can see, the aggregative models and discrete event models use different approaches to the description of the same class of complex systems. One can note that almost all the approaches to modeling can be considered as an extension of the basic (discrete or continuous) model, so the behavior of discretecontinuous system is represented in them from different viewpoints and from different, sometimes contradictory, emphases. The “hybrid” line of study of discrete-continuous systems emerged in the early 90’s. A. Pnueli and D. Harel, the founders of hybrid approach, introduced a new class of complex systems, hybrid reactive systems. Investigation of the behavior of the hybrid system reduces to static qualitative analysis of behavioral properties, without the use of point-wise numerical simulation of the global system behavior. Several software tools have been developed for modeling hybrid systems, for example, HyTech is an automatic tool for the analysis of embedded systems. 4.3. System Dynamics Model For the analysis of complex systems with nonlinear feedbacks, the Forrester’s system dynamics is used [47]. The method of system dynamics is employed for modeling systems from various backgrounds [4850]. System Dynamics as a method of simulation includes the following stages: Structuring of an object; Building a system diagram of the object, where the links between the elements are specified; Determining system variables for each element and the rate of their growth; Adopting the hypotheses about the dependence of each rate of growth on the variables, and formal description of these hypotheses; Evaluating the process for the parameters introduced with the use of available statistics. To construct and study models with system dynamics method, a specialized programming language Dynamo that combines simulation tools and graphical notations was developed. The Forrester’s model includes the following components: Levels (resources); Flows that move the content of one level to another level; Decision Functions that govern the rate of flows between the levels; Information channels that connect the above functions with the levels. Levels characterize the resulting accumulations within the system. Each level is described by its variable that depends on the difference between the incoming and outgoing flows. The rates determine the instantaneous current flows between the levels in the system and model the jobs, while the levels measure the state which the system reaches as a result of some job. Decision functions and equations of rates formulate the rules of behavior that determine how the available information about the levels leads to the choice of decisions related to the values of the current rates. The basic structure of the model, presented in Fig. (1), shows only one network with the elementary scheme of information links between levels and rates. However, to model the activities, for example, of a whole industrial enterprise, one needs to construct multiple interconnected networks.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 25

Level Level

Decision functions Flow channels

Level

Information sources

Figure 1: Basic Structure of Forrester’s Model.

There are six types of networks which represent substantially different types of variables: orders, materials, finances, manpower and equipment, connected together through the information network. Each of these networks can further be broken down into several separate parts. Information network serves as a connective tissue for other types of networks. It sends the information from the levels to the decision points, as well as the information about the rates in two other networks to the levels of information network. There exist levels and rates in the information network as well. For instance, information on the actual current rate in the flow of materials is averaged to determine the level of the average rate of flow of materials. This level refers to the information network. The basic structure of the model is supplemented by a system of equations, which connect the characteristics of the levels of this structure. Basically this system consists of the equations of two types: the equations of levels and the rate equations. When constructing the equations, the time axis is divided into intervals Δ between -th and -th time instants. The new values of levels are calculated at the end of the interval, and they are used to determine the new rates (decisions) for the next interval Δ . The level equations have the form ,

Δ

where

,

,

,

,

,

,

is the set of levels related to the -th level;

is the value of -th level at -th time instant; Δ

is the length of the interval from time instant ,

,

to time instant ;

,

is the rate of input flows for -th level at the interval between time instant

,

is the rate of output flows for -th level at the interval between time instant

The rate equation has the form ,

where

/

is the value of level that determines the delay at time instant ;

Δ is a constant, mean time, required to overcome the delay.

and ; and .

26 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

The stages of building of the model are the following: 1.

Construction of the basic structure of the model as a specialized graph;

2.

Parameterization of the graph and the construction of the corresponding system of equations;

3.

Description of the model, using a simulation language, and conducting experiments.

The advantages of the model include: (1) the ability to reflect almost any causal relationships, (2) simple mathematical formulation, and (3) the use of terminology, synonymous to the concepts of the languages of economy, automation, and engineering. For the main phase variables, the so-called system levels, the following differential equations, the same for all variables, are used.

where

is the positive rate of variable , which includes all the factors that cause its growth;

is the negative rate of variable , which includes all the factors that cause the decrease of . These rates are supposed to be expressed in terms of the product functions that depend only on the so-called “factors”, the auxiliary variables that are combinations of the main variables: ,

,…,

,

,…,

… 

where ,…, are factors; , , is the number of levels, that is, the number of factors is less than that of variables which allows one to simplify the problem and consider only the functions of one variable. The software tools that implement system dynamics models and, in particular, the model of Forrester are the well-known simulation environments, such as AnyLogic, VenSim, PowerSim, ModelMaker, etc. To construct the models they use a graphical representation of the dependent variables in the form of the socalled “stock and flow diagrams”. 4.4. Cellular Automata Cellular automata [51-53] have played a considerable role as simple models for the study of complex systems, and have recently been popularized by Steven Wolfram in his well-publicized book “A New Kind of Science” [54, 55] and by John Conway’s model Game of Life. Cellular automata were originally invented and studied by the mathematicians Stanislaw Ulam and John von Neumann. Von Neumann introduced them as a biologically motivated computation models, and adopted cellular automata as a substrate for constructing a self-reproducing automaton [56]. A cellular automaton is a decentralized model providing a platform for performing complex computations with the help of only local information. The cellular automata paradigm of local information, decentralized control and universal model of computations is exploited by many researchers and practitioners from different fields for modeling various applied systems [57-69]. Cellular automata, both deterministic and stochastic, are used for modeling of various complex phenomena in different branches, from physical to social to engineering ones [58, 59, 68, 69]. The popularity of cellular automata can be explained by their simplicity, and by the enormous potential they hold in modeling complex systems, in spite of their simplicity. Cellular automata can be viewed as a

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 27

simple model of a spatially extended decentralized system made up of a number of individual components (cells). The communication between constituent cells is limited to local interaction. Each individual cell is in a specific state which changes over time depending on the states of its local neighbors. The overall behavior can be viewed as a simultaneous change of states of each individual cell. A cellular automaton consists of a number of cells organized in the form of a lattice. It evolves in discrete space and time, and can be viewed as an autonomous finite state machine. A cellular automaton is typically . Because of its inherent simplicity, the onedefined over a -dimensional integer regular lattice dimensional cellular automaton, 1, with two states per cell became the most studied variant of cellular automaton. More often, a cellular automaton is defined over a two-dimensional lattice such as . Each lattice point , is referred to as a cell, site, or node, and is denoted by , . Each cell has a state which often takes on its values from 0, 1 , that is, each cell stores a discrete variable at time that refers to the present state of the cell. For each cell, a notion of a neighborhood is defined. The neighborhood of a cell is the collection of cells that can influence the future state of the given cell (Fig. (2)). A common choice is the Moore neighborhood, which is the 2 1 2 1 square block centered at the cell , , where is a positive integer parameter called the range. More precisely, it is the set  |

,

|

 

 

Another choice in the two-dimensional case is the von Neumann neighborhood defined as ,

 |

|

 

The neighborhood generally varies from three to five or seven cells. The next state of the cell at 1 is affected by its state and the states of its neighbors at time . Based on its and the current states of the sites in its neighborhood , a function   (called next state current state 1 of the cell . function, update rules, or local transition function) is used to compute the next state That is, we have the equation

where ̃ 

denotes the set consisting of all the states

such that

.

The configuration of a cellular automaton is the tuple consisting of the states of all the cells. The above equation is used to map the configuration to 1 . The cellular automaton dynamics or the dynamical system defined by the cellular automaton is the map that sends s to 1 . The study of cellular automaton consists mainly in understanding its evolution, how configurations evolve, under the repeated iteration of the map , so the dynamical behavior is generated and then can be studied. The local rules applied to each cell can be either identical or different. These two different possibilities are termed as uniform and hybrid cellular automaton respectively. While the next state function (local rule) in general is deterministic in nature, there are variations in which the rule sets are probabilistic [64, 66], or fuzzy [68, 69]. The nature of next state functions also varies significantly; researchers have defined the rule set according to the design requirements of the applications. In another type of cellular automata, the states are assumed to be a string of elements in a Galois field , where is the number of states of a cellular automaton cell.

28 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

Square lattice Hexagonal and triangular lattices Stepwise change of neighborhood cells configuration influencing a central cell

Central cell Neighborhood cells

Figure 2: Types of neighborhoods in cellular automata.

4.5. Neural Networks The process of complex systems modeling requires a large amount of knowledge about the objects, including experimental, monitoring, and expert information. The last decades are witnessed with the wide use of neural networks to cope with large amounts of data and for processing of information [70, 71]. Neural network based modeling has various application areas, such as pattern recognition, adaptive control, functional approximation, prediction, expert systems, the organization of associative memory, as well as study and analysis of technical and engineering systems and automation processes, and other applications. Each neural network consists of a collection of neurons (Fig. (3)), which are simple elements of information transformation.

Inputs

Weights

x1 w1

Output

x2 w2

y

xn wn Figure 3: Model of artificial neuron.

The most well-known model of neural network is the Hopfield network [72]. Hopfield networks were proposed as a model of associative memories. Hopfield network is a recurrent artificial neural network constructed from artificial neurons; it is a network of some fixed numbers of such artificial neurons, which are in most cases fully connected. A discrete Hopfield neural network consists of an undirected graph , . At any time , each node has a state 1, 1 . Each node has an associated threshold . Each edge , has an associated weight . For each node , the neighborhood of is defined, which includes itself and the set of nodes that are adjacent to in . More formally,   States of nodes are updated as follows. At time , node

,

computes the function

defined by

Systems Theoretic Techniques for Modeling

where sgn is the map from

to

Artificial Intelligence Resources in Control and Automation Engineering 29

1, 1 , sgn

1, 1 , defined by ,

Now, the state of

at time

,  

1 is

It is assumed in many works that the underlying undirected graph is complete, that is there is an edge between every pair of nodes. In the definition presented above, the graph need not be complete. However, this does not cause any difficulties since the missing edges can be assigned weight 0. As a consequence, such edges will not play any role in determining the dynamics of the system. So, given the weights, thresholds, and the updating rule for nodes the dynamics of the network is defined if we determine in which order the nodes are updated. There are two ways of updating them: both synchronous and asynchronous update models of Hopfield networks have been considered in the literature. Asynchronous: one fix one node, calculates the weighted input sum and updates immediately. This can be done in a fixed order, or nodes can be picked at random, which is called asynchronous random updating. Synchronous: the weighted input sums of all nodes are calculated without updating the nodes. Then all nodes are set to their new value, according to the value of their weighted input sum. Neural networks are related to the class of informational models. There are several types of informational models based on neural networks that are presented in the literature: Modeling a system in response to external action; Classification of internal states of a system; Prediction of dynamics of changes in a system; Assessment of completeness of description of a system and determination of the comparative importance of system parameters; Optimization of system parameters with respect to a given objective function; System control. Typically, informational models are less expressive compared with formal mathematical models and expert systems by the criterion of “explicability” of granted results, but the lack of restrictions on the complexity of systems simulated determines their important practical significance. However, in some cases, neural networks and mathematical models can be combined in one model, for example, when external conditions are described by the equations of mathematical physics, but the response of a system is modeled by neural network. Sometimes, hybrid neural networks, which have fuzzy parameters [73-75], are used. Synthetic models, which are based on a synthesis of system components, are practically the only alternative modeling tools in the area of complex systems and their control, examples are sociology, long-term weather

30 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

forecasting, macro-economy, and medicine. Recently, synthetic information models, which include neural networks, have become widely used in the modeling and study of technical, engineering, and automation systems. 4.6. Cognitive Analysis and Cognitive Maps Among the control problems the most difficult are those connected with the solution of complex problems. The aim of these kinds of problems is to shift the situation in a problem domain to a desired direction. In this case, the control object is the whole problem domain, which is regarded as a dynamic situation, consisting of a set of heterogeneous interacting factors. Some of these factors directly depend on the decisions of Decision-Maker (DM); other factors depend on DM only indirectly, while others do not depend at all and are considered as external disturbances. Dynamics of the situation is reflected in the fact that the situation changes with time under the influence of DM actions, external disturbances, and under the effects of some factors on others. As a rule, when solving this kind of complex problems, one evidently faces the fact that, unlike most of the technical and engineering systems, the control objects (i.e., situations) are both weakly-formalized and illstructured: The system of concepts (factors) and connections between them is not defined with sufficient degree of completeness; The basic parameters of the situation (values of the factors, degree of influence of some factors on the others) are mostly not quantitative but have qualitative characteristics numbers, intervals, fuzzy values, linguistic estimates that form a linearly ordered scale; Non-stationarity of the processes themselves, and the variation of certain characteristics of the processes is often unknown, making it difficult to build their quantitative models; The values of parameters of the situation, factors and connection strength are obtained mainly not on the basis of objective measurements but they are based on expert knowledge and estimates, which are subjective opinions; The alternatives of how the situation will evolve cannot be formulated beforehand; they arise in the process of the situation analysis. The above features restrict the capabilities of simulation modeling, oriented on the use of quantitative characteristics, and of methods of traditional decision theory which relies on the methods of selecting the best possible alternative from a set of well-formulated alternatives. For this reason, these approaches became less efficient when applied to decision support and modeling in ill-structured problem domains. The modern approach to the modeling, control, and analysis of ill-structured problem domains and complex control problems, is based on the notion of cognitive map [76, 77], and is called cognitive analysis of situations. Cognitive map is a model of representation of expert knowledge about the situation under study. Cognitive maps are used to describe causal relationships and influences between factors, as well as to model the dynamics of weakly-formalized systems [78-83]. Mainly, cognitive approach, based on cognitive aspects of model construction, includes the processes of perception, thinking, knowledge, explanation and understanding. To picture this, the schematic, simplified description of the world, related to the problematic situation, is portrayed as a cognitive map. From the standpoint of cognitive approach the process of modeling can be divided into several stages as represented in Fig. (4).

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 31

Object

Cognitive model

Conceptual model

Formal model (mathematical, physical, simulation model)

Figure 4: Generalized scheme of the process of modeling based on cognitive approach.

The main purpose of the use of cognitive maps is a qualitative analysis and modeling of the dynamics of situations (tendencies, directions of changes of the values of factors, the study of scenarios, etc.). For the purposes of quantitative analysis, the theory of differential or difference equations and optimal control theory are traditionally used, and in case of game-theoretic setting the theory of dynamic or differential games is applied (see Table 1). Table 1: Methods for qualitative and quantitative analysis of dynamics of situations Purpose

Modeling Method Qualitative analysis

Quantitative analysis

Description of situation

Cognitive maps

Differential or difference equations

Analysis and control of situation

Simulation modeling

Optimal control theory

Analysis of interrelationship of agents interested in the development of situation

Cognitive games

Dynamical games

The mathematical model of directed graph (digraph), and its extensions, underlies the notion of cognitive map. The mathematical model of digraph is extended to get the mathematical models of signed, weighted signed and functional signed digraphs. ,

The model of digraph ; 

is extended by the components: | | ; each vertex

,

is assigned a parameter

;

, - a functional that determines the arcs transformation; each arc is corresponded with either a sign or a weight or a function. If the functional

has the form ,   ,

; 

 

   

,  

 

   

 

 

           

32 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

then the model is called a signed digraph. If the functional

has the form

,

; 

,     ,    

 

   

 

   

then the model is called a weighted signed digraph; If the functional

           

   

is called a weight of the arc.

has the form ,

; 

,

then the model is called a functional signed digraph. The choice of concrete model depends largely on the problems of analysis to be addressed in the process of usage of the model. The problems of analysis of situations based on the cognitive maps can be divided into two types: static and dynamic. There are two kinds of models that correspond to these types: (1) static analysis, or analysis of influences, is the analysis of the current situation that involves the separation and comparison of causal chains, paths of influence of some factors on the others through the third ones, i.e., indirect influence. The aim of dynamic analysis is to generate and analyze possible situation development scenarios at time scales. In both cases, the purpose of the analysis consists in the formation of possible alternative control decisions. These alternatives are the sets of control factors, i.e. factors, the change of which can be directly influenced by decision maker. When setting control problems on cognitive maps, the following concepts are often used. Control factors are those factors which the decision maker can change. The purpose of control is to achieve certain values of some selected factors, which are called the target factors. External, or input, factors are the factors that are not influenced by the other factors of a cognitive map. Analysis of influences identifies the factors with the strongest influence on target factors, that is, it determines the most effective points for applying control actions. Dynamic analysis considers the development of situation as a process of changes of its states in discrete time, and under the state of the situation at time the set of values of all its factors ,…, at this time moment is understood. Dynamic analysis solves two main problems. The direct problem is a prediction of the situation development for the given control or external actions (change in the values of some control or external factors), that is, it is the computation of the sequence 1 , 2 , … , for a given change of the state 0 . The inverse problem is the calculation of control actions that result in the situation having a given state, for example, the state where the target factors have the desired value or some close to it. We can now distinguish several main directions of control of ill-structured situations on the basis of cognitive models: Developing methods of analysis of cognitive maps and decision support techniques based on models of cognitive maps; Developing the techniques of problem domain structuring, in other words, the methods for construction of cognitive maps; Developing software tools and information technologies that implement the above methods.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 33

By interpreting the vertices, arcs and weights, and different functions that define the influence of connections on factors, in various ways, one can arrive at different models of cognitive maps and at different means of their analysis. The most common classes of models are signed digraphs, weighted cognitive maps, linear models, and fuzzy models. Signed digraphs. According to the above definitions, one considers a digraph , and obtains a signed digraph if there is a function of sign:   1, 1 . The weight sign 1 means the positive influence, the sign 1 means negative influence. The weight of a path is the product of weights of its arcs; it is positive if the number of negative arcs is even, and is negative if this number is odd. If there are both positive and negative paths between vertices and , then the character of the total influence of factor on factor remains uncertain. The computation of influences can be defined as follows. Indirect influence

of factor

on factor

via the path  

from

to

is determined as

  ,

where

is the set of arcs of the path , and

The total influence

,

equals 1 if all

is the weight (sign) of the arc 0, and is equal to 1 if all

.

0.

The analysis of cycles in signed digraph is one of the problems that have to be solved in the process of its analysis. The positive cycle is a positive feedback loop; for example, if the factors are assigned some values, then an increase of the value of a factor in cycle leads to its further increase and then to its unbounded growth, which, in turn, leads to the loss of stability. The negative cycle counteracts the deviations from the initial state and contributes to stability; however, some instability in the form of significant fluctuations occurring during the passage of excitation along the cycle is still possible. Structural analysis and study of structural properties of signed digraphs, development of heuristic algorithms and estimations of significance of the elements of signed digraph, verification of weights of arcs, and estimates of preference degree of factors are the main analytical problems in the area. The main disadvantage of signed models is the impossibility to cope with the strengths of influences over different arcs and paths, as well as the lack of a mechanism to resolve the uncertainties that arise in case of both positive and negative paths between two vertices. The basic approach to address them is to introduce weights that characterize the strength of influence, which leads to the weighted signed (cognitive map), linear or fuzzy models. Weighted signed digraphs - deterministic cognitive map. Cognitive map (CM) is a directed graph (digraph) , with vertex set and edge set , which includes two functions and . The CM is uniquely defined by the adjacency (or weight) matrix , where is the number of vertices and is the weight of the arc ; 0 means that the corresponding vertices are not connected. The vertices of CM correspond to concepts (factors) that characterize a situation (or a system), and the arcs define causal connections between concepts. Each concept represents a characteristic of the situation. In general, it can stand for events, actions, goals, values, trends of the situation which is modeled as a cognitive map. Each vertex-concept is characterized by a number (the function ) that represents its value and it results from the transformation of the real value of the situation’s variable, for which this concept stands. Between concepts there are three possible types of causal relationships that express the type of influence going from one concept to the others. The weights of the arcs between concept and concept (the

34 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

0, which means that an increase in the value of concept leads to the function ) could be positive, increase of the value of concept , and a decrease in the value of concept leads to the decrease of the value of concept ; or, there could be negative causality, 0, which means that an increase in the value of concept leads to the decrease of the value of concept , and vice versa (Fig. (5)). Mathematical model of CM consists of an 1 state vector which includes the values of the concepts and weight matrix which gathers the weights of the connections between the concepts of CM. The matrix has rows and columns where equals the total number of distinct concepts of CM and the matrix is considered to have diagonal elements equal to zero, since it is assumed that no concept causes itself.

12

1 

2 26

15  

  5 

212 51

41

32 24

6 

13 34 35 64 3 

43

4

Figure 5: A simple model of cognitive map.

The value of each one concept is influenced by the values of the connected concepts with the appropriate weights and by its previous value. So, the value for each concept is updated by the following rule:

 

where 1 is the value of concept at time 1, is the value of concept at time , is the value of concept at time , and is the weight of the connection between and , and is a threshold function. Thus, in vector form

So, the new state vector is computed by multiplying the previous state vector by the weight matrix . The new vector shows the effect of the change in the value of one concept in the whole CM. The above equality includes the value of each concept at previous time instants, so the CM possesses memory capabilities and there is smooth change after each new updating step of CM. 1 Linear models. The behavior of linear models is associated with the notion of increment value 1 of the factor ; the increment value in linear models is referred to as an impulse. The increment value is computed by the formula

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 35

where is the set of all vertices from which there are paths to the vertex

.

The most important characteristic of linear model is stability. The vertex is called pulse-resistant if its 1 for every . The vertex impulse is bounded, that is, there exists a number 0 such that is called absolutely pulse-resistant if its value is bounded. The graph is called (absolutely) pulseresistant if all its vertices are stable in the appropriate sense. The analysis of stability is conducted in terms of eigenvalues of the incidence matrix of the graph. It is known, that the graph is pulse-unstable if there exists an eigenvalue exceeding |1|; the graph is absolutely stable if and only if it is pulse-resistant for every pulse process and there is no eigenvalue equal to 1 among all its eigenvalues. To stabilize the unstable graphs, different methods can be used. One method is to change the adjacency matrix (adding or removing the arcs) of strongly connected components of the graph; another one is to construct an additional graph-regulator that closes, by means of feedback loops, the inputs and outputs of the initial graph. The drawback of linear models, essential for applications, consists in rigidity of these models; this means that it is necessary to specify the weights in the form of precise numerical values, whereas the main feature of ill-structured situations is impossibility to obtain the reliable numerical estimates of the weights. So, fuzzy models serve as the most adequate models as alternatives to linear models. Fuzzy models - fuzzy cognitive maps. Cognitive maps were introduced by a political scientist R. Axelrod [76] who used cognitive maps for representing social scientific knowledge and describing the methods that are used for decision making in social and political systems. Then B. Kosko [70, 77] enhanced the power of cognitive maps, considering fuzzy values for the concepts of cognitive map and fuzzy degrees of interrelationships between concepts. After this pioneering work, fuzzy cognitive maps attracted the attention of scientists in many fields and have been used in a variety of different scientific problems. Fuzzy cognitive maps have been used for planning and making decisions in the field of international relations and political developments [78] and for analyzing graph theoretic behavior [79], been proposed as a generic system for decision analysis [80] and for distributed cooperative agents [81]. Fuzzy cognitive maps have also been used to analyze electrical circuits [82], to structure virtual worlds [83]. In the control related themes fuzzy cognitive maps have been used to model and support plant and manufacturing control [84, 85], to represent failure models and effects analysis for a system model [86, 87] and to model the supervisor of control systems [88], to model dynamic system control [89, 90]. It is obvious that there is high interest in the use of fuzzy models in a wide range of different fields. As with the deterministic cognitive maps, fuzzy cognitive map theory makes use of a symbolic representation for the description and modeling of system. It utilizes concepts to illustrate different aspects in the behavior of the system and these concepts interact with each other showing the dynamics of the system. A fuzzy cognitive map integrates the accumulated experience and knowledge on the operation of the system, as a result of the method by which it is constructed, i.e., using human experts’ knowledge related to the operation of system and its behavior in different circumstances [91, 92]. It should be mentioned that since all the values in the digraph are fuzzy, so concepts take values in the range between (0, 1) and the weights of the arcs are in the interval 1, 1 , or, in general, are the values from a linguistic scale (linearly ordered set of linguistic values that describe all possible strengths of influences). Let , , … , be the set of all factors which are the inputs for the factor , i.e., they are the vertices of the arcs entering . Then, in general case, the value of at time 1 depends on the values of input factors at time and on the weights of the arcs that connect these factors with the factor :

36 Artificial Intelligence Resources in Control and Automation Engineering

,

,…,

; 

Armen Bagdasaryan ,

,

,

,…,

,

The selection of the functions (influence functions, aggregation functions), which in general case can be different for different vertices, defines every concrete model. Usually, in applications the simpler models are considered, when these functions are the same for all factors. Such models are called homogeneous and to solve problems of analysis of situations within the framework of these models, matrix methods can be applied. The process of cognitive maps building precedes the work with them. Obviously, this process cannot be completely formalized and to large extent is subjective. On the other hand, it can be seen as a process of extracting knowledge from experts, and results are presented in the form of cognitive maps. The components of this process are the construction of the conceptual structure of the problem domain (identification of key factors and relationships between them), the selection of aggregation function, and the construction of linguistic scales (for fuzzy models) and the assignment of weights to the arcs. Cognitive maps as models of representation of expert knowledge reflect a subjective vision of a situation. Different experts can build different cognitive maps for the same problem domain; these maps can differ not only by the values and signs of weights, but also by the set of factors. In this sense, cognitive maps can be considered as a tool of rough, qualitative description of situation. Cognitive models and cognitive analysis with some confidence may indicate a possible trend of the situation as a result of various control actions, identify the various side effects of solutions, but in principle cannot give guaranteed estimates and predictions. The adequacy of a cognitive model can be judged only by the results of its application. Let us note some actual directions for further development of cognitive approach: Modeling the development and control of development of dynamic situations under resourcelimited settings; Modeling of conflict situations, threats and counter threats in terms of cognitive maps; Structural analysis of cognitive maps: identification of unwanted cycles, stability analysis (i.e., robustness - insensitivity to small perturbations) of a given situation, etc.; Physical time in cognitive models; Heterogeneous cognitive maps with different influence functions for different factors, and methods of their analysis; Building techniques for cognitive maps with help of typical structures and procedures; Studying the prediction reliability in cognitive models; Studying the adequacy of various models of cognitive maps in different problem domains; Building of space-time cognitive models, multidimensional and multilevel hierarchical cognitive maps and methods of their analysis. It should be noted that the theory of (fuzzy) cognitive maps is a powerful tool for modeling, analysis and control in weakly-formalized and ill-structured problem domains, as well as in domains with uncertainties and information incompleteness. The method of cognitive modeling is the method of soft modeling and simulation. The closest analogues of this method are simulation modeling and the method of system dynamics. The advantage of the method of

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 37

cognitive modeling is that it can operate not only with precise quantitative values and formulas, but with the qualitative values and estimates as well. But this advantage can also be in some sense regarded as a drawback, since the results are qualitative. Cognitive models help quickly get the initial results, more detailed understanding of simulated system, and identify regularities and then move on to more accurate models (if this is possible and necessary). Therefore, the most reasonable and efficient level of application is the use of cognitive modeling at the top level of decision-making, upon the analysis of complex socio-economic, technical, techno-economic, and other weakly-formalized and ill-structured systems. 4.7. Multi-Agent Models Discrete individual-based or agent-based modeling [93-95] has become a very promising and powerful methodology to describe the occurrence of complex behavior in diverse systems. The advantage of such an individual-based approach is given by the fact that it is applicable also in cases where only a small number of agents govern the system evolution. Agent-based model is the real world construed from many separate active subsystems, or units. Each unit interacts with other units, which constitute for the unit the external environment, and this unit, in the process of operation, may change both the external environment and its behavior. In agent-based modeling, a system is modeled as a collection of autonomous decision-making entities called agents. Each agent individually assesses its situation and makes decisions on the basis of a set of rules. Agents may execute various behaviors appropriate for the system they represent, for example, producing, consuming, or selling. Repetitive competitive interaction mode between agents is the main feature of agent-based modeling, which relies on the power of computers to explore dynamics out of the reach of pure mathematical methods [96, 97]. At the simplest level, an agent-based model consists of a system of agents and the relationships between them. Even a simple agent-based model can exhibit complex behavior patterns and provide valuable information about the dynamics of the real-world system that it emulates. In addition, agents may be capable of evolving, allowing unanticipated behaviors to emerge. Sophisticated agent-based models sometimes incorporate neural networks, evolutionary algorithms, or other learning techniques to allow realistic learning and adaptation. There are many definitions of an agent. Common in all these definitions is that the agent is an entity that is active, with autonomous behavior, can make decisions in accordance with a certain set of rules, can interact with the environment and other agents, and can evolve [95, 98, 99]. The purpose of agent-based models is to get an overview of these global rules, the general behavior of the system, based on assumptions about the individual, the local behavior of its individual active sites and the interaction of these objects in the system. Multi-Agent System (MAS) may be considered as an intelligent tool for the solution of such problems as planning, scheduling, decision making and control in the framework of production processes [105, 106]. The MAS approach seems to be the most feasible. It respects the complicated characteristics of the goal that one aims to achieve. There are some significant reasons that can motivate one to choose the MAS approach to the solution of complex problems and decision making, such as: Modularity. Each agent is an autonomous module and can work without interventions of the external world. Each agent can possess different capabilities or functionalities and through cooperation the agents are able to achieve a variety of goals. Parallelism. The MAS approach enables to work in parallel. A complicated problem could be solved in an acceptable time by using a number of agents, e.g., gathering information from various resources allocated in different places.

38 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

Flexibility. The MAS approach is able to react in a flexible manner to each change in the environment. Through cooperation the agents can assist each other to compensate the lack of capability or knowledge. They can share information or own capacity to resolve a newly appeared situation, if one agent is not able to do so. Besides that, each intelligent agent can do reasoning about whom and when it has to cooperate with, in order to achieve the effective performance. It is also supposed that agents have the following properties: Autonomy. Each agent, as mentioned before, thinks and acts locally. It means that agent operates without direct interventions from other agents to achieve its own goals. Social ability. Agents can cooperate with other agents to achieve common goals. Reactivity. Agents react on changes in environment; it is needed to describe the negotiation process. Pro-activeness. Agents do more than response on events generated by environment; they can show goal-directed behavior. Generally, multi-agent systems consist of the following main components: A set of system units, which is divided into two subsets, active and passive; members of the active subset, active units, called agents that manipulate the members from the passive subset, passive units called objects; Environment, or space, in which agents and objects have to function and act; Tasks (functions, roles), which are assigned to agents; Relations, interactions, between agents; Organizational structures, configurations, which are generated by the agents; Agent actions, for example, different operations over objects, communication acts. Interaction between agents means establishing bilateral and multilateral dynamic relations between the agents. Interactions between the agents have a definite direction - positive or negative, i.e., they have the character of assistance or resistance, attraction or repulsion, cooperation or competition, cooperation or conflict, coordination or subordination, etc. Interconnections and interdependencies between agents are characterized by certain intensity. Interactions between agents are dynamic. Multi-agent models are used to study decentralized systems, the dynamics of functioning of which is determined not by global rules and laws, but on the contrary, these global rules and laws are resulted from individual activity of a group of agents. Typically in such systems there is no global centralized management, agents operate under their own laws asynchronously. Agent-based models capture emergent phenomena. Emergent phenomena result from the interactions of individual entities. By definition, they cannot be reduced to the system’s parts: the whole is more than the sum of its parts because of the interactions between the parts. An emergent phenomenon can have properties that are decoupled from the properties of the part. Highly flexible nature of agent-based technique allows one to apply it in many cases, especially when there is potential for emergent phenomena:

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 39

Individual behavior is nonlinear and can be characterized by thresholds, if-then rules, or nonlinear coupling. Describing discontinuity in individual behavior is difficult with differential equations; Individual behavior exhibits memory, path-dependence, and hysteresis, non-markovian behavior, or temporal correlations, including learning and adaptation; Agent interactions are heterogeneous and can generate network effects. Aggregate flow equations usually assume global homogeneous mixing, but the topology of the interaction network can lead to significant deviations from predicted aggregate behavior; Averages do not work. Aggregate differential equations tend to smooth out fluctuations, not agent-based model, which is important because under certain conditions, fluctuations can be amplified: the system is linearly stable but unstable to larger perturbations. Or when describing the system from the perspective of its constituent units, i.e., when The behavior of individuals cannot be clearly defined through aggregate transition rates; Individual behavior is complex. Everything can be done with equations, in principle, but the complexity of differential equations increases exponentially as the complexity of behavior increases. Describing complex individual behavior with equations becomes intractable; Activities are a more natural way of describing the system than processes; Validation and calibration of the model through expert judgment is crucial. Agent-based model is often the most appropriate way of describing what is actually happening in the real world, and the experts can easily “connect” to the model, modify it and make improvements; Stochasticity applies to the agents’ behavior. With agent-based model, sources of randomness are applied to the right places as opposed to a noise term added more or less arbitrarily to an aggregate equation. Moreover, the flexibility of agent-based models can be observed through many other aspects. For example, it is easy to add more agents to an agent-based model or delete agents. Agent-based models also provide a natural framework for adjusting the complexity of the agents: behavior, degree of rationality, ability to learn and evolve, and rules of interactions. Another aspect is the ability to change levels of description and aggregation: one can easily play with aggregate agents, subgroups of agents, and single agents, with different levels of description coexisting in a given model. One may want to use agent-based modeling when the appropriate level of description or complexity is not known ahead of time and finding it requires some tinkering. Multi-agent approach allows one to investigate the problem of collective interaction, effectively solve prediction problems, investigate the processes of self-organization, and also allows natural descriptions of complex systems [100-107]. So, the agent-based modeling is a powerful simulation modeling technique for studying the behavior and evolution of complex systems. Presently, the use of the multi-agent systems paradigm for the modeling of complex systems has many successful applications, as it allows specialists to gather information quickly and process it in various ways. 5. HIERARCHICAL STATE GRAPH DIAGRAMS The above review reveals that conventional methods in modeling and control of systems have contributed a lot in the research and the solution of many complex problems, but their contribution to the solution of the

40 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

increasingly complex dynamical systems in ever changing environments will be limited. It has become quite clear that the requirements in the control and modeling of systems cannot be met with the existing conventional control theory techniques and it is necessary to use new methods that will exploit past experience, rely heavily on expert knowledge-bases, will have learning capabilities and will be supplied with intelligent simulation tools [108-119]. The main idea behind attempts to cope appropriately with complex problems is to describe relationships between various elements (objects, agents, parameters, variables, etc.) of a system and thus provide knowledge representation and inference. Such description of a problem should utilize experts’ beliefs and cognition about a problem, yielding thorough analysis, reliable forecasting and decision-making. Problem solving planning and control in complex systems is an activity which deals with problems related to (optimal) selection of control actions, operations, system parameters, etc., required for achievement of prescribed goals. Optimality of generated solution depends significantly upon the problem domain expert experience, beliefs, and knowledge about the system behavior [114, 115]. In addition, in real world (complex) situations we face two important issues. On one side, we find causal and structural dependencies between system variables; on the other side, different experts provide different views of the same problem, they build different models of situation development and thus propose different solutions, which in turn may perform different output and control effects. Modeling taxonomy based on graphical representation of situation (object, system, etc.) development and structural relations in concrete problem domain by means of state diagrams [121, 123] allows for taking into account of each possible view of a problem and thus modeling and then generate global model by augmenting a set of separate state diagrams [122, 123]. Providing a description of each object state development and then the overall complex system behavior, based on knowledge bases and domain experts’ experience and monitoring data, state transition diagrams enable thorough analysis and come up with an answer to “what-if” question. An “if” input vector is composed of a set of control actions on lower level objects; however, our model, Hierarchical State Graph Diagrams - HSGD [120-123], does not restrict us in selection of control objects and the input vector components can have a distributed nature and be applied at different levels of abstractions. What happens when an input vector affect a system, we can find as a hierarchical state diagram (hierarchical network) output, suggesting possible actions that steer a system to the desired states or bring the system to equilibrium or stable states. That is, state diagrams technique is mostly qualitative tool [124] but also provides some quantitative analysis of system development, but it cannot present exact mathematical answer but rather to point out the gross behavior of a system, to show the global patterns of how the whole of our hierarchical network of state diagrams behaves, and to get a view of what goals can be achieved by means of applying one or another set of control actions. The methodology that we propose aims to contribute to the overcoming of shortcomings of approaches based on traditional knowledge-based systems that lead to expert system failure related to, for instance, incomplete, inconsistent, and ambiguous knowledge bases. Another shortcoming that troubles conventional approaches to complex systems modeling is related to the type of relationships between system parameters and variables. These appear quite often to be rather causal and structural than just the only explicit “if-then” rules. Moreover, depending on a system we are modeling, its dynamics can additionally bring difficulties in expert knowledge base development. The aim of the approach is to promote the methodology for dynamic modeling, multi-criteria decision analysis and reasoning about potential effects of initially generated system development plans and related parameters with respect to control strategies. One technique for modeling systems which contributes to the effort for more intelligent simulation and control methods is based on the HSGD technique. 5.1. Conceptual Basics of Agent Oriented Hierarchical Parametric Modeling We use several concepts [121, 122, 125, 126] to model complex systems. They simplify complex problem solving in multi-parameter setting and divide it into more simple, manageable and understandable units.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 41

The modeling paradigms, which are the most close to our approach, use the concepts of modeling complex systems in an agent- and object oriented point of view, and discrete event and finite state machines methodologies. The concepts are as follows: Decomposition: divides a large complex system consisting of a set of interrelated subsystems (objects, elements, agents) into set of small subsystems. The small subsystems can be easily modeled, executed and are manageable. It also divides the problem environment into a set of separate problem domains. By integrating (models of) small subsystems and considering them in each of the problem domains, we can build the large system for the whole problem environment. In the agent oriented view, we divide the complex system into a collection of sets of agents, which are studied in every specific problem domain (Fig. (6)). Abstraction: represents complex system into simple systems conceptually. It focuses on the interested parts of complex system. Other detail parts are hided for simplicity. Abstract representation provides for qualitative description and analysis of complex system. Using conceptual models that have only essential features necessary to represent or solve complex problem, we can understand and analyze complex system. Problem domain Problem domain

Problem domain

Problem domain Agent Problem environment of complex system

Interrelation

Figure 6: Problem environment and its representation in complex system.

Polymorphism: introduces a set of polymorphic parameters which are applied to a collection of system agents. It enables one to turn from the concept of modeling and control at object level to the concept of modeling and control at the level of classes of objects. This helps turn form individual models to the integral models at arbitrary level of abstraction. Hierarchy: represents the system agents, the problem and control domains and their qualitative characteristics, i.e., polymorphic parameters (Fig. (7), (8)). The principle of hierarchy allows us to structure agents relations in a system and distinguish the essential interrelations in the system for aggregation and scaling (recount) of dependent parameters, and also helps structure the problem and control domain of an object. Layering: separates system functions into layers according to their roles or responsibility. Complex system can be represented as a layered system in which each layer plays its role. In general, layering concept helps understand and design complex system. The above concepts lead to the model scalability [120, 123] that provides simultaneous representation of goals, parameters and development plans of various objects, which is very important in the problem of building the models of development of large complex systems (Fig. (8)).

42 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

Agents

Agents

Interaction (interrelation)

Object

between agents

Interaction between agents Interaction between objects

(a)

(b)

Figure 7: Principle of hierarchization: (a) flat network structure, (b) hierarchical structure.

Control object

Problem domains

Hierarchical parameter

State diagrams

Figure 8: Generalized structure of the hierarchical decomposition of development model.

The important features of our model are formulated as follows: Model of development of each object at any level of hierarchy is sufficiently autonomous. This provides a sufficient degree of decomposability and therefore results in flexibility of building large models; Objects in a system that we model, being separate units, are not modeled as such separate units but as classes, within each class the objects have common development goals; Models of development of objects at different levels are information compatible, that is, outputs of one object model at some level serve as the input for another object model at some other levels. The principle of hierarchy is common in the real-world systems. There are enormous number of examples of it, beginning from ecosystems and biosystems to neuronal ensembles and cognitive networks to organizational and political systems to social and economic ones. So, the emergent (collective) characteristics of a particular lower level system frequently form an individual object (agent) at a higher

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 43

level of the hierarchical system. This aspect has been emphasized by many researchers on artificial intelligence and complex systems [127]. Our model HSGD accommodates a hierarchical multilevel multi-agent dynamical system, in which an agent can itself be a collection of other agents. The HSGD structure is as follows: HSGD is composed of a number of levels. Each level consists of a number of dynamical multi-agent systems which describe the behavior composed of sets of agents; Each set of

1 level agents is aggregated into a

level agent;

Behavior and goal achievement of level agent emerges from the organization of inter-level dependencies and the behavior and goal achievements of 1 to level agents.

Interactions/transitions Aggregation/generalization Transitions/development diagram

Level agent development diagram Level agent development diagram Level agent development diagram

Figure 9: Hierarchical state graph diagrams model using multi-agent multilevel dynamical system in nested hierarchies.

HSGD naturally admits a description in terms of higher level and lower level, where the lower level is nested within the higher level. Any agent at any level is both a component of a given collection in its own level and a subsystem decomposable into a set of other agents at its adjacent lower level of HSGD (Fig.

44 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

(9)). Note that the agents in the lowest level are the minimum units, which are indecomposable of this hierarchical system. HSGD is a heterogeneous system where each set of agents in each level is evolved in its own goal direction and adapts to the requirements of problem domain environment through the application of its own development plans. The interaction topology of HSGD can also be heterogeneous hierarchical structures. Namely, the development rules, the inter-level dependencies rules and the interaction topology of distinct sets of agents can be different, and these different schemes hierarchically construct the HSGD model and lead to the hierarchical network of dynamical processes which, properly defined, leads to intelligent description of behavior. In mathematical terms, the HSGD model can be in generalized form defined as follows: , , , , , , where : agents grouped in objects that lie at various hierarchical levels; : dynamic systems represented as state graph diagrams that model development plans for each group of agents (object); : coordination rules for dynamic systems at different (adjacent) hierarchical levels; : the number of levels in hierarchy; : the hierarchical interaction topology of HSGD given by the rules of inter-level dependencies; : the objects of each class in each hierarchical level; : the control scenarios/strategies used for each class of objects to achieve their goals. Considering the problem of model building and simulation of complex system, we distinguish global goals lying at higher levels of hierarchy and local goals lying at the lower levels. The goals of objects at different levels of hierarchy are highly interconnected. Interaction between higher-level object and lower-level objects is such that the achievement of goals of lower-level objects immediately influences the achievement of goal of the higher level object. This leads to the concept of hierarchical state which corresponds to the global goal of higher level (Fig. (10)). This means that each of the objects or a class of objects is immersed onto the intersection of states that correspond to the concrete set of the objects’ goals, but the whole system is immersed into the hierarchical state. This approach is applicable at any level of hierarchy. The approach is useful for different kinds of systems [128, 129]. A B

C G

H

D

E

Figure 10: The scheme of decomposition of a hierarchical state.

Using the appropriate semantic interpretation, the hierarchical state shows how the current states of objects of different levels of hierarchy are related to each other. Our approach to the representation of states has the following useful properties:

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 45

Aggregation of parameters and therefore simplification of modeling of complex system; Formalization of information gathering and its assessment for getting integrated and individual estimates and global and local evaluations of the system at any level; Ability to analyze the multi- and inter-level dynamics of system and study different aspects of inter-connected dynamic processes in a unified way. 5.2. Model of State Diagrams The main idea underlying the abstract representation of control and development processes in multilevel dynamic system relies on the use of the model of state diagrams [125]. State diagrams provide the qualitative description of dynamics of parameters and of controlled state dynamics of objects with use of control scenarios. The use of state diagrams technique supposes the initial classification of control objects over the system state space and the construction of canonical model of state dynamics represented by the model of state transition diagram. The state space is defined as follows (Fig. (11)). The continuous time interval is divided into parts by means of the interval partition. On each time interval we have some subsets of states, in which objects remain during this interval. Every state is defined by the vector of values of corresponding parameters. The state of the object is thought of as a situation which is described by the state vector of each agents of the object. The canonical model is constructed by using (1) databases containing the information about the dynamics of values of parameters that characterize the set of objects at a given time interval, and (2) expert knowledge-base consisting of declarative and procedural knowledge containing the rules of classification.

state

state

dynamics of values of parameters values of parameters at time

transition

Figure 11: The definition of state of an object.

The state transition diagram (Fig. (12)), in terms of which the canonical model is described, is defined as: ∆,

,

,

,

, ,

,

,

,

,

, ,

where ∆,

: the finite time interval ∆ divided into parts ∆ by the partition and ∆ ∆, ∆ ;

, , : the set of states ordered by the classification rule , , the rule divides into equivalence classes such that we get ∆ ∆ ∆ , , and , ;

, 1,

, :

,

,…, ∆

1, ;

, where ∆

; more precisely, ∆ ,

46 Artificial Intelligence Resources in Control and Automation Engineering

,

Armen Bagdasaryan

: the initial and final state respectively;

: the set of weighted arcs that determine state transitions, each arc is assigned the transition time ; if an arc , then   , where is the order relation determined by , i.e. there is an arc from (previous state) to (subsequent state); , , : the distributions , , … , without loss of generality, one can take

over the vertices-states of the diagram at time moments ;

∆;

: is the initial distribution; : is the final distribution. The canonical model is used as a tool for formalization of qualitative properties of multilevel dynamical system and represents hypothetical model, based on expert knowledge, of state dynamics of a set of objects. The canonical model describes the qualitative character of state dynamics, using the distributions of the objects; the distributions determine the states in which the objects at some time can be found.   0 

0 

1

∆ time moment

state transition

Figure 12: The diagram of canonical model of state dynamics.

The canonical model is then used for comparative analysis with the actual state dynamics of the set of objects. For this purpose, the states of the objects are consecutively re-estimated at time moments in order to get the actual distributions of the objects over the states of canonical model, and then to compare this distribution with the required one. This helps represent the core essence of system control problems and state dynamics of control objects. The description of actual process of state dynamics at arbitrary time interval ∆ is based on the use of states of the canonical model as objects’ classifier. The state transition diagram of actual state dynamics (Fig. (13)) is represented as follows: ,

,

,

where : the state transition diagrams, each one extended by the components: : the set of arcs, that describe the state backstep. Thus, the set of is defined as , where is the set of arcs that describe state transitions; if , then but if , then while there is an arc from (subsequent state) to (previous state) or ;

, ,

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 47

, ,…, : the vector-function called the counter of objects, ; each component of the vector determines the number of objects that change their state from to , are assigned to each arc , , at some time interval ∆ ; the counters , ; The counters assigned to the arcs characterize the intensity of objects’ state transitions (positive processes); the counters assigned to the arcs estimate the intensity of objects’ state backsteps (negative processes); , ,…, of objects having a fixed state

,

: the vector function, each component of which .

state

time moment

defines the number

transition – positive process transition – negative process the number of objects with positive/negative tendency number of objects in fixed state at time

Figure 13: The diagram of actual state dynamics.

The functions and allow us to obtain the information on the relation between processes of development and degradation, and to qualitatively estimate control actions and their efficiency. 5.3. Coordination of State Diagrams and Their Compositions Coordination [130-143] is one of the key issues in modeling, control and design of complex systems, and has been the subject of numerous investigations in areas such as sociology, economics and organizational theory. From an engineering point of view, coordination is conceived as a means to integrate various activities or processes in such a way that the resulting ensemble shows desired characteristics and functionalities. The design of coordination mechanisms is particularly challenging in the field of multiagent systems, as they are usually embedded in highly dynamic environments, and neither the number nor the behavior of agents can be directly controlled at design time. We argue that additional high-level abstractions need to be integrated into agent oriented design methodologies in order to exploit the full potential of coordination schemes, and to engineer coordinated multi-agent system in open environments in an efficient manner.

48 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

Maybe the most widely accepted conceptualization of coordination in the multi-agent field originates from work in the area of organizational science [144] that defines coordination as the management of dependencies between organizational activities. It is straightforward to generalize this approach to coordination problems in multi-agent systems. The subjects whose activities need to be coordinated are the processes in agents. However, the entities between which dependencies arise (or object of coordination) and should be coordinated are usually come down to goals, actions and plans. Depending on the characteristics of the system environment, taxonomy of dependencies can be established, and a set of potential coordination rules are assigned [145]. Within this model, the process of coordination is to accomplish two major tasks: establishing the dependencies in the system, and then, decision respecting which coordination rules must be applied. The coordination mechanism is the way to perform these tasks [146]. We put the problem of coordination within the context of state transition diagrams that model the state dynamics of agents. We introduce several compositional operations giving the rules of consistency of different state diagrams. These rules help one to construct complex models of state dynamics that combine the interrelations between different sets of parameters and represent the conditions for coordination of state dynamics for objects at different levels of hierarchy. Structural composition of state diagrams provides a synthesis of complex requirements set to the dynamical characteristics of controllable object. The structural composition of simple models is one of the key issues in building the complex models of hierarchical state dynamics. So, we say that for state diagrams the property of consistency holds if the attainability of certain states takes place in prescribed time-event sequence. The operations of sequential and parallel compositions and operation of aggregation are introduced. Let and be two state diagrams given at time intervals ∆ 0, Then the operations of compositions for the diagrams are as follows: a)

and ∆

0,

correspondingly.

Sequential composition The diagrams and are sequentially composed, that is, they compose a linear fragment if for their time intervals one has (Fig. (14)).

b)

Parallel composition The diagrams and are composed in parallel, that is, they compose a parallel fragment if they are defined on the same time interval, (Fig. (14)).

c)

Aggregation The aggregation is defined for state diagrams at different levels of hierarchy. In this case, for coordination of state diagrams at neighbor levels of hierarchy the Cartesian product of states of diagrams of lower level of hierarchy is defined (Fig. (15)). To do this, one should specify the ordering relation on the subsets of Cartesian product of states of diagrams of lower level of hierarchy.

The above defined compositions are straightforwardly generalized for arbitrary number of state diagrams. Combining the above two compositions, we get a sequential-parallel composition when the time intervals at which the state diagrams are given has an intersection. The operation of aggregation can be defined not only on the single states, but also on the subgraphs of state diagrams of lower level of hierarchy.

Systems Theoretic Techniques for Modeling

initial state

Artificial Intelligence Resources in Control and Automation Engineering 49

final state

(a) sequential composition

(b) parallel composition

Figure 14: Sequential (a) and parallel (b) compositions of state diagrams.

 

1 

2

III

4

1

6 3

I

5

1

1, 2, 3

I, II   

2

4, 5, 6

III, IV, V   

1 

2

Figure 15: Aggregation of state diagrams - children dynamical systems

II

V

 

IV

, parent dynamical system

1 .

The composition of state diagrams allows one to formally represent different combinations of complex criteria sets in order to perform objects classification and to solve control problems. Using the consistency rules and operations with state diagrams, one can model diverse schemes of inter-level relations and influence of states of lower level diagrams on the processes at higher levels of hierarchy. As a result, certain value is produced at the output of the highest level; this value is considered as a response of the hierarchical system on the input control symbols. 5.4. Model of Controllable Development of System Elementary and complex state diagrams enable one to construct clear and graphical development models. The nodes of diagrams are states, and the arcs are intensities of objects transitions from one state to another. The ordering of states demonstrates the process of objects development. Using the modeling tools, the

50 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

development model can be redefined and new states and new ordering relations can be added. Considering the state diagrams in time domain (time-domain analysis) - animation of objects’ flows - allows forming the time characteristics of the process of development of a set of objects under study. The various approaches to the control processes require consideration of development models, in which the representation of controllable dynamics of hierarchical object initiated by input signals comes to the forefront. The model of controllable development is based on the following principles: Selecting the control actions that influence the controllable system; this is important for autonomous construction of control scenario and for flexible modification of the model to the alternative control scenarios; Taking into account the states that have been attained on the previous control stages (system state history); this provides a succession of multistage control scenarios; Comparing with the results of alternative control scenarios; this provides basic arguments upon assessment of the efficiency of control scenarios. The model of controllable development illustrates the key dynamic characteristics depending on whether or not the control actions corresponding to the current states are performed. In this sense, the model of controllable development is constructed in the form of “what if” hypothesis. A hypothesis of controllable development is defined as the tuple , ,

,

, ,

where : the set of states; ,

: the initial and final states respectively;

: the set of input control symbols; : the set of arcs, by input control symbols, enter the input;

, ; is a subset of arcs that define state transitions initiated is a subset of arcs that define state backsteps when neither of control symbols

: the one-to-one correspondence that defines for each input control symbol the state transition initiated by this symbol; To model and analyze the interconnection between state diagrams at different levels of hierarchy we introduce to the model the rules of inter-level dependencies. These rules can be considered as a kind of win/loss scheme that formally describes what one agents (objects) can obtain (benefit, profit), depending on the states of other agents. So, we have : the inter-level connection rule between state transitions at neighbor levels of hierarchy. The rule is determined by the mechanism of after-effect by means of splitting and into two subsets , and , , respectively. The arcs of are called isolated, and the arcs of are called coupled. According to this partition, control symbols of are called individual, and control symbols of are called general. The coupled arcs are defined by introducing the parent-arcs as a Cartesian product of child-arcs for state transition diagrams at neighbor levels of hierarchy. The isolated arcs describe the state transitions initiated by individual input symbols ; this kind of symbols do not influence the state transitions of other diagrams. The coupled arcs describe the state transitions initiated by general input symbols ; this kind

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 51

of symbols initiate the state transition on the parent-arc, which means, as a consequence, the initiation of state transitions on the corresponding child-arcs. And conversely, state transitions on all/several child-arcs initiate a state transition on the parent-arc of the diagram of the higher level of hierarchy. The model of control scenario that manages the development of objects in complex hierarchical system is represented as , , , , where Ω: the set of state transition diagrams that describe the state dynamics - development plans - for each object; : the hierarchical structure identifier; in general, the identifier is related with the topology of the system; this is done by extending the model of control scenario by some variable that will define the system topology and, as a consequence, the structural relations in the system, for example, hierarchical structure, networked structure, etc.;  

 Ω: the functional that assigns the hierarchical number to each diagram from Ω;

: the time diagram for control symbols symbols entering;

; it determines the sequential-parallel process of input control

: the scheme of after-effect given by the inter-level connection rule between state transitions. The time diagram can be given by the use of different ways, including the estimation rules of each current state of the system. The trajectory of attainable states represents general and local goals solved by control scenario on arbitrary time interval. Several properties can be considered to evaluate the quality and efficiency of scenario: Scenario is called complete if all subsystems move to the final states of the corresponding state diagrams; Scenario is redundant if both individual and general symbols, which are coupled in the “parent-child” hierarchy of state diagrams, enter the input of subsystem; Scenario with omitted possibilities exhibits high frequency of transitions on the arcs that stand for the backsteps of the states already reached; Complexness of scenario is estimated by frequency of transitions on coupled arcs. Generally, the study of basic properties of control scenario is based on the analysis of the trajectory of attainable states and its comparison with the expected or predicted effect. 5.5. Dynamic Classification of Control Objects In section 5.2. we pointed out that upon constructing the canonical model the rules of classification are used. Indeed, the use of hierarchical state diagrams technique supposes the initial classification of control objects over the system state space in order to build the canonical model of state dynamics of a set of objects under study. The rules of classification are represented in the form of matrices with production rules as elements, which are the formulas of some language . An element , of classification matrix, where is a parameter and is a class of objects, contains a formula that determines the current process of dynamics

52 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

of -th parameter changes at time interval. The matrices of this type give rules of one-level classification. However, the rules of multilevel classification are more important in hierarchical models. Multilevel classification is based on the gradual specification of conditions that should be satisfied by objects from a class. In general case, the rules of multilevel classification are heuristic, and reflect the knowledge and experience of problem domain experts. The subclass of multilevel classification rules which along with the grouping of objects reflect the semantics of state dynamics is of the most interest. To define multilevel classification, the notions of state scale and classifier are introduced [120]. Let , ,…, , set of parameters , be a set of predicates related to the values of parameters of a set of objects. Then the ordered set of propositions , , , , where is the truth domain of , is called a one-level scale if each defines the state . It is assumed that propositions and the corresponding states have the same ordering, that is, if then . The scale determines the values of parameters and allows one to compare the states of the objects. The scale

is said to be the hierarchical continuation of the scale if the propositions , 1, are the set of sub-propositions of .

The hierarchical system of scales is referred to as classifier for a set of objects over the set of parameters at time interval Δ. The classifier is then used for formal description of state dynamics of the objects from the set. The classification of objects over the states allows us to construct the state space of the system. 5.6. General Algorithm for Construction of System Development Model and its Analysis We outline a general algorithm for construction of development model for objects at one level of hierarchy. The algorithm is a basic algorithmic process for building the development model of complex hierarchical system with polymorphic parameters [120]. Let us denote by

the set of objects of one level of hierarchy. The algorithm is divided into four stages.

Stage 1: includes the preliminary study; at this stage one should establish the parameters which dynamics goes in parallel and which characterize an object from . At first stage we choose the set of parameters and draw the graph representation of their parallel dynamics at a given time interval. Using a graph representation, we compare the character of parameter value changes of the object. Stage 2: the stage of estimation of dynamics of the parameters; it consists in getting the comparative dynamical characteristics of polymorphic parameters for different objects from , and in extrapolating the dynamics of parameter values for arbitrary object with simple relationships, which describe the essence of processes that are being studied. The analysis of parameter dynamics gives answers to the following questions: whether a parameter is a function of time of any standard type - monotone increasing or decreasing, with one or several critical points, whether the function is bounded, whether it has a point of inflexion, or it can be described by a cyclic process. Stage 3: the stage of recognition of the type of dynamic processes; it consists in estimation of states of parameter dynamics. This includes heuristic analysis of a sequence of parameter values 1 , 2 , 3 , … at discrete time moments, which then produces the estimate of the current state at arbitrary time moment , 1 , 1 , , where is a function, 1 and 1 are respectively the state and the value of parameters at previous time moment 1 . This heuristic process is universal and applicable for every parameter, for which values the operation of comparison is defined. A qualitative estimation of the current process of dynamics of the parameters allows one to create diverse classification rules . Stage 4: at this stage the classifier determined by the classification rules is used for formal description of dynamic development model of objects from . Formally, the description of the dynamical system is given in the form of canonical model of development of objects from .

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 53

Canonical models along with the actual state dynamics allow one to get a qualitative picture of the development processes of the dynamical system under study. These four stages of the algorithm comprise the general scheme of study of a set of objects at arbitrary level of hierarchy as a unified dynamical system. 5.7. Criteria for Efficiency of Control Scenarios One can see that the method of HSGD formalizes the state dynamics processes in the form of mathematical mappings. In a generalized form, the model of system development and hierarchical control can be represented as follows. Let be a set of control actions for -th subsystem, be a subset that corresponds to the -th state, and let ∆ be the control time interval and , , the control action on -th subsystem at time ∆. Then the control process is formally described by the vector-function , ,

, , ,

, , ,…,

, ,

in control space ∏ of Cartesian product of sets of control actions on different subsystems. It is assumed that , , has a unique influence on subsystem state and on the value of its efficiency criterion. Then, let , , be the process of state changes, and , , be the process of changes of efficiency criterion for -th subsystem at control time interval ∆, ∆. Then, the vector-functions , ,

, , ,

, , ,…,

, ,

, , ,

, , ,…,

, ,

and , ,

formally describe the attainable configurations that represent the efficiency of control process instant ∆.

at time

The above vector-functions can be used to define the concrete efficiency criteria in accordance to the needs of simulation and priorities of decision-maker. 5.8. Modeling System States and Process of Analysis The tool of state diagrams and HSGD method enable one to describe the process of development of complex system in highly information-intensive environments. This information (problem) environment is broken down into a collection of problem domains which represent the information levels of the system. Each information level consists of a number of information contexts. The concept of information context allows one to combine in one model a large amount of diverse information of different character (Fig. (16)). This helps one to explore the model in different aspects and, based on the knowledge obtained by simulation, to synthesize a holistic view on the system. Based on the agent oriented model of the system and object oriented approach to the control and problem domains, each information level describes the system as a discrete-continuous dynamic multilevel model, which reflects the process of state changes of the system in the phase space. Discrete properties of each of the information levels of the system are determined by the necessity to divide the state space of each of the objects into subspaces in order to reflect the observations that characterize the change of states of the objects upon transition from one subspace to another. Our approach uses a combination of analytical and empirical relations with the methods and means of artificial intelligence, where the available analytical and empirical relations are supplemented by formalized or weakly-formalized expert knowledge.

54 Artificial Intelligence Resources in Control and Automation Engineering

R& D Accountin g division

Economic planning

Armen Bagdasaryan

Production plants

division

Electric equipment

Problem domain (Scientific & production department)

Mechanical equipment

Problem domain Problem domain

(Financial department)

(Equipment servicing department) Problem environment (industrial enterprise)

Figure 16: The demonstration of dividing of problem environment into information levels and information contexts: problems environment - enterprise, problem domains (information levels) - financial department, scientific & production department, etc., information contexts - economic planning division, accounting division, R&D division, production plants, etc.

The state transitions are described by the information-mathematical model provided by the combination of data and knowledge stored in databases, knowledge bases, in the existing ontologies and mathematical modules. The subspaces of states are defined by means of the classifier. Using the selected information levels and contexts and the subspaces of states, the overall process of modeling system states and its analysis is formally presented as follows: ∆, , ,

, , , ,

,

where ∆

: the finite time interval of system modeling;

, ,…, , where is the phase coordinate. Each can be bounded from both : the state space; sides, , and are the restrictions on the values of phase coordinates, 1, ; is the phase trajectory of state changes. The phase coordinates describe the properties and states of the system on different information levels. The set of phase coordinates has an object-oriented structure, that is, , ,…, , each coordinate is described by a collection of its own properties - factors. The phase space is represented as a partition ∏ that corresponds to the hierarchical structure of state changes and incorporates the notion of hierarchical state, is the number of nesting hierarchy levels. : the set of admissible inputs, , ,…, , is the number of inputs, each input accepts information of its type that corresponds to the information contexts; : the set of output results

of monitoring and/or diagnosing of control object,

,

,…,

.

: the set of control actions, , ,…, . The control action is determined by the causality “current state - control action”, needed to steer the objects to the desired state with prescribed values of parameters; control actions can be formalized by means of production rules. : the set of output information that characterizes the values of parameters that define the states of objects, , ,…, .

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 55

, , , , , : the transition operator that defines the set of current states, based on the results , of the previous modeling step (prehistory), with some priority value , that is, 1 , , , where 1, , is the number of current states under study; is the operator of synthesis of new initial conditions and new states that depends on the input information, is the operator of generation of information on the results of monitoring and/or diagnosing, is the operator of formation of the control actions, is the operator of formation of information from lower level of hierarchy, it uses the inter-level connection rules - the mechanism of after-effect; , , , , , is the information-mathematical model that describes the behavior and state dynamics of objects between the events, - the databases, - the knowledge-bases, - the analytical models of state dynamics of objects at time intervals, - the ontologies of problem domains (information levels), - production rules constructed by experts and based on and , which give rules for re-estimation of current states around the dynamics of parameters and serve for possible generation of new states; is the priority of the behavior of state dynamics of the objects, which characterized by expert knowledge and decision-maker; : the output operator, 1 , , that transforms the information on the state of the object to the values of parameters to be controlled on the next step; : the qualitative characteristic of the system state; it is determined by the combination of expert estimates of this state and the profit of reaching this state - what goals are achieved; it depends on the priorities of the previous states. The possibilities provided by the information-mathematical model and its analysis are the tool for decision support. The simulation process on the above models allows one to predict the changes in values of parameters over all problem domains of the system and predict future system states, and thus justify the decisions to be made. Finally, we would like to outline some directions for further development of HSGD tool: Developing probabilistic model of HSGD and methods of its analysis; Describing HSGD components and dynamics by means of mathematical functions (operators) to get rigorous mathematical analysis of the model; Studying HSGD as hierarchical dynamical network, using mathematical methods and means of dynamical systems theory; Describing HSGD in hierarchical game-theoretic setting and developing the methods of its analysis; Modeling and control of conflict situations with conflict goals at different hierarchy levels; Modeling and control of system development under resource- and time-limited settings (or, some other interested criteria), using methods of optimal control theory; Building heterogeneous and distributed space-time HSGD models; Structural graph-theoretic analysis of HSGD: identification of unwanted cycles, stability analysis, robustness of given situations, etc.; Applying HSGD for modeling and solving software engineering problems, and in some other areas, for example, social sciences, ecology, etc. Some improvements, extensions, or new variables and functions may be included in the current model of HSGD to get an adequate model for the above directions.

56 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

6. INTELLIGENT INFORMATION SYSTEM FOR SIMULATION AND DECISION SUPPORT Computer information system intended for large scale simulations and decision support should inevitably be based on the comprehensive use of information technologies [147, 148]. The system should have a modular structure that provides sufficient convenience and facility of editing of the separate modules, not influencing the functioning of the others, and adding of new functional capabilities. If it is possible for application domain, the information system should be built in the form of master-system that could be able to dynamic adjustment to the specific problem domain, and in order the information environment of the system could be adapted to the current range of problems. 6.1. Characteristics of Intelligent Simulation Environment Computer simulation models that provide intelligent simulation environment within the information system should meet the following main requirements: Model completeness. The models should provide sufficient possibilities for obtaining the necessary characteristics of system with the required accuracy, reliability, and confidence; Model flexibility. The models should enable one to reproduce various situations upon changing of system parameters; Model structure. The models should provide the possibility of modification of their separate parts; Information support. It should provide the information compatibility of models with computer databases. An intelligent simulation environment is a large knowledge-based integration system, which consist of several symbolic reasoning systems (LISP, PROLOG, etc.) and numerical simulation software. Such environments suggest a framework for integration of numerical simulation, expert system and artificial intelligence techniques. In a goal-oriented environment, once the system is described and the goals specified, the simulation system drives itself to goal achievement. We propose intelligent simulation environment of various control strategies and scenario modeling. Several studies show the applications of intelligent simulation in the area of production systems. Recently, an integrated knowledge-based model is developed for complex man-machine systems [149]. Intelligent simulation environments are also proposed for flexible manufacturing systems, information systems, process plants, etc. [150-153]. In our approach, an intelligent modeling environment is a flexible, integrated, and knowledge-based framework capable of extending, learning and correcting itself. It is goal oriented and searches for the best solutions by referring to desired target. In parametric modeling and analysis, the knowledge of values of various parameters and their dynamics is one of the most important elements that provides adequate representation and modeling of state dynamics of complex systems. Monitoring schemes allow one to carry out the observation for the current values of parameters and for the actual information on the character of system parameter dynamics. This information is then used to evaluate conditions/situations around system and to predict possible events in the system and consequences following from them, which can be caused by changes in values of parameters. Intelligent simulation environment is proposed by integration of: 1) an integrated database and modeling, 2) rule-based (goal-oriented) behavior and 3) parametric and flexible structures. It is a goal oriented, flexible and integrated approach and produces the optimal solution by referring to integrated models and knowledge- and databases. The properties and modules of the prescribed intelligent simulation environment are: 1) parametric modeling, 2) flexibility, 3) integrated modeling, 4) rule-based module, 5) integrated knowledge- and databases and 6) learning module.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 57

Generally, the information on the problem domain and properties of system is contained in specialized databases; knowledge about parameters and processes is contained in knowledge bases; information about the current values of parameters and on the character of state dynamics of object is contained in monitoring databases. The investigations on the models are provided by the combination of the methods of (1) dynamic knowledge-based expert systems, (2) production expert systems, (3) database processing techniques, (4) monitoring/ diagnostic data analysis, (5) scenario control and modeling. 6.2. Characteristics of Decision Support System A Decision Support System (DSS) is an information system that supports decision-making and system management activities [154-157]. A properly-designed DSS is an interactive software-based system intended to help decision makers in compiling useful information from raw data, documents, personal knowledge, business models, etc., to identify and solve problems and make decisions. A DSS enables the user to make fast, responsive decisions using all the necessary information appropriate to the task at hand. According to Sprague and Carlson [157], a basic DSS framework contains a database and model base, with associated management systems, and a dialog component through which the decision maker interacts. Other features include graphical-based dialog interface (a graphical user interface, GUI), output facilities and report generators, and event logging. Haag et al. [148] describe these three components in more detail. The Data Management Component stores information (which can be further subdivided into that derived from an organization’s traditional data repositories, from external sources, or from the personal insights and experiences of individual users); the Model Management Component handles representations of events, facts, or situations (using various kinds of models, two examples being optimization models and goalseeking models); and the User Interface Management Component is, of course, the component that allows a user to interact with the system. Levin [158] analyzes a number of works and names the following components as essential for a modern DSS: (1) models, which include multi-criteria techniques, problemsolving schemes, data processing and knowledge management; (2) analytical and numerical methods of data pre-processing and identification of problems for the preliminary stages of decision making; (3) human-computer interaction and its organization through graphic interface and others; (4) information support, communication with databases, web-services, etc. According to Power [155], academics and practitioners have discussed building DSS in terms of four major components: (a) the user interface, (b) the database, (c) the modeling and analytical tools, and (d) the DSS architecture and network. The definition of a DSS, based on Levin and Power, in that a DSS is a system to support and improve decision making, represents, in our opinion, an optimal and suitable to our needs background for information DSS requirements. The traditional decision making workflow consists of several standard steps (Fig. (17)). The DSS structure has to satisfy the requirements, imposed by specialists, and characteristics and restrictions of the application domain. The decision making process includes the preparatory period, situations simulation, analysis of influence of control scenarios, the development of decisions and, finally, the decision making itself and its realization. As a rule, characteristics of successful DSS experiences include: assistance in semi-structured decision tasks, support of managerial judgment, useful to non-computer specialists working interactively with the system, exploits both models and databases to generate information, and adapts to the decision-making approach of the user. A DSS does not necessarily look for optimal solutions to complex and/or operational problems, but rather as Ackoff [159] states, a DSS supports “a decision for which adequate models can be constructed but from which optimal solutions cannot be extracted”. The levels of automation and support to the decision maker can vary from high to low. Strong [160] found that high levels of decision automation and high levels of decision support provided a best DSS environment to support decision makers. Other approaches and techniques for successful decision making and analysis have also been proposed [161-165] recently.

58 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

Background information and data about the situation – 1

Stating the general goal and the sub-goals 2

Creating evaluation system for the situation assessment – 3

Analysis of the situation and diagnostic 4

Forecasting of situation dynamics 5

Generating alternatives of situation development – 6

Selecting the main variants of control influence 7

Working out scenarios of situation development – 8

Selecting the optimal scenario 9 Figure 17: The traditional scheme of decision-making.

6.3. Architecture of Intelligent Information System The architecture of information system consists of several independent but logically related to each other subsystems [128, 129]. The subsystem of Direct Planning is intended to establish complex problem points, to cope with a collection of interconnected complex control problems, to construct control scenarios for solving complex problems and to compare them in accordance to the efficiency criteria. The subsystem includes the following components (Fig. (18)): User interface provides interaction of user with the system. The software of user interface serves as a tool that realizes all functions of computer system associated with information exchange with the user. Library of parameters contains blocks of parameters for supporting the continuous process of observing for a number of parameters; the library is extendable and editable. Dynamic Knowledge-based Expert System is a computer realization of formalized expert knowledge about problem and control domains, and it is used in building dynamic models. Builder of canonical model of state dynamics is a specialized module of entering of state diagrams as input information. The state diagrams tool provides clear and precise formalization of states, inherent for one process and not typical for others. It can be used for representation of regularities and typical models of state dynamics. Monitoring databases. Direct planning in control systems assumes a high level of informatization and operative connection with monitoring database. Interpreter of monitoring database. The interpreter of monitoring database and the model of controllable state dynamics are the basic components in automated computer information system. The interpreter of monitoring database operates according to the composition of canonical models of state dynamics specified by the user and generates the description of actual multilevel dynamics of the object. Model of controllable state dynamics is constructed as expert subsystem for qualitative estimation of control scenarios defined by the user.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 59

Library of Parameters

User Interface

Model of Controllable State Dynamics

Builder of Canonical Models of State Dynamics

Interpreter of Monitoring Database

Knowledge-based Expert System

Monitoring Databases

Figure 18: A structure of direct planning subsystem.

Some explanation should be given for the component Dynamic Knowledge-based Expert System. We wish to note that one of the approaches to the synthesis of dynamic models of complex systems is based on the use of the so-called master-systems consisting of canonical templates and expert knowledge-bases. The knowledge-base consisting of declarative and procedural knowledge realizes a conceptual model of complex system. The declarative knowledge contains: Objectives tree of complex system that provides a decomposition of global goal on subgoals and description of relation between them; The architecture and/or structure of complex system; The set of canonical templates; The set of models of canonical templates; Problem domain databases. The information about objectives tree can be represented as the tuple ,

, ,

where is a structure that determines the decomposition of global goal, is the structural identifier for nodes, is a goal assigned to the node, is a rule/law that describes the connection between the neighbor nodes. The canonical template can be realized with the use of the language of system dynamics [47] or state transition diagrams. The canonical template has a certain structure, a set of input, output, and initial values/conditions. Formally the canonical template can be described as , , , , ,

,

where is the structure of the template, is a rule/law of template functioning/behavior, is a set of input parameters, is a set of output parameters, is a set of control symbols, is a set of initial values/conditions, is a set of rules that govern the transformation of template structure, which means adding, modifying, removing links and/or nodes. The canonical template is a separate object having basically information about its components and certain internal structure. But the canonical template model is the object that may contain information not only

60 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

about its components and structure but also about the concrete input and output values and values of initial conditions. Each canonical model is assigned to one of the goals of the objectives tree. The synthesis of dynamic models of complex system is realized by transformation of declarative knowledge about problem domain to the algorithms of system state dynamics with the help of procedural knowledge. The procedural knowledge is realized in knowledge-bases in the form of inference rules. They formalize the process of dynamic models synthesis. The inference rules provide the mapping of structure of conceptual model into the structure of dynamic models. The knowledge-base can contain different groups of inference procedures, depending on the purposes of the investigation. For example, they can be of the following types: correspondence rules that determine for each canonical model the goal problems it solves; the inference rules that define informational relations between the templates in canonical model, etc. The representation of conceptual model of complex system in the form of knowledge-bases provides the autonomous usage of expert knowledge upon synthesizing the dynamic models. The above model is extended by adding to the canonical templates a set of input control symbols, thus providing the dynamic models with the mechanism of system control. So, the Dynamic Knowledge-based Expert System is constructed in the form of master-system, it dynamically adjusts to the specific problem domain requested by the user through the Interface, provides corresponding templates for synthesis of models, connects with the appropriate database, and provides the relevant to the selected problems knowledge-base. The subsystem of Direct Planning realizes the two stage process of simulation and control (Fig. (19)). The first stage is the stage of retrospective analysis consisting in the construction of predictive model of inertial state dynamics, which is the model of dynamics of object when no control actions are undertaken. The retrospective analysis provides the means for event prediction. When predicting events, the parameters of system are continuously measured. If there was some event in a system and for some time before the event a parameter has sharply changed, or there was a gradual change of values of parameter up to some critical, then such anomaly is related with this event. The dependencies of such kind confirmed repeatedly, i.e. becoming stable, are used for estimation and prediction of possible future events in the system. Actually, knowledge and experiences obtained in the past and expert knowledge are used. The stage of retrospective analysis provides user with the tools of selection of objects, study of chosen parameters, and construction of state diagram, which interprets the monitoring data. This implements the diagnostic analysis of objects’ state dynamics. By analysis, experimentation, and selection of different sets of parameters, the diagrams that most expressively depict “negative” (positive) trends are found. These diagrams formally represent the current control problems and answer the question “what will be if no control actions are performed”. The results of retrospective analysis help put forward the goals and control problems and help one to form possible alternatives of controllable state dynamics for the perspective period. The second stage consists in construction of the model of controllable state dynamics which includes statement of control problem, alternative control scenarios, expert estimation and selection of control scenarios of object’s state dynamics. The stage includes the construction of the model of controllable state dynamics, analysis of controllable processes of objects’ state dynamics, and obtaining the answer to the question ”what control actions should be undertaken to achieve the required goals”. At this stage, an initial state and expected final state are described and the space of intermediate states is constructed. Then, the conceptual model of control scenario in the form of States Generator is defined. The subsystem of Multilevel Dynamics Simulation includes the components (Fig. (20)): System of canonical models of state dynamics of hierarchical object provides the necessary tools for construction of canonical state dynamics models of simulated objects.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 61

Scheme of coordination of canonical models is based on the rules of composition of state diagrams. Description of actual state dynamics of hierarchical object uses the monitoring databases that store the information on the actual dynamics of parameters. Monitoring databases contain the current information about the dynamics of parameters, which is the result of monitoring or diagnosing of the object. Partial/incomplete canonical model of state dynamics. The model of controllable state dynamics is used for checking a hypothesis about the efficiency of scenario being estimated. The scenario estimation criterion is given in the form of “partial” or “incomplete” state dynamics diagram determining support states that should be reached with the specified restrictions on time and resources. Stage 1. Retrospective analysis Predictive Model of Inertial Dynamics

Stage 2. Direct Model of Controllable State Dynamics Statement of Control Problem

Alternative Control Scenarios

Expert Estimation and Selection of Control Scenarios

Figure 19: Generalized scheme of the process of direct planning.

The special case of “partial/incomplete” state dynamics diagram is the pair of states: initial state and desirable final state. In this case, the expert subsystem should: either confirm a hypothesis that the model of state dynamics, controlled on the basis of the scenario, meets the given criteria or requirements, and supplement the input diagram with the specifying intermediate states, or refute the hypothesis and generate computer prediction in the form of alternative state dynamics diagram. Scenarios of state dynamics/Conceptual model of scenarios - States Generator. The Scenarios of State Dynamics serves as an inference system. It is considered as generator of consecutive states of object under investigation. The rules of States Generator are represented in the format of tree-like decomposition of global goal on the sub-goals; to each terminal node an elementary rule is assigned. The rules are represented in the IF-THEN format (Fig. (21)): ,

,

,

,

,

where is the control action needed to be undertaken for an object to be steered from the state to the state with the use of resources and in time , while not admitting the backstep to the previous state .

62 Artificial Intelligence Resources in Control and Automation Engineering

Canonical Models of State Dynamics

Partial/Incomplete Canonical Models

Coordination of Canonical Models

Scenarios of State Dynamics

Armen Bagdasaryan

Conceptual Model of Scenarios States Generator

Actual State Dynamics

Monitoring Database

Figure 20: Structure of Multilevel Dynamics Simulation Subsystem.

The construction of scenarios is divided into several steps: (1) analysis of initial state of object and of possible trends of state’s changes, (2) exploration of a spectrum of possible future states of the object, (3) formulation of hypotheses about tendencies in transitions from those states to the subsequent ones, (4) analysis and formulation of desired end results - final state of the object. ,

Figure 21: The format of elementary IF-THEN rule.

The subsystem of Simulation Process Control includes two modules (Fig. (22)), Executive Module and Control Module: Executive Module consists of database of objects’ control models, database of state dynamics simulation models, database of analyzable control actions, simulation system of controlling scenarios, and database of complex control actions. Simulation system of controlling scenarios that uses the database of objects’ control models, the database of state dynamics simulation models, and the database of analyzable control actions provides a tool for formal representation of goals, control problems and state dynamics, time and resource characteristics. The simulation system of controlling scenarios enables user to analyze global efficiency of control actions directed on the achievement of goals at different levels of hierarchy. The system allows user to not just compare separate control actions but also to formally synthesize complex control actions (control strategies) for hierarchical system as a whole, and then provides their further comparison. The functional sub-modules of Executive Module reproduce the stages of control actions selection, including the stage of automatic synthesis and initiation of problem domain and control models. Control Module realizes the functions of expert estimation and comparison of control action sets, knowledge-base support, and decision making. The simulation process control subsystem provides the tools of synthesis, simulation, and analysis of control scenarios.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 63

Control Module

Simulation System of Control Scenarios

Database of Control Models

Database of State Dynamics Simulation Models

Database of Integrated Control Actions (control strategies)

Database of Control Actions

Figure 22: Structure of Simulation Process Control Subsystem.

The rules of state transformations and the scheme of construction of control scenarios: (1) allow one to easily realize iterative process of creation and modification of control scenarios, (2) admit the efficient realization by means of executive procedure, (3) possess the sufficient expressiveness of specification of control processes. The State Generator enables user: (1) to study effects of integrated and multi-aspect control regarding different objects of complex system, (2) to divide the control process into stages, (3) to perform decompositional schemes of prediction, in which each subsequent model is an integrated or detailed elaboration of the previous, (4) to construct and analyze the interconnected aggregated and detailed models of state dynamics of the system. The flexibility and comprehensiveness of the architecture of information system provide the implementation of the following functions: Identification and registration of the information about the events and the current situation around the complex system. Information and expert knowledge storage, maintaining and management; Description of system parameters and those of monitoring and/or diagnosing; Description of control actions; Description of information-mathematical model; Description of the structure of state space; Description of the structure of control and problem domains and informational levels of system dynamic models. The overall architecture of computer information system for simulation and decision support is presented on Fig. (23). The general scheme of the process of system simulation analysis and decision making based on the model of HSGD with use of the methodology of hierarchical system scenario control and control strategies consists of five interconnected levels (Fig. (24)).

64 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

Direct Planning Subsystem

Multilevel Dynamics Simulation Subsystem

Decision Support Module

Simulation Process Control Subsystem

Figure 23: General architecture of information system.

The computer information system allows user to: Define global goal of complex system and to represent a decomposition on the subgoals, and to describe relations between them; Synthesize dynamic models of complex system; Determine efficient control actions in solving control problems and achieving system goals; Realize the iterative process of creation and modification of control scenarios; Study multi-aspect control of different subsystems and analyze integrative behavior of complex dynamic system as a whole; Construct and analyze different control scenarios, study and compare them for efficiency; Study behavior of system under different initial conditions and to study state dynamics of system for different groups of parameters; Get a holistic view on a complex system and its behavior; Make integrated and well-founded decisions. The proposed architecture provides the most complete tools of simulation and decision support in relation to the problems and goals that were outlined in the beginning of this section. This information system is quite suitable for applications in weakly-formalized and ill-structured problem domains. It enables one to: Involve modelers and decision-makers in the process of formalization of criteria for scenarios evaluating; Provide users with the ability to put the current tasks of problem analysis in a language close to the professional; Provide the possibility of considering the problem with various degrees of specification, using operational data of the level requested; Provide users with the possibility to conduct long-term computer archives of statistical and monitoring data of specific applied models of systems;

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 65

User

Report Documents

DM priorities and preferences

(simulation results analysis, decision making, reports)

DM/modeler simulation environment

(control scenario simulations, assessment, efficiency analysis)

DM/expert preferences and system characteristics

DM/expert/ modeler experience Expert knowledge

Decision Making

Simulation

Model Analysis and Control Strategy Development (interaction topology, inter-level compositions, scenarios)

Model Building (determining states, dependencies, development diagrams)

Information Fusion (data and information gathering, aggregation)

Different information and data sources Figure 24: The general scheme of system simulation analysis and decision making.

Accumulate knowledge about the problem and control domain, build and use the information system, open to correction and supplementation; Use expert knowledge about the quantitative and qualitative assessments of interrelationships between dynamic system parameters. The system enables to conduct the analysis of significance of control scenarios in relation to the complex problem solving and provides the ability to integrate it with the actual process of planning and control. 7. CONCLUSIONS To adequately model and analyze processes in complex real-world systems, we need the holistic and integrative methods that combine in them both top-down and bottom-up approaches. It is often not necessary to cope with the all available system parameters and functions in order to get a good approximation of modeled system. Even simpler models lead to very complex behaviors [166] and allow us to obtain sufficiently detailed and comprehensive understanding of the processes in the system. Although it is true for physical and biological systems, for many other kinds of systems, like social, cognitive, engineering, business-process, some systems of artificial intelligence, and others, we have to take into account as many system interrelations, processes, dependencies as it possible. This can only be done by

66 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

first using methods of systems analysis, and then one needs techniques that have been developed in the field of systems theory and control sciences. In this chapter we have discussed the problems of modeling, control and decision support in complex systems from the viewpoint of systems theoretic approaches and methods. We considered the basic characteristics of complex systems and analyzed system theoretic approach to complex systems study. We have also considered the main frameworks and paradigms of modern system modeling and control, and analyzed the most widely used methods for mathematical modeling and simulation of complex dynamic systems. We have proposed the general dynamic modeling technique for complex hierarchical systems consisting of many objects functioning in control loop. The generalized algorithmic schemes for analysis of the proposed models are also presented. The proposed technique uses the object-oriented multi-agent paradigm, and is based on the information-mathematical models and described in terms of the hierarchical state transition diagrams. The method allows both qualitative and quantitative analysis of system behavior and state dynamics through hierarchical scenario calculus. For evaluation of different scenarios the efficiency criteria related to the control strategies are presented. We have also proposed a general structure of computer information system for simulation and analysis of dynamic processes, control strategies and development scenarios in complex systems, which can be used in decision making process. The technique presented can also be used as a technology for design and building of information systems for simulation analysis of development strategies and control scenarios of complex objects, and it has been applied in several information systems and decision support systems. The models proposed are especially powerful in information-intensive environments. The information can be simultaneously aggregated in several directions: by hierarchical structure of processes and states embedding, by parallel representation of dynamical characteristics of several processes within one state, and by dividing the observation time interval in accordance to the events associated with the state changes in dynamics of system. The proposed models and technique are sufficiently universal and at the same time they are problem-oriented. The technique can be equally used for various kinds of systems such as technical, engineering, organizational, socio-economic, strategic planning, long-term forecasting systems, and decision support systems. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

Y. Bar-Yam, Making things work: Solving complex problems in a complex world. Cambridge, MA: Knowledge Press, 2004. Y. Bar-Yam, Dynamics of complex systems. Reading, MA: Addison-Wesley, 1997. M. Mesarovic, D. Macko, and Y. Takahara, Theory of hierarchical multilevel systems. New York: Academic Press, 1970. M.D. Mesarovic, Theory of hierarchical multilevel systems. In: Mathematics in Science and Engineering. New York: Academic Press, 1970. M.L. Estep, Self-organizing natural intelligence: Issues of knowing, meaning, and complexity. Springer-Verlag, 2006. H.H. Pattee, Ed., Hierarchy theory: The challenge of complex systems. New York: George Braziller, 1973. S. Salthe, Evolving hierarchical systems: Their structure and representation. New York: Columbia University Press, 1985. V. Ahl and T.F.H. Allen, Hierarchy theory: a vision, vocabulary, and epistemology. New York: Columbia University Press, 1996. R. Badii and A. Politi, Complexity: hierarchical structures and scaling in physics. Cambridge: Cambridge University Press, 1997. B. Zeigler, H. Praehofer, and T. Kim, Theory of modeling and simulation. Academic Press, 1999. P. A. Fishwick, Handbook of dynamic system modeling. Chapman & Hall/CRC, 2007.

Systems Theoretic Techniques for Modeling

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43]

Artificial Intelligence Resources in Control and Automation Engineering 67

V. Latora and M. Marchiori, The architecture of complex systems. Santa Fe Institute for Studies of Complexity, Oxford University Press, 2003. H. A. Simon, Sciences of the Artificial. Cambridge, MA: MIT Press, 1969. N.A. Avouris and L. Gasser, Eds., Distributed artificial intelligence: Theory and praxis. Kluwer Academic Publishers, 1992. T.I. Oren and B.P. Zeigler, “Artificial intelligence in modeling and simulation: Direction to explore”, Simulation, vol. 50, pp. 131-134, 1988. D. Norman and M. Kuras, “Engineering Complex Systems”, in D. Braha, A. Minai, and Y. Bar-Yam, Eds., Complex Engineered Systems: Science Meets Technology, Springer, 2006, pp. 206-245. B. Blanchard and W. Fabrycky, Systems engineering and analysis. Prentice-Hall, 3rd ed., 1998. E. Laszlo, The systems view of the world. New York: George Braziller, 1972. M. Mesarovic and Y. Takahara, General systems theory: Mathematical foundations. New York: Academic Press, 1975. L. von Bertalanffy, General system theory. New York: George Braziller, 1968. S.A. Levin, "Complex adaptive systems: Exploring the known, the unknown and the unknowable”, Bulletin of the American Mathematical Society, vol. 40, pp. 3-19, 2003. M. Gell-Mann, “Complex adaptive systems”, in G. Cowan, D. Pines, D. Meltzer, Eds., Complexity: Metaphors, Models and Reality. Addison-Wesley, 1994, pp. 17-45. R. Rosen, “Complexity and system descriptions”, in W.E. Harnett, Ed., Systems: Approaches, Theories, Applications. Dordrecht, Holland: D. Reidel, 1977, pp. 169-175. R.J. Nelson, “Structure of Complex Systems”, Philosophy of Science Association, vol. 2, pp. 523-542, 1976. J.M. Ottino, “Engineering complex systems”, Nature, vol. 427, pp. 399-399, 2004. D.W. Oliver, T.R. Kelliher, and J.G. Keegan Jr., Engineering complex systems with models and objects. McGraw Hill, 1997. Z. Bubnicki, Modern control theory. Springer- Verlag, 2005. J.L. Casti, “On system complexity: Identification, measurement and management”, in J. Casti and A. Karlquist, Eds., Complexity Language and Life: Mathematical Approaches. Berlin: Springer, 1986, pp. 146-173. M. Heimdahl and N. Leveson, “Completeness and consistency in hierarchical state-based requirements”, IEEE Trans. Software Engineering, vol. 22, pp. 363-376, 1996. G. Pappas, G. Lafferriere, and S. Sastry, “Hierarchically consistent control systems”, IEEE Trans. Automatic Control, vol. 45, pp. 1144-1160, 2000. P. Hubbard and P.E. Caines, “Dynamical consistency in hierarchical supervisory control”, IEEE Transactions on Automatic Control, vol. 47(1), pp. 37-52, 2002. H. Garcia, “A Hierarchical platform for implementing hybrid systems in process control”, Control Engineering Practice, vol. 5(6), 1997. P. Albertos, R. Strietzel, and N. Mart, Control engineering solutions: A practical approach. IEEE Computer Society Press, 1997. A. Meystel and J.S. Albus, Intelligent systems - architectures, design and control. John Wiley & Sons, 2002. I. Dumitrache, “From model-based strategies to intelligent control systems”, WSEAS Transactions on Systems and Control, vol. 3(6), pp. 569-575, 2008. J.C. Willems, “Paradigms and puzzles in the theory of dynamic systems”, IEEE Trans. Automatic Control, vol. 36, pp. 258-294, 1991. M. Law and W. D. Kelton. Simulation modeling and analysis. Tata McGraw-Hill Publishing Company Ltd., 3rd ed., 2003. N.P. Buslenko, Complex systems modeling. Moscow: Nauka, 1978. (in russian). V.V. Rykov. “Aggregative systems: their modeling and simulation”, in International conference on Simulation, Gaming, Training and Business Process Reengineering in Operations, Riga, 1996, pp. 38-39. V.V. Rykov, Controllable aggregative systems and their simulations. IMACS Trans. Comp. Sci., Amsterdam: North-Holland, 1985. C. G. Cassandras and S. Lafortune, Introduction to discrete event systems. Norwell, MA: Kluwer, 1999. J. Banks, J. S. Carson, B. L. Nelson, and D. M. Nicol III, Discrete-event system simulation 3rd ed., New Jersey: Prentice-Hall International Series in Industrial and Systems Engineering, 2001. K. Wong and W. Wonham, “Hierarchical control of discrete-event systems”, Discrete Event Dynamical Systems, vol. 6, pp. 241-273, 1995.

68 Artificial Intelligence Resources in Control and Automation Engineering

[44] [45] [46] [47] [48]

[49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74]

[75]

Armen Bagdasaryan

Y.-L. Chen and F. Lin, “Safety control of discrete event systems using finite state machines with parameters”, in Proceedings of the American Control Conference, 2001, pp. 975-981. A.E.C. da Cunha, J.E.R. Cury, and B.H. Krogh, “An assume guarantee reasoning for hierarchical coordination of discrete event systems”, in Workshop on Discrete Event Systems, 2002. R.de Souza, Zhao Zhen Ying, “Intelligent Control Paradigm for Dynamic Discrete Event System Simulation”, Discrete Event Dynamic Systems, vol. 9, pp. 65-73, 1999. J. Forrester, Industrial Dynamics. Portland: Productivity Press, 1961. Bin Hu, DeBin Zhang, CaiXue Ma, Yong Jiang, XiongYing Hu, and JinLong Zhang, “Modeling and simulation of corporate lifecycle using system dynamics”, Simulation Modeling Practice and Theory, vol. 15, pp. 12591267, 2007. M. Ozbayrak, T.C. Papadopoulou, and M. Akgun, “System dynamics modeling of a manufacturing supply chain system”, Simulation Modeling Practice and Theory, vol. 15, pp. 1338-1355, 2007. C. Eden, “Cognitive mapping and problem structuring for system dynamics model building”, System Dynamics Review, vol. 10(2-3), pp. 257-276, 1994. S. Wolfram, Theory and application of cellular automata. World Scientific, 1986. A. Wuensche and M. J. Lesser, The global dynamics of cellular automata. Santa Fe Institute Studies in the Science of Complexity, Addison Wesley, 1992. P. Pal Chaudhuri, D. R. Chowdhury, S. Nandi, and S. Chatterjee, Additive cellular automata - Theory and applications, vol. 1. IEEE Computer Society Press, 1997. S. Wolfram, A new kind of science. Wolfram Media, 2002. L. Gray, “A mathematician looks at Wolfram’s New Kind of Science, Notices of the American Mathematical Society, vol. 50(2), pp. 200-211. J. von Neumann, The theory of self-reproducing automata. Urbana: University of Illinois Press, 1966. A. Adamatzky, “Hierarchy of fuzzy cellular automata”, Fuzzy Sets and Systems, vol. 62, pp. 167-174, 1994. B. Chopard and M. Droz, Cellular automata modeling of physical systems. Cambridge University Press, 1998. R. Hegselmann and A. Flache, “Understanding complex social dynamics: A plea for cellular automata based modeling”, Journal of Artificial Societies and Social Simulation, vol. 1(3), June 1998. W. Li, N. H. Packard, and C. G. Langton, “Transition phenomena in cellular automata rule space”, Physica D, vol. 45, pp.7-94, 1990. T. Toffoli and N. Margolus, Cellular automata machines. The MIT Press, 1987. S. Wolfram, “Computation theory of cellular automata”, Commun. Math. Phys., vol. 96, pp. 15-57, 1984. S. Wolfram, “Universality and complexity in cellular automata”, Physica D, vol. 10, pp. 1-35, 1984. S. A. Billings and Y. Yang, “Identification of probabilistic cellular automata”, IEEE Trans. System, Man and Cybernetics, Part B, vol. 33(2), pp.1-12, 2002. O. Martin, A. M. Odlyzko, and S. Wolfram, “Algebraic properties of cellular automata”, Commun. Math. Phys., vol. 93, pp. 219-258, 1984. G. Grinstein, C. Jayaprakash, and Y. He, “Statistical mechanics of probabilistic cellular automata”, Phys. Rev. Lett., vol. 55, pp. 2527-2530, 1985. H. Gutowitz, “A hierarchical classification of CA”, Physica D, vol. 45, pp. 136, 1990. G. Cattaneo, P. Flocchini, G. Mauri, C. Q. Vogliotti, and N. Santoro, “Cellular automata in fuzzy background”, Physica D, vol. 105(1-3), pp. 105-120, June 1997. P. Flocchini, F. Geurts, A. Mingarelli, and N. Santoro, “Convergence and aperiodicity in fuzzy cellular automata: Revisiting rule 90”, Physica D, vol. 142(1-2), pp. 20-28, August 2000. B. Kosko, Neural networks and fuzzy systems - A dynamical systems approach to machine intelligence. New Jersey: Prentice Hall, 1992. S.J. Russell and P. Norvig, Artificial intelligence: A modern approach. New Jersey: Prentice Hall, 1995. J.J. Hopfield, “Neural networks and physical system with emergent collective computational abilities”, Proceedings of National Academy of Sciences, vol. 79, pp. 2554-2558, 1982. H. Ying, Fuzzy control and modeling: Analytical foundations and applications. Piscataway: IEEE Press, 2000. O. Castillo and P. Melin, “A new fuzzy inference system for reasoning with multiple differential equations for modeling complex dynamical systems”, in Proceedings of CIMCA’99, IOS Press, Vienna, Austria, pp. 224-229, 1999. R.R. Yager, “On the construction of hierarchical fuzzy systems models”, IEEE Trans. on Systems, Man and Cybernetics, vol. 28(1), pp. 55-66, 1998.

Systems Theoretic Techniques for Modeling

[76] [77] [78] [79] [80] [81] [82] [83] [84]

[85] [86] [87] [88]

[89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103]

Artificial Intelligence Resources in Control and Automation Engineering 69

R. Axelrod, Structure of decision: the cognitive maps of political elites. New Jersey: Princeton University Press, 1976. B. Kosko, “Fuzzy cognitive map”, Int. J. Man-Machine Studies, vol. 24, pp. 65-75, 1986. R. Taber, “Knowledge processing with fuzzy cognitive maps”, Expert Systems with Applications, vol. 2(1), pp. 83-87, 1991. W.R. Zhang and S. S. Chen, “A logical architecture for cognitive maps”, in Proceedings of the IEEE International Conference on Neural Networks, 1988. W.R. Zhang, S. S. Chen, and J.C. Besdek, “Pool2: a generic system for cognitive map development and decision analysis”, IEEE Transactions on Systems, Man, and Cybernetics, vol. 19(1), pp. 31-39, 1989. W.R. Zhang, S.S. Chen, W. Wang, and R.S. King, “A cognitive map based approach to the coordination of distributed cooperative agents”, IEEE Trans. System, Man, and Cybernetics, vol. 22(1), pp.103-114, 1992. M.A. Styblinski and B.D. Meyer, “Signal flow graphs vs fuzzy cognitive maps in application to qualitative circuit analysis”, International Journal of Man-Machine Studies, vol. 35, pp. 175-186, 1991. J.A. Dickerson and B. Kosko, “Fuzzy virtual worlds”, AI Expert, pp. 25-31, July 1994. K. Gotoh, J. Murakami, T. Yamaguchi and Y. Yamanaka, “Application of fuzzy cognitive maps to supporting for plant control”, in Proceedings of SICE Joint Symposium of 15th Systems Symposium and 10th Knowledge Engineering Symposium, pp.99-104, 1989. C. Stylios and P. Groumpos, “Application of fuzzy cognitive maps in large manufacturing systems”, in Proceedings of the IFAC LSS’98, Rio, Patras, Greece, vol. 1, pp. 531-536, 1998. C.E. Pelaez and J. B. Bowles, “Using fuzzy cognitive maps as a system model for failure models and effects analysis”, Information Sciences, vol. 88, pp. 177-199, 1996. C.E Pelaez and J. B. Bowles, “Applying fuzzy cognitive maps knowledge-representation to failure modes effects analysis”, in Proceedings of Annual Reliability and Maintainability Symposium, pp. 450-455, 1995. C.D. Stylios, V. C. Georgopoulos and P. P. Groumpos, “Applying fuzzy cognitive maps in supervisory control systems”, in Proceedings of the European Symposium on Intelligent Techniques, Bari, Italy, March 1997 , pp. 131-135. L. Chun-Mei, “Using fuzzy cognitive map for system control, WSEAS Transactions on Systems, vol. 7(12), pp. 1504-1515, 2008. E. Koulouriotis, I. Diakoulakis, D. Emiris, et al., “Efficiently modeling and controlling complex dynamic systems using evolutionary fuzzy cognitive maps, Int. J. Computational Cognition, vol. 1(2), pp. 41-65, 2003. J.R. Anderson, C.F. Boyle, A.T. Corbett, and M.W. Lewis, “Cognitive modeling and intelligent tutoring”, Artificial Intelligence, vol. 42, pp. 7-49. T. Kohonen, Self-organizing maps. Springer-Verlag, 2001. M. Wooldridge, An introduction to multi-agent systems. Chichester: John Wiley and Sons, 2002. G. Weiss, Multiagent systems: A modern approach to distributed artificial intelligence. Cambridge: The MIT Press, 2000. M. Wooldridge and N. R. Jennings, “Intelligent agents: theory and practice, The Knowledge Engineering Review, vol. 10(2), pp. 115-152, 1995. J.M. Epstein and R.L. Axtell, Growing artificial societies: Social science from the bottom up. Cambridge: MIT Press, 1996. R. Axelrod, The complexity of cooperation: Agent-based models of competition and collaboration. Princeton: Princeton University Press, 1997. C. Iglesias, M. Garijo Ayestaran, and J. Gonzalez, “A survey of agent-oriented methodologies”, in Intelligent Agents V. Springer-Verlag, 1999. L. Padgham and M. Winikoff, Developing intelligent agent systems: A practical guide. Chichester: John Wiley and Sons, 2004. L. SeongKee, C. SungChan, L. HyengHo, and Y. ChanGon, “An agent-based system design for complex systems”, WSEAS Transactions on Systems, vol. 5(9), pp. 2140-2146, 2006. S. Lee, S. Cho, et al., “A Layered agent oriented engineering approach for building complex systems, in Proceedings of the WSEAS International Conference on Systems, Athens, Greece, 2006, pp. 681-686. J. Cuena and S. Ossowski, “Distributed models for decision support”, in Weiss, Ed., Multi-Agent Systems - A Modern Approach to DAI. MIT Press, 1999. M.V. Sokolova and A. Fern andez-Caballero, “Agent-based decision making through intelligent knowledge discovery”, in I. Lovrek, R.J. Howlett, L.C. Jain, Eds., KES 2008, Part III., LNCS (LNAI), vol. 5179, Springer, Heidelberg, 2008, pp. 709-715.

70 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

[104] B. Frankovi and V. Oravec, “Design of the agent-based intelligent control system”, Acta Polytechnica Hungarica, vol. 2(2), pp 39-52, 2005. [105] F. Zambonelli, N. Jennings, and M. Wooldridge, “Organizational abstractions for the analysis and design of multi-agent systems”, in Ciancarini and Wooldridge, Eds., Agent-Oriented Software Engineering, SpringerVerlag, 2000, pp. 235-252. [106] D. Xu, R. Volz, T. Ioerger, and J. Yen, “Modeling and verifying multi-agent behaviors using predicate/transition nets”, in Proceedings of the International Conference on Software Engineering and Knowledge Engineering, 2002, pp. 193-200, ACM Press. [107] H. L. Zhang, C. H. C. Leung, and G. K. Raikundalia, “Classification of intelligent agent network topologies and a new topological description language for agent networks,” in Proceedings of the 4th IFIP International Federation for Information Processing, vol. 228, Springer, 2006, pp. 21-31. [108] C. Castelfranchi, “Founding agent’s autonomy on dependence theory”, in Proceedings of the European Conference on Artificial Intelligence, Berlin, Germany, 2000, pp. 353-357. [109] S.C. Bankes, “Tools and techniques for developing policies for complex and uncertain systems”, Proceedings of National Academy of Sciences, vol. 99, suppl. 3, pp. 7263-7266, 2002. [110] M. Schneider, E. Schneider, A. Kandel, G. Chew, “Automatic construction of FCMs”, Fuzzy Sets and Systems, vol.93, pp.161-172, 1998. [111] D. Harel, “Statecharts: A visual formalism for complex systems”, Science of Computer Programming, vol. 45, pp. 231-274, 1987. [112] J. Ryan and C. Heavey, “Development of a process modeling tool for simulation”, Journal of Simulation, vol. 1, pp. 203-213, 2007. [113] N. Boccara, Modeling complex systems. Graduate Texts in Contemporary Physics, New York: Springer, 2004. [114] T. Dean and M. Wellman, Planning and control. Morgan Kaufmann, 1991. [115] M. Klein and L. Methlie, Knowledge-based decision support systems. John Wiley & Sons, 1995. [116] O. Balci and W. F. Ormsby, “Conceptual modeling for designing large-scale simulations”, Journal of Simulation, vol. 1, pp. 175-186, 2007. [117] L.A.N. Amaral and B. Uzzi, “Complex systems - A new paradigm for the integrative study of management, physical, and technological systems, Management Science, vol. 53(7), pp. 1033-1035, 2007. [118] K. van der Heijden, Scenarios: The art of strategic conversation. New York: John Wiley and Sons, 1996. [119] A.G. Bagdasaryan, “System theoretic viewpoint on modeling of complex systems: Design, synthesis, simulation, and control”, in A. Zaharim, N. Mastorakis, and I. Gonos, Eds., Recent Advances in Computational Intelligence, Man-Machine Systems and Cybernetics, WSEAS Press, Stevens Point, 2008, pp. 248-253. [120] Armen Bagdasaryan, “Discrete dynamic simulation models and technique for complex control systems”, Simulation Modeling Practice and Theory, vol. 19(4), pp. 1061-1087, 2011. [121] A.G. Bagdasaryan, Discrete modeling and analysis of complex dynamic systems in control mode. Moscow: Institute for Control Sciences RAS, 2005. [122] A.G. Bagdasaryan, “Mathematical and computer tool of discrete dynamic modeling and analysis of complex systems in control loop”, International Journal of Mathematical Models and Methods in Applied Sciences, vol. 2(1), pp. 82-95, 2008. [123] A.G. Bagdasaryan, “Mathematical tool of discrete dynamic modeling of complex systems in control loop”, in C. Long, S.H. Sohrab, G. Bognar, and L. Perlovsky, Eds., Recent Advances in Applied Mathematics, Mathematics and Computers in Science and Engineering: A Series of Reference Books and Textbooks, WSEAS Press, Stevens Point, March 2008, pp. 136-142. [124] R.C. Thomas, “Qualitative models of complex systems”, in Wharton Workshop on Complexity and Management, April 1999. [125] A.G. Bagdasaryan, “System approach to synthesis, modeling and control of complex dynamical systems”, WSEAS Trans. Systems and Control, vol. 4(2), pp. 77-87, 2009. [126] A.G. Bagdasaryan and T.-h. Kim, “Dynamic simulation and synthesis technique for complex control systems”, in D. Slesak, T.-h. Kim, A. Stoica, and Byeong-Ho Kim, Eds., Control and Automation, LNCS-CCIS, vol. 65, Springer-Verlag, Berlin-Heidelberg, 2009, pp. 15-27. [127] H. Chen, Y. Zhu, K. Hu, X. He, “Hierarchical swarm model: A new approach to optimization”, Discrete Dynamics in Nature and Society, vol. 2010, Article ID 379649, 30pp. [128] A.G. Bagdasaryan, “A model of automated information system for solving control problems of large-scale systems”, Control Sciences, no. 6, pp. 65-68, 2005.

Systems Theoretic Techniques for Modeling

Artificial Intelligence Resources in Control and Automation Engineering 71

[129] A.G. Bagdasaryan, “A general structure of information expert system for simulation and analysis of complex hierarchical systems in control loop”, Control of Large-Scale Systems, vol. 21, pp. 58-70, 2008. [130] G.S. Cumming and J. Collier, “Change and identity in complex systems”, Ecology and Society, vol. 10(1), pp. 29-41, 2005. [131] S. Wilson and C. Boyd, “Structured assessment of complex systems”. ACPL-REPORT-12-2006-J101, April 2008, Aerospace Concepts Pty Ltd. [132] J. Keppens and Q. Shen, “On compositional modeling”, Knowledge Engineering Review, vol. 16, pp. 157-200, 2001. [133] C.A. Knoblock, “Building a planner for information gathering: A report from the trenches”, in Proceedings of the Third International Conference on Artificial Intelligence Planning Systems’AIPS96, Edinburgh, Scotland, 1996. [134] H. Pattee, “Dynamic and linguistic models of complex systems”, International Journal of General Systems, vol. 3, pp. 259-266, 1997. [135] F. Bergenti and A. Ricci, “Three approaches to the coordination of multiagent systems”, in Proceedings of the 2002 ACM Symposium on Applied Computing, 2002, pp. 367-372. [136] J.J. Bryson, “Intelligence by design: Principles of modularity and coordination for engineering complex adaptive agents”, Ph.D. Thesis, MIT, USA, 2001. [137] R. Axelrod, The evolution of cooperation. Basic Books, 1984. [138] N. Busi, P. Ciancarini, R. Gorrieri, and G. Zavattaro, “Coordination models: A guided tour”, in A. Omicini, F. Zambonelli, M. Klusch, and R. Tolksdorf, Eds., Coordination o f Internet Agents: Models, Technologies, and Applications, 2001, pages 6-24. [139] F. Schweitzer, J. Zimmermann, and H. Muhlenbein, “Coordination of decisions in a spatial agent model”, Physica A, vol. 303 (1-2), pp. 189-216, 2002. [140] E. Elliott and L.D. Kiel, “Exploring cooperation and competition using agent-based modeling”, Proceedings of National Academy of Sciences, vol. 99, pp. 7193-7194, 2002. [141] F. Atay and J. Jost, “On the emergence of complex systems on the basis of the coordination of complex behavior of their elements”, Tech. Rep. 04-02-005, Santa Fe Institute for Studies of Complexity, Santa Fe, NM, USA, 2003, http://www.santafe.edu/media/workingpapers/04-02-005.pdf. [142] F. Zambonelli, N.R. Jennings, and M.J. Wooldridge, “Organizational rules as an abstraction for the analysis and design of multiagent systems”, International Journal of Software Engineering and Knowledge Engineering, vol. 11(4), pp. 303-328, 2001. [143] K.M. Carley, “Computational organizational science and organizational engineering”, Simulation Modeling Practice and Theory, vol. 10, pp. 253- 269, 2002. [144] T. Malone and K. Crowston, “The Interdisciplinary study of coordination”, ACM Computing Surveys, vol. 26(1), pp. 87-119, 1994. [145] F. von Martial, Co-coordinating plans of autonomous agents. Springer-Verlag, 1992. [146] S. Ossowski, Coordination in artificial agent societies. Social structure and its implications for autonomous problem-solving agents. Springer-Verlag, 1999. [147] F. Kuhl, R. Wetherly, and J. Dahmann, Creating computer simulation systems: An introduction to the high level architecture. Prentice Hall, 1999. [148] S. Haag, M. Cummings, D. McCubbrey, Management information systems for the information age. New York: McGraw-Hill, 2003. [149] M.A. Azadeh, “Design of an intelligent simulation environment for manufacturing systems”, in Proceedings of the Third International ICSC Congress on World Manufacturing , Symposium on Manufacturing Systems (ISMS'2001), Center for Integrated Manufacturing Studies, Rochester, New York, September 2001. [150] M. Rao, T.S. Jiang and J.P. Tsai, “Integrated intelligent simulation environment”, Simulation, vol. 54, pp. 291295, 1990. [151] S. Benjaafar, “Intelligent simulation for flexible manufacturing systems: An integrated approach”, Computers and Industrial Engineering, vol. 22, pp. 297-311, 1992. [152] Sakthivel and Agarwal, “Knowledge-based model construction for simulating information systems”, Simulation, vol. 59, pp. 223-236, 1992. [153] W.M. Sztrimbely and P.J. Weymouth, “Dynamic process plant simulation and scheduling: An expert system approach”, Simulation, vol. 56, pp. 175-178, 1991. [154] S.Y. Xu, Z. P. Jiang, et al., “Control-theoretic results on dynamic decision making”, WSEAS Transactions on Systems and Control, vol. 3(6), pp. 576-584, 2008.

72 Artificial Intelligence Resources in Control and Automation Engineering

Armen Bagdasaryan

[155] D.J. Power, Decision support systems: Concepts and resources for managers. Westport: Quorum Books, 2002. [156] A.A.B. Pritsker, Decision support systems for engineers and scientists. London: Intl. Computer Graphics User Show, 1985. [157] R.H. Sprague and E.D. Carlson, Building effective decision support systems. Prentice-Hall, Englewood Cliffs, 1982. [158] M.S. Levin, Composite systems decisions. Springer, 2006. [159] R.L. Ackoff, “Management mis-information systems”, Management Science, vol. 14(4), pp. 147-156, 1967. [160] D.M. Strong, “Decision support for exception handling and quality control in office operations”, Decision Support Systems, vol. 8(3), pp. 217-227, 1992. [161] P.Y.K. Chau, “Decision support using traditional simulation and visual interactive simulation”, Information and Decision Technologies, vol. 19, pp. 63-76, 1993. [162] R.J. Lempert, “A new decision sciences for complex systems”, Proceedings of National Academy of Sciences, vol. 99, suppl. 3, pp. 7309-7313, 2002. [163] V.V.S. Sarma, “Decision making in complex systems”, Systems Practice, vol. 7(4), pp. 399-407, 1994. [164] S.R. Watson and D.M. Buede Decision Synthesis: The Principles and Practices of Decision Analysis. Cambridge Univ. Press, New York, 1987. [165] S. French. Decision analysis and decision support systems. University of Manchester, 2000. [166] R.M. May, “Simple mathematical models with very complicated dynamics”, Nature, vol. 261, pp. 459-467, 1976.

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 73-91

73

CHAPTER 3 Fuzzy Controllers Design for the Inertia Wheel Inverted Pendulum Fatah Chetouane* IEEE senior member, Electrical and Industrial Engineering Department, Université de Moncton, New Brunswick, E1A3E9 Canada Abstract: The purpose of this chapter is to introduce the control problem of a complex system called the Inertia Wheel Inverted Pendulum (IWIP) using fuzzy logic technique. In this study, the IWIP is controlled using three different fuzzy controller designs: a self-tuning fuzzy Proportional-Integral-Derivative controller, a Mamdani-type fuzzy logic controller, and a Sugeno-type fuzzy logic controller. The performance of the designed controllers in regard to achieving stable control of the IWIP is compared and discussed. The main objective of this chapter is to address fuzzy logic controller design efficiently in a simple manner without prior knowledge of fuzzy sets theory. The only mathematics used is to describe the IWIP nonlinear physical model. Fuzzy Logic Controllers (FLC) design is explained based on the intuitive and experimental functioning of the IWIP system. The IWIP is simulated under different fuzzy control methods using Simulink™ fuzzy logic toolbox, Mathworks Inc. The IWIP parameters are provided, and our hope is that this study will serve as a benchmark for graduate students and engineers interested in applying fuzzy logic techniques in their project.

Keywords: Inertia wheel pendulum, fuzzy controllers. 1. INTRODUCTION Conventional and modern control techniques are achieved principally in a two stage process. In the first stage all the information regarding the system to be controlled is gathered and assumptions are made (such as superposition and causality principles, linearity assumption), to deduce mathematical model of the system. In the second stage, control synthesis techniques such as frequency domain, root loci, and pole-placement control, are applied to design a control law that will meet performance specifications. Usually, the designed control law requires real-life performance assessment on the real system (complex and non linear) and several tuning heuristics needs to be implemented in an ad hoc manner based on human deductive process and knowledge of the system. Thus, expert knowledge of the system is tentatively integrated to the control law through tuning actions in response to uncertainties, made on a predetermined controller structure, leaving several uncertainties not accounted for during control design. As an advance to the two stage design methodology, robust, stochastic, and nonlinear control theories were introduced to be able to integrate few types of structured uncertainties throughout the entire design process resulting in a control able to some extent to cope with system disturbances and parameters drift around their nominal values. Fuzzy logic control technique is different from conventional control engineering approaches in the sense that human knowledge and expertise gained from the interaction with the real system is primarily used at the first stage throughout the entire controller design process. Fuzzy logic is a computing approach that is based on "degrees of truth" rather than the usual "true or false" (1 or 0) Boolean logic on which modern computers are based. It was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960. Fuzzy control is based on mimicking human inference and deductive process, by leveraging his expert knowledge of the system to build a set of rules that will be used by a fuzzy inference mechanism to control the system. General rules of thumb on how to react facing the response observed on the system to bring performance to desired values are usually sufficient to build a fuzzy controller. An accurate deterministic model of the system is rarely needed and fuzzy rules can be described in a linguistic manner

*Address correspondence to Fatah Chetouane: IEEE senior member, Electrical and Industrial Engineering Department, Université de Moncton, New Brunswick, E1A3E9 Canada; Tel: +1 (506) 863-2074; E-mail: fatah.chetouane@ umoncton.ca Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

74 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

which make the control law more robust and open to extensive integration of new rules to account for set point and system parameter changes and to obtain higher performance control systems. Fuzzy control provides a systematic methodology for describing, modeling, and integrating human’s knowledge through coding, and deducing the control action to be applied on the system through decoding stage. Fig. (1), shows fuzzy controller structure and main components.

Figure 1: Fuzzy controller architecture.

The fuzzy controller has four main components: a)

A rule-base where the expert knowledge on how to control and interact with the system under different conditions is implemented via a set of logic rules in the form of IF-THEN statements, where the IF part is called the "antecedent" and the THEN part is called the "consequent".

b)

An inference engine, called also the Fuzzy Inference System (FIS) is the mechanism used to evaluate actual control conditions and invokes inputs and rules to be applied for best control performance.

c)

A data coding interface, called also fuzzification used to map inputs to appropriate membership functions and truth values.

d)

A data decoding interface, called also defuzzification used to convert and interpret the combined result from the inference process into specific control output values.

In practice, the controller receives the inputs (usually error signal between system response and set point value) and maps them into their membership functions and truth values. These mappings are then fed into the rules. If the antecedent part of the rule (premise) uses several input values a combined truth value is deduced based on a specific inference method. The appropriate output state is selected and assigned a membership value at the truth level of the premise. The truth values are then defuzzified and a control signal is generated. The performance of a fuzzy controller depends on several design parameters such as the number of rules; and the specification of rule conditions (premise), which determine the structure of the knowledge base. It is important to gather information on how the artificial decision maker should act in the closed-loop system and to organise the information in a relevant way to the control objective. Sometimes it is not practically feasible to interact with the real plant, simulation can be used to understand the plant dynamics and design a set of rules about how to achieve the control of the system. In the following sections of this chapter, the described ideas will be applied with more details to design a controller that will achieve stable operation of the Inertia Wheel Inverted Pendulum (IWIP). 2. DESCRIPTION OF THE WHEEL INERTIA PENDULUM Development of control techniques for inverted pendulum has always remained an interesting topic to control engineers for decades. This is largely due to its physical simplicity along with complete instability.

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 75

Also this simple system can be used as a benchmark to develop complex techniques that may be applied to control rockets, walking robots, and anti-seismic buildings. Most of the inverted pendulums studied so far have restoring force(s) applied somehow at the fulcrum. Some contributions have considered an alternative control action consisting of an oscillatory vertical force applied to the pendulum pivot [1, 2]. The stabilizing effect of a fast vertical oscillation applied to the pendulum base is known from the early work of Stephenson [3]. Another design pendulum stabilization method is based on the application of a rotational torque to the pendulum base, as proposed in [4]. Humans manage to balance the pendulums intuitively, by applying actuation at the fulcrum, and their complicated counterparts. The Inertia Wheel Inverted Pendulum (IWIP) stabilisation principle is based on creating a change in the angular momentum of an inertial wheel mounted on the top of the pendulum rode. This is similar to the situation when a person spreads their arms and rotates them rapidly in a reverse direction to restore balance and keep from falling forward. The same principle is used instinctively by most biped creatures to walk and balance in everyday life. Fig. (2) shows the IWIP. The fulcrum of the pendulum is kept in a groove so that it is only free to move on either side. The restoring torque is applied through a DC motor-flywheel fixed at the top. It is a freestanding pendulum where it is swung around the fulcrum to achieve stability. The GIP has much less actuating power making it a weak system [5]. The restoring torque depends on the rotational movement of the flywheel, and DC motor supplies a limited voltage due to its small size.

Figure 2: The inertia wheel inverted pendulum IWIP.

In modeling a DC motor connected to a load via a shaft, the general approach is to neglect the nonlinear effects and build a linear transfer function representation for the input–output relationship of the DC motor and the load it drives. This assumption is satisfactorily accurate as far as conventional control problems are concerned. However, when the DC motor driven flywheel operates at various speeds and rotates in two directions, the assumption that the nonlinear effects on the system are negligible resulted in poor control performance for the GIP. A great advantage of fuzzy control is that nonlinear and linear systems are equally treated. To account for the nonlinearity in the system, membership functions can be customized to bring the system to a more linear behaviour. One can still achieve to some extent an acceptable stability and control action for the IWIP with a PID controller using conventional control design techniques. However, several tuning actions are constantly needed to maintain IWIP in stable mode especially when vibration caused by the rotational motion of the wheel at the base of the pendulum cause disturbances for the controller. Fig. (3), shows an IWIP system with its associated analog PID controller.

Figure 3: IWIP with its analog PID controller.

76 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

3. MODELING AND SYSTEM PERFORMANCE The GIP system has a motor and flywheel mounted atop the body. Assuming such a mechanism is present in zero gravity, if the flywheel is made to rotate in the clockwise direction, the beam will rotate in the opposite direction so that the angular momentum about center of gravity of the whole assembly is conserved. Now assume that the flywheel increases its angular velocity. Hence the angular velocity of beam around the center of gravity increases (i.e. an angular acceleration is produced). The physical parameters of the pendulum assembly are as follows:

mp : Mass of pendulum assembly J p : Pendulum’s moment of inertia around fulcrum l p : Effective length of GIP (fulcrum to centre of gravity) J f : Moment of inertia of flywheel and motor’s rotor R : Motor’s electrical resistance L : Motor’s inductance K : Motor’s torque constant b : Motor’s friction factor : Pendulum’s angular position from the vertical : Flywheel’s angular position i : Motor’s armature current V : Motor’s drive voltage

Tf : Flywheel’s generated torque Tg : Gravitational torque acting on pendulum’s center g : Acceleration due to gravity

L

di dt

R i V

K

d dt

d2 .... dt 2

Jf

Jf

d2 dt 2

Tg

m p g l p sin( )....

Tg

Tf

Jp

....

(1)

(2)

Tf

K .i b

d dt

d .... dt

d2 .... dt 2

(3) (4) (5)

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 77

Numerical values of IWIP parameters of Fig. (3) are given in the appendix at the end of this chapter. Equations (1) to (3) describe the motor-flywheel part of the system. Equation (4) describes the non-linear gravitational torque that tends to destabilize the IWIP system (gravitational pull). Equation (5) describes the net torque that governs the pendulum movement around the furculum. In order for us to analyse the functioning of the IWIP system the nonlinear model given by equations (1) to (5) is programmed using Matlab™, Simulink™ software products of Mathworks Inc, see Fig. (4).

Figure 4: Nonlinear IWIP Simulink model.

The input of the IWIP plant nonlinear model (nonlinear torque due to gravitational pull) is the voltage supplied by the controller to the DC motor-wheel assembly. The output is the measured angular position of the rod from the vertical. The analog PID controller is also incorporated in the model to analyse control performances. The plant model can be coupled in a control loop with any type of controller as shown in Fig. (5).

Figure 5: Closed-loop control of the nonlinear IWIP system.

The control goal aims at keeping the IWIP at an upright position, despite the natural tendency of IWIP to fall on either side. Various types of control methods, e.g. Proportional-Integral-Derivative (PID), Fuzzy Logic (FL), Linear-Quadratic-Gaussian (LQG), Genetic Algorithms (GA) and Artificial Neural Networks (ANN), or any combination of these techniques can be tested using the Simulink™ development for different inputs (set-points or trajectory tracking). Fig. (6) shows the IWIP response with PID controller for an impulse at time 0.12 s of 4.5 deg. amplitude around vertical with duration of 0.07 s. The PID controller ensures stability, and fast response with a settling time Ts=0.64 s (5% from steady state response). While the PID performs well it requires complex

78 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

tuning when applied to the real non-linear plant (Fig. (3)), here the PID parameters are P=10, I=0.5, D=0.01 and an approximate derivative factor of N=500 is used. Thus, in the next sections different types of Fuzzy Logic Controllers (FLCs) will be designed to address the limitation of the PID controller. The performance of each FLC is investigated via simulation.

Figure 6: Pulse response for IWIP under PID control.

4. IWIP FUZZY CONTROL DESIGN APPROACH Based on the intuitive understanding of controlling the IWIP with the flywheel generated torque several Fuzzy Logic Controllers (FLC) were designed. The structure chosen for the Fuzzy Inference Systems (FIS) for all FLC have two inputs: error and its derivative error rate, and one output called control. The input fuzzy variable error characterizes IWIP angular displacement from the vertical position while the input fuzzy variable error rate characterizes the DC motor rotation speed level and direction. We define a set of seven (07) linguistic values for each input and output: Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Medium (PM) and Positive Big (PB). For a FLC with two inputs and one output with seven linguistic values for each, the rule base will have 72=49 possible rules. If all combinations of the inputs are used in a rule we say that this rule has as complete structure. We consider in this design only complete rule-base (populated with all possible rules) with complete structure rules. The FLC structure we will use throughout the design stage of the different FLCs is shown by Fig. (7).

Figure 7: Fuzzy control system structure.

The parameters Ke and Kde are amplifier gains for the error signal and its derivative respectively. These parameters are used to tune-up fuzzy control system sensitivity with respect to input signals. The topic of stability and sensitivity analysis of fuzzy control systems will not be addressed in this chapter. Based on the set of the defined linguistic values LV= {NB, NM, NS, ZO, PS, PM, PB}, the mapping of the fuzzy controller actions consists of defining for each input couple (u, v) = (error, error rate) LV2, a scalar or a

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 79

vector w corresponding to the fuzzy output of the fuzzy inference system. If the output is the control signal to be applied to the IWIP system, then w is a voltage value (scalar) within the voltage limits of the IWIP motor. If a self-tuning fuzzy PID controller is used, then w is a vector containing the PID parameter values (proportional P, integral I, derivative D). Based on the number of input linguistic values defined in our case, 7 in this case), the mapping table contains 27=49 possible fuzzy output values w. 5. SELF-TUNING FUZZY PID CONTROLLER The Proportional- Integral- Derivative (PID) controller involves three separate parameters; the proportional (P), the integral (I) and derivative (D) values. If the PID controller parameters are chosen incorrectly or not tuned to account for any changes occurring in the process the resulting control performances can be very poor. Tuning a PID is adjusting its parameters. This can be done using tuning heuristics well documented in conventional control theory. Manual tuning is also widely used in industry based on observation and human knowledge of the process. Based on this, it is possible to create a fuzzy controller for each PID action that will be responsible of its tuning according to process measured output. In this section we will use the structure of the fuzzy system given by Fig. (7) to design a fuzzy inference system for each control action of a PID controller. Such controller is called a self-tuning fuzzy PID because, the actions P, I, and D are not fixed but are constantly adjusted (self-tuning) by their corresponding fuzzy system. The structure of the self-tuning fuzzy PID is shown in Fig. (8).

Figure 8: Self-tuning fuzzy PID controller structure.

As a first approach for designing the self-tuning fuzzy PID controller, we summarized our experience of controlling the IWIP gained through long hours of interaction with the plant using the analog PID supplied with the IWIP system shown in Fig. (3), and by experimenting with the simulation model of Fig. (5), we were able to define FIS mapping for each action P, I, and D as shown by Tables 1, 2, and 3 respectively. Table 1. Fuzzy values table for the proportional action (P) Error rate

Error

NB

NM

NS

ZO

PS

PM

PB

NB

PB

PB

PB

PB

PB

PB

PB

NM

PB

PB

PM

PM

PM

PB

PB

NS

PB

PM

PS

PM

PS

PM

PB

ZO

PM

PS

PS

PM

PS

PS

PM

PS

PB

PM

PS

PM

PS

PM

PB

PM

PB

PB

PM

PM

PM

PB

PB

PB

PB

PB

PB

PB

PB

PB

PB

80 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

Figure 9: Fuzzy system parameters for the proportional action (P). Table 2. Fuzzy values table for the integral action (I) Error rate

Error

NB

NM

NS

ZO

PS

PM

PB

NB

PB

PB

PB

PM

PB

PB

PB

NM

PB

PB

PM

PS

PM

PB

PB

NS

PM

PM

PM

PS

PM

PM

PM

ZO

PM

PS

PS

PS

PS

PS

PM

PS

PM

PM

PM

PS

PM

PM

PM

PM

PB

PB

PM

PS

PM

PB

PB

PB

PB

PB

PB

PM

PB

PB

PB

In this controller design, each PID control action has four (4) linguistic values: zero (ZO), Positive Small (PS), Positive Medium (PM) and Positive Big (PB). A Mamdani type FLC is used with triangular membership functions for the inputs and a combination of triangular and z-shaped membership functions for the output [6]. The FLC uses MIN for t-norm operation (mathematical model of AND operation), MAX for s-norm operation (mathematical model of OR), MIN for implication (fuzzy reasoning), MAX for aggregation (producing one value from several input values), and CENTROID for defuzzification (the coordinate of the resulting centroid is the defuzzified value) as shown in Fig. (9). Input membership functions are defined using a normalised universe of discourse (-1, 1), and output membership functions a normalised universe of discourse (0, 1). This is shown by Fig. (10).

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 81

Table 3. Fuzzy values table for the derivative action (D) Error rate

Error

NB

NM

NS

ZO

PS

PM

PB

NB

PB

PM

PS

PS

PS

PM

PB

NM

PM

PS

PS

PS

PS

PS

PM

NS

PS

PS

PS

PS

PS

PS

PS

ZO

ZO

ZO

ZO

ZO

ZO

ZO

ZO

PS

PS

PS

PS

PS

PS

PS

PS

PM

PM

PS

PS

PS

PS

PS

PM

PB

PB

PM

PS

PS

PS

PM

PB

The three PID controller parameters (P, I and D) corresponding to the highest degree of truth (also called full members) of their membership functions are: (ZO, PS, PM, PB) = (0, 3, 6, 10) for the proportional parameter (P) (ZO, PS, PM, PB) = (0, 0. 25, 0.5, 0.75) for the integral parameter (I) (ZO, PS, PM, PB) = (0, 0.01, 0.015, 0.02) for the derivative parameter (D)

Figure 10: Proportional action fuzzy inference system inputs and output membership functions.

For the two other actions I and D, the value of the fuzzy system output changes according to Tables 2 and 3. Similarly, a combination of triangular and z-shaped membership functions are used for integral (I) and derivative (D) parameters fuzzification. Fig. (11) shows the IWIP response with self-tuning fuzzy PID controller for an impulse at time 0.12 s of 4.5 deg. amplitude around vertical with duration of 0.07 s. The self-tuning fuzzy PID ensures stability and faster response compared to the conventional PID (Fig. (6)) with a settling time Ts=0.56 s with less oscillations. Similar performances were observed for different Ke and Kde values. Changing triangular membership functions to Gaussian functions slightly increased oscillations and settling time duration: Ts=0.65 s, see Fig. (12).

82 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

Figure 11: Pulse response for IWIP under Self-tuning fuzzy PID control.

Figure 12: Pulse response with Self-tuning fuzzy PID control with Gaussian membership functions.

So far, a first design approach of a self-tuning fuzzy PID controller was detailed. We showed how to design Fuzzy Inference Systems (FIS) by selecting, or changing membership functions, defining inference and aggregation methods. The most important part of FIS design is defining linguistic variables for inputs and outputs and defining their correspondence as shown in Tables 1, 2 and 3. The self-tuning fuzzy PID studied in this section has a FIS for each one of its control actions P, I or D. In this case the output of each FIS (after defuzzification) represents the gain parameter for the corresponding control action (not a control voltage). These outputs need to be combined to produce the PID control action (control voltage) for the IWIP system (see Fig. (8)).

Figure 13: Fuzzy logic controller structure.

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 83

In the remainder of this chapter, we will design pure fuzzy controllers with a different structure from the self-tuning fuzzy PID presented, in the sense that their responses give directly the control signal (voltage) to be applied on the IWIP input as shown by Fig. (13). For this FLC design structure, the same inputs error and error rate are used with the same seven linguistic values and 49 rules. Note that, output control voltage can be negative. This is opposite to the self-tuning PID inference system where P, I and D are positive numbers (not control voltage). Therefore, seven linguistic variables are used for the output control namely: Negative Big (NB), Negative Medium (NM), Negative Small (NS), Zero (ZO), Positive Small (PS), Positive Medium (PM) and Positive Big (PB). The fuzzification is completed using these linguistic values to quantify the knowledge on how to control the IWIP plant. Table 4 gives for each input values error and error rate the corresponding output control value. Table 4. Fuzzy values table for the output control. Error rate NB

Error

NM

NS

ZO

PS

PM

PB

NB

NB

NB

NB

NB

NM

NS

ZO

NM

NB

NB

NB

NM

NS

ZO

PS

NS

NB

NB

NM

NS

ZO

PS

PM

ZO

NB

NM

NS

ZO

PS

PM

PB

PS

NM

NS

ZO

PS

PM

PB

PB

PM

NS

ZO

PS

PM

PB

PB

PB

PB

ZO

PS

PM

PB

PB

PB

PB

Figure 14: Mamadani FLC membership functions for inputs and output.

Membership functions are defined in a normalised universe of discourse (-1, 1), voltage values corresponding to the highest degree of truth for each linguistic variable defined for the output control are: (NB, NM, NS, ZO, PS,

84 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

PM, PB) = (-1, -0.67, -0.33, 0, 0.33, 0.67, 1) in volts. A preamplifier gain (pre-amp) is used to bring the defuzzified output control to the proper voltage range at the input of the IWIP plant (see Fig. (13)). In the next sections, two different FLC designs will be presented based on the explained structure: Mamdani type FLC and Sugeno type FLC. Each FLC design will be simulated using Gaussian and triangular membership functions for linguistic variables representation. 6. MANDAMI TYPE FUZZY LOGIC CONTROLLER A Mamdani type FLC can be easily created using the fuzzy toolbox. Here we used triangular membership functions for both inputs error and error rate, and for the output control. Fig. (14) displays input (error, error rate) and output control membership functions. The FLC uses MIN for t-norm operation, MAX for s-norm operation, MAX for aggregation, MIN for implication, and CENTROID for defuzzification as shown by Fig. (15).

Figure 15: Mamadani FLC parameters for the IWIP.

Testing Mamdani FLC with triangular membership functions for the IWIP control under the same pulse at time 0.12 s of 4.5 deg. amplitude around vertical with 0.07 s duration, the settling time needed by the FLC to stabilise the IWIP was found Ts=0.2 s compared to Ts=0.64 s with the conventional PID controller see Fig. (16). Based on the previous Mamdani FLC, we designed another Mamdani type FLC using Gaussian membership functions for both inputs and output as shown on Fig. (17). The fuzzy engine inference and deduction mechanism are also changed to: PROD for t-norm operation, PROBOR for s-norm operation (probabilistic OR calculated according to: PROBOR(a, b) = a+b-ab), MAX for aggregation, PROD for implication and CENTROID for defuzzification, see Fig. (18).

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 85

Figure 16: Mamdani FLC compared to the PID controller.

Figure 17: Gaussian membership functions for inputs and output.

The response of the IWIP under the Mamdani FLC with Gaussian MF is shown by Fig. (19). The settling time needed by this FLC to stabilise the IWIP is Ts=0.18 s compared to Ts=0.64 s with the conventional PID controller. The fuzzy inference process discussed so far is Mamdani's fuzzy inference method, the most common methodology. The Sugeno inference process operates in the same manner as Mamdani inference process. The main difference is that the Sugeno output membership functions (consequent of the fuzzy rule) are whether a constant or a linear function of the linguistic values in the antecedent part of the fuzzy rules [7]. A typical Sugeno fuzzy rule has the form: z

a x b y c ....

Such as: IF: error = x AND error rate = y THEN: control is z

(6)

86 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

Figure 18: Parameters of Mamadani FLC with Gaussian MF.

Figure 19: Mamdani FLC compared to the PID controller.

As described by equation (6), the output level in this case is a linear function with parameters a, b, and c to determine during the design of the Sugeno FLC. If a constant output is used for all outputs by fixing a and b to zero, the corresponding fuzzy system is called zero-order Sugeno model. In the next section a Sugeno type FLC is designed and tested for the IWIP control.

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 87

7. SUGENO TYPE FUZZY CONTROLLER Using the fuzzy toolbox, a Sugeno type FLC is built with triangular membership functions for the inputs and a linear output function for the output, see Fig. (20). The value of (a, b, c) used here is (-1.33, -1, -0.67) for each linguistic variable of the output. This FLC uses PROD for t-norm operation, MAX for s-norm operation, and WTAVER for defuzzification as shown by Fig. (21).

Figure 20: Sugeno inputs and output linear membership functions.

Figure 21: Sugeno FLC parameters for the IWIP.

88 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

The designed Sugeno FLC with triangular membership functions for the inputs is tested for the IWIP control under the same pulse input starting at time 0.12 s, with an amplitude of 4.5 deg around vertical, and a duration of 0.07 s. The settling time needed by the FLC to stabilise the IWIP is Ts=0.35 s compared to Ts=0.64 s with the conventional PID as shown on Fig. (22).

Figure 22: Sugeno FLC compared to the PID controller.

As for the Mamdani FLC, we tested the same Sugeno FLC using Gaussian membership function for both inputs error and error rate. The value of (a, b, c) used is (0.25, 0.25, -1) for each linguistic variable of the output The influence of this change had a negligible effect on the performance of the response compared to the case with Sugeno FLC with triangular membership function. The settling time is Ts=0.34 s compared to Ts=0.64 s with the conventional PID, see Fig. (23).

Figure 23: Sugeno FLC with Gaussian MF for the inputs versus PID controller.

8. TRACKING PERFORMANCE OF THE CONTROLLED IWIP The IWIP model was submitted to an additional test of tracking a square wave of 0.1 degree around vertical with a 0.5 Hz frequency and all discussed controllers were compared to the conventional PID controller, see Fig. (24).

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 89

Figure 24: Controllers under tracking test of a square wave.

Obtained results show that the Mamdani FLC gives the best performance for the tracking test and the least performing fuzzy controller for this case is the Sugeno FLC, see Fig. (25). This may be improved by further investigation on the Sugeno FLC rule base design and output function parameters.

Figure 25: IWIP response under different controllers for the tracking test.

9. CONCLUSIONS In this chapter the nonlinear IWIP plant was introduced. The complexity of the IWIP makes it an interesting system to design sophisticated controllers. Therefore, based on the expertise gained from several interactions with the IWIP plant, fuzzy logic control technique is investigated to build three fuzzy controllers with different structures: the fuzzy self-tuning PID, the Mamadani type FLC and the Sugeno type FLC. The FLC inputs used are error measured by the deviation angle of the IWIP from the vertical position and its derivative error rate. The output is the gain parameters P, I, and D for the fuzzy PID and

90 Artificial Intelligence Resources in Control and Automation Engineering

Fatah Chetouane

the control voltage to be applied on the IWIP for the Mamdani and Sugeno type FLCs. All input and output variables were fuzzified in linguistic terms and fuzzy rule tables were populated based on the process learned on how to control the IWIP plant. The influence of two inference methods and membership functions were tested on the performance of the FLC controller via simulation. A rule set of 49 rules was formulated for each design. Simulation results show that all of the three designed fuzzy controllers lead to good performances and stable functioning of the IWIP system. Although fuzzy control technique does not require a model to develop a fuzzy controller, a nonlinear mathematical model was used for simulationbased evaluations of the IWIP operation under different fuzzy logic control strategies. For safety-critical applications, simulation is frequently used to verify the safe operation of the control strategy before applying it on the real system. Essentially, the role of modeling in fuzzy control design is quite similar to its role in conventional control system design. One important feature of fuzzy control technique is its portability and flexibility: the designed inference mechanism can be kept to be used for many other different plants. Even if FLC structure and type are changed, the rule-base can remain unchanged since it represents the expert knowledge on how to control the system. The essential stages in the process of designing a fuzzy controller are: a)

Selecting FLC input and outputs.

b)

Fuzzification and membership functions selection.

c)

Design rule-base and inference mechanism.

d)

Defuzzification process.

The three fuzzy controllers developed here gives better performance compared to the conventional PID. The self-tuning PID with its good performance during the tracking test of variable square wave input, constitute a better controller than the PID. In addition, the expertise of tuning a conventional PID can be easily incorporated in the rule base to enhance its performance. Its self-tuning capability makes it easier to deal with unmodeled dynamics and nonlinearities affecting the plant. The Mamdani type FLC with its simpler structure compared to the self-tuning PID. The Mamdani types FLCs is the most common choice used in fuzzy control. Gaussian membership functions allow smooth transition between different control linguistic variables leading to a better performance than when triangular functions are used. The output response can further be improved (faster settling time Ts) by adjusting the error rate factor Kde, which will adjust the universe of discourses for the input and output membership functions. Sugeno FLC can be improved to exceed those of Mamdani type FLC, especially if more detailed expertise is incorporated into the rule-base. This challenge is left to the reader as a first experiment with FLC design using the model and approaches detailed in this chapter. For this purpose the IWIP parameters are provided in Table 5 (see Appendix). We presented a first approach on how to integrate intelligent controller for mechanical systems using nonlinear approaches. Fuzzy control is based on the use of rules to represent how to control the plant quite similar to the way that a conventional control depends on ordinary differential equations (ODE). Simulink™ fuzzy logic toolbox with it fuzzification and defuzzification user friendly interfaces provides all necessary tools to approach the design of FLC in an efficient manner.

 

Fuzzy Controllers Design for the Inertia Wheel

Artificial Intelligence Resources in Control and Automation Engineering 91

10. APPENDIX Table 5. Numerical values of the IWIP parameters

mp

0.37 kg

Jp

0.025 kg.m2

lp

0.25 m

Jf

9.8 10-6 kg.m2

R

4.0

L

4 10-3 H

K

20.5 10-3 N.m.A-1

REFERENCES [1] [2] [3] [4] [5] [6] [7]

P.L. Kapitsa, “Dynamical stability of a pendulum with an oscillating suspension point,” Zh. Eksp. Teor. Fiz., vol. 24, no. 5, pp. 588-597, 1951. D. Maravall, C. Zhou, and J. Alonso, “Hybrid fuzzy control of the inverted pendulum via vertical forces,” Int. J. Intell. Syst. vol. 20, no 2, pp. 195-211, 2005. A. Stephenson, “On a new type of dynamical stability,” Mem. Proc. Manch. Lit. Phil. Soc., vol. 52, no 8, pp. 110, 1908. I. Fantoni, and R. Lozani, “Nonlinear control for underactuated mechanical systems,” Appl. Mech. Rev., vol. 55, # 4, pp. 67-68, 2002. A. Shiriaev, A. Pogoromsky, H. Ludvigsen, and O. Egeland, “On global properties of passivity-based control of an inverted pendulum,” Int. J. Robust Nonlin. vol. 10, pp. 283-300, 2000. L.X. Wang, and J.M. Mendel, “Fuzzy basis functions, universal approximation, and orthogonal least-squares learning,” IEEE Trans. Neural Netw. vol. 3, no 5, pp. 807-814, 1992. T. Takagi, and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst. Man Cybern. vol. 15, no 1, pp. 116-132, 1985.

92

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 92-107

CHAPTER 4 Engineering Congestion Control of Internet Video Streaming with Fuzzy Logic Martin Fleury, Emanuel A. Jammeh* and Mohammed Ghanbari University of Essex, School of Computer Science and Electronic Engineering, Multimedia Network Laboratory, Colchester, CO4 3SQ, United Kingdom Abstract: Congestion control of video streaming over the Internet is necessary, as access to these telecommunications networks is unregulated. A commercial IPTV service in this environment faces unacceptable quality degradation, if the video stream does not respond to the presence of other competing traffic flows. As a solution, fuzzy logic control offers real-time performance, comparatively simple models, fairness to other traffic, and a smooth response. This Chapter introduces the control problem faced in designing a fuzzy logic congestion controller in terms of the restrictions of a compressed video bitstream and the uncertainties that affect congestion control. The Chapter outlines the design of a congestion controller that relies on network packet delay and delay trend as inputs. The controller has been extensively tested and favorably compared to the standard congestion controller. Multimedia applications over telecommunications networks are a promising area to apply computational intelligence.

Keywords: Congestion control, fuzzy logic, internet video straming. 1. INTRODUCTION This Chapter concerns the application of Fuzzy Logic Control (FLC) to video streaming over the Internet. Realtime video applications [1], such as IPTV (IP networked TV), Video-on-Demand (VoD), and network-based video recorder interest telecommunication companies, because of their high bitrates, though they also risk overwhelming existing networks if it is not possible to control their flows. Notice that this is still this case even though raw video is normally compressed prior to transmission or storage (except for a few purposes such as medical imagery and studio production). (The compression rate is between 15 and 30 times for the legacy MPEG-2 codec and approximately twice that for a H.264 codec.) The unicast variety of IPTV is especially attractive, because it allows streaming of individual TV programs at a time chosen by the end user. Video streaming is a way of delivering video, audio, or other multimedia content, without the need for extensive buffering at the user’s device. This allows: commercial confidentiality to be preserved; bandwidth consumption to be limited or balanced over time; and the extension of video delivery to mobile devices with limited storage capacity. As such it is preferable to video file download [2], which results in considerable start-up delay for long movies. Streaming could also replace progressive download, which is a piecewise version of download, commonly used for video clip delivery. However, despite its attractions, controlling streaming in the face of competing traffic across the best-effort Internet is a demanding control task. This is because bottlenecks exist along the Internet path that can restrict the flow of data. As such a classic control problem exists that presents many uncertainties to the controller. Therefore, we have applied a FLC congestion controller to solve this problem. The congestion controller responds to the volatile traffic conditions in the network by adapting the bitrate of the streamed video. We now sketch out the problem and show why FLC is necessary. The Internet consists of heterogeneous networks [3], which are linked together through common protocols, namely the TCP/IP suite of protocols. Data, including video streams, are routed as packets by means of the Internet Protocol (IP) through these networks. Intervening routers dynamically decide on the routes taken by the packets to their destination. The protocols are implemented as software, which provides flow control *Address correspondence to Emanuel A. Jammeh: University of Essex, School of Computer Science and Electronic Engineering, Multimedia Network Laboratory, Colchester, CO4 3SQ, United Kingdom; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 93

and congestion control. As there is no access control, packets enter the Internet from many sources given rise to congestion. (Flow control is about ensuring the data sending rate does not overwhelm the receiver machine’s capacity — which is a separate issue.) In fact, in the early days of the Internet congestion reached such a level that congestion collapse followed. Most of these data traffic sources are controlled by the reliable Transmission Control Protocol (TCP) that basically resends any packets that are dropped at intervening routers. However, this is not possible for video streaming, as it is a real-time service. For streamed data, User Datagram Protocol (UDP) provides a basic unreliable delivery mechanism that must be supplemented at the application by a congestion controller. Congestion control ensures that data does not enter the Internet only to be dropped at the buffers of intermediate routers along the path over the Internet. As there is no access control in the Internet, there must be some way to provide feedback to the congestion controller to form a closed loop. Though the Internet is a collection of networks, it is possible to distinguish between different network zones: the core network, which is usually over-provisioned in terms of bandwidth capacity; the edge network, which lies between the core and surrounding campus or corporate networks; and the access network which provides the link between the core and household users or small businesses. A tight link (or more loosely a bottleneck) on the Internet path [4] travelled by the video stream commonly exists at the network edge [5] and is the link of minimum available bandwidth on a network path. A tight link is a dynamic concept, as its location will vary: firstly over time, according to background traffic patterns; and secondly according to the network path’s route, which is not fixed, because of dynamic routing on the Internet. These two factors can create uncertainty in any video streaming response. Available bandwidth is restricted by coexisting cross-traffic, which is most likely carried by TCP and predominantly originates from web-servers or peer-to-peer file transfer [6]. Transport-layer protocols like TCP, sitting above IP, are responsible for end-to-end negotiation of delivery between applications. Therefore, TCP also provides its own form of congestion control. However, this is unsuitable for video delivery [7], because it produces a ‘sawtooth’ rate of delivery that results in rapid fluctuations in bitrate. If the compression rate were to be varied according to these fluctuations then the user would experience unacceptable variations in video quality after decoding. Congestion control is vital to avoid undue packet loss from the fragile compressed video stream [8]. At the sub-frame level, because Variable Length Coding (VLC) prior to outputting the bitstream introduces a dependency between each encoded symbol, there is a fragility that error resilience techniques such as decoder synchronization markers and reversible VLC only partially address. Because successive video frames are broadly similar (except at scene cuts and changes of camera shots), only the difference between successive frames is encoded in order to increase coding efficiency. Consequently, at the frame-level, removing temporal redundancy introduces a dependency on previously transmitted data, which implies lost packets from reference frames will have an impact on future frames. Though congestion control is vital, there are various sources of uncertainties facing the congestion controller, some of which are listed here: The measurements employed to estimate the amount of congestion are not accurate as they are based on partial information from a small set of packets. If packet delay-based estimation is used, the resolution of time measurements may be limited and clock synchronization at the end points of the network path may well be periodic, resulting in clock drift between synchronization times. In time-varying paths, path measurement systems, which rely on feedback of measurements, will produce results lagging the variation in traffic conditions, creating uncertainty. The available bandwidth is restricted by coexisting cross-traffic arising from short- and longterm flows that share the tight link. The extent of these competing flows is difficult to predict in advance in any precise way.

94 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

Mathematical modeling is difficult to accomplish, especially in real-time, resulting in uncertainty. Mathematical modeling is normally most robust within a linear system. However, in the fixed Internet (where the TCP protocol remains dominant) TCP control is essentially non-linear, with its two phase start-up, dynamic sliding window, congestion avoidance and so on. This suggests that observed ‘bursty’ or even fractal traffic patterns are due to the congestion control algorithms themselves. Certainly, web-server sourced cross traffic is marked by the occasional presence of large files, which are subsequently broken up into packets forming packet bursts. Statistically file size is long-tailed, commonly modeled by a Pareto probability distribution. Video sources may also be ‘bursty’ owing to the propensity of encoding software to release packets at process rescheduling points. Aggregated flows can also create packet bursts. These bursts create uncertainty in the background traffic, even over intervals shorter than the duration of a video frame. As previously mentioned, the tight link or bottleneck is a dynamic concept, as its location will vary over time according to background traffic patterns and the network path’s route, both of which factors create uncertainty in the streaming response. The very heterogeneity of the underlying networks, due to the evolving nature of telecommunication networks, especially wireless networks, creates uncertainty in network behavior. As the Internet is overlaid across a variety of underlying networks, a form of congestion control is required that is resilient to differences in the response of any type of network, through which a video stream may be routed. In addition to the uncertainties mentioned above, there is also short term variation in the video input rate due to the pattern of purely spatially encoded frames and those employing some form of temporal prediction. This creates problems in buffering (either under- or over-flow) the video unless some means of regulating the flow is available. The video’s encoded bitstream, if encoded at a Variable Bit Rate (VBR) to preserve its quality (rather than at a Constant Bit-Rate (CBR)), changes its statistical characteristics over time, because of varying scene complexity and because of the motion both of objects within the scene and relative to the camera. In general, fuzzy logic control is a methodology for the design of robust systems that can contend with the uncertainty, measurement noise and imprecision attributable to real world settings. In addition, fuzzy logic provides a way of constructing controller algorithms by means of linguistic labels and linguistically interpretable rules in a user-friendly way closer to human thinking and perception. Moreover, the fuzzy logic controller in this Chapter has the advantage over congestion controllers that are essentially TCP emulators because it can employ packet delay without the need for packet loss as a feedback. This allows queue build-up at intermediate buffers to be anticipated, hopefully before packet loss occurs. Prior to our research, analytical methods have been almost exclusively applied to congestion control of video on the Internet. For example, the industry standard approach [9] models the video stream’s rate with a complex equation designed to replicate the average flow of other competing flows across network bottlenecks. In that way it is hoped that further network congestion will be avoided. Unfortunately, this approach may lead to unnecessary packet loss, because of the need to probe the network using the video stream itself. Inevitably, as the video rate is increased packet loss occurs once the availably bandwidth or capacity limits are reached. Based on fuzzy logic, we have devised a more flexible method that estimates traffic conditions without the need for probing. In our application, a FLC is used as a sender-based system for unicast video streams. The receiver returns a feedback message indicating changes to the delay experienced by video stream packets crossing the Internet. This allows the sender to compute the network congestion level and from that the FLC estimates the response. An FLC controller can be efficiently implemented directly in hardware. The need for a hardware congestion controller implies that once developed the FLC models should have wide applicability whatever the traffic conditions at a bottleneck or tight link. The same

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 95

controller should also be able to cope with a range of Internet path delays and with video streams with differing characteristics in terms of scene complexity, motion, and scene cuts. 2. RELATED RESEARCH ON CONGESTION CONTROL Existing congestion controllers (such as TCP-Friendly Rate Control (TFRC) [9], TCP Emulation at Receivers (TEAR) [10], the Loss-Delay Based Adjustment Algorithm (LDA+) [11] and Quality-Oriented Adaption Scheme (QOAS) [12]) are analytically-based systems and in the case of TFRC are precisely formulated by a complex equation specifying the sending rate. Hence, the congestion controller can react to congestion by varying the sending rate. Traffic volatility (due to its observed ‘bursty’ or fractal nature) requires constant adjustment of the sending rate so that TFRC responds every packet round-trip-time (RTT). The equation governing TFRC is parameterized by mean RTT and packet loss rate, with, as for TCP, the latter being more prominent. Most existing congestion controllers are TCP-emulators [7] in the sense that their long-term sending rate aims to be that of an equivalent TCP stream. This is because TCP employs a cooperative form of congestion control that historically may have prevented congestion collapse in the public Internet [13], after its initial development stage. Because of TCP’s sending rate variations, the TCP emulators tend to have less aggressive sending rates, though they may be slower in their response to congestion. TCP also accepts unbounded delay, as it offers a completely reliable form of data delivery, whereas, as we have mentioned, video streams must meet frame display deadlines, without the need to guarantee completely consistent data delivery. In a congested network, a key problem for video is the delicate nature of the compressed stream, (as mentioned earlier) which means that the loss of particular packets and more generally particular pictures or frames has a knock-on effect at the decoder. Compressed video frames are sequenced into groups of pictures [8]. (The terms ‘picture’ and ‘frame’ are interchangeable for progressively displayed video, whereas ‘picture’ is a term that is appropriate for interlaced broadcast TV.) A Group of Pictures (GOP) commonly consists of 12 or 15 pictures with the first intra-coded picture forming a decoding anchor for the others in the GOP. Intra-coded pictures are those that are coded without reference to other pictures except to themselves, usually by block-wise backward reference. They are introduced to prevent temporal error propagation and to act as a resynchronization point in the event of packet loss. Consequently, loss of packets from an intra- or spatially-coded packet is especially harmful, though predictively-coded pictures (ones employing motion compensation to reduce temporal redundancy), which also act as reference pictures, should also be protected. As frames are displayed at a constant frame rate of 25 or 30 frames/s, video streaming is a delay-intolerant application, implying that it is better to deliver a lower-quality video clip or film than to resend packets. A measurement of available bandwidth is generally performed, because of the unpredictable nature of cross-traffic. This is accomplished by observing in real-time the packet arrival statistics of the video stream packets. Available bandwidth volatility means that an analyticallybased congestion controller, especially those that rely on packet loss feedback, may be unsuitable for efficient video stream congestion control. However, when considering the industry standard TFRC [9], this has the advantage that, at least in principle, its basis is a mathematical formula, giving confidence in the ability to understand its response in different network conditions. Unfortunately, its equation, which was derived under simplified circumstances, is specialized for the New Reno variant of TCP, whereas other TCP variants have since emerged, some of which, including TCP-SACK or the newer BIC-TCP, behave more aggressively. TFRC’s TCP-friendliness has even been challenged [14]. All of which illustrates the difficulty of arriving at a precise mathematical formulation. FLC is, of course, a form of computational intelligence. In a survey of congestion control through computational intelligence, the authors of [15] observe that little work has been reported on deploying natural algorithms including fuzzy logic within the Internet. Asynchronous Transfer Mode (ATM) networks, which employ access control to virtual switched circuits, are one domain to which fuzzy logic has been more extensively applied [16, 17] but for the purpose of access control. However, it should be remarked that access control does not involve dynamically controlling a video stream once it is admitted to the network, unlike congestion control. This is because once a virtual circuit is established it is assumed that sufficient capacity already exists within the network. Moreover, there is currently strong pressure from

96 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

telecommunications manufacturers to move away from ATM and towards Ethernet framing on fixed networks. Consequently, ATM is losing its relevance to contemporary networks. Because of wireless Bluetooth (IEEE 802.15.1)’s centralized scheduling, which resembles ATM admission control, fuzzy-logic video bitrate control was applied in a similar manner to a Bluetooth wireless link in [18]. An interesting modular design was employed but the main input to the fuzzy models was the Bluetooth send buffer fullness, which does not account for a number of important factors in wireless transmission including energy consumption. Again, because the problem resembles ATM admission control, in a number of research papers, the authors of [19] have explored fuzzy logic to improve the performance of the Random Early Discard (RED) router queue algorithm and in [20] fuzzy logic was applied to DiffServ buffer occupancy for each class of layered video packets. Both these systems control the quality-of-service of video streams at routers in the face of other competing traffic. These are not end-to-end solutions to the problem of network congestion but rely on deployment of quality-of-service strategies, which in practice are confined to particular internet service providers. In the case of RED, packets are dropped to signal to TCP controlled flows that congestion is about to occur. Within video coding, fuzzy logic has found an application [21, 22] in maintaining a constant bitrate video stream by varying the encoder quantization parameter according to the output buffer state, which is a complex control problem without an analytical solution. This is an open loop solution to the problem of controlling access to the network and should be compared to the ATM-based solutions previously discussed. In research by the authors of this Chapter, we have preferred a closed-loop solution, in which feedback for the network state from the receiver serves as input to the FLC. This allows greater awareness of traffic conditions experienced by the video stream within the network itself. In [23], fuzzy logic determines the size of different video frame type sizes and classifies the video genre. The intention is to allow modeling of Variable Bit Rate (VBR) video traffic without the need for video sources. However, there is no attempt at real-time control. Wireless networks represent a promising application of fuzzy logic, as not only are there uncertainties inherent in network traffic but the wireless channel is more error prone and takes a wider variety of forms than a wired link. Additionally, the need to conserve battery energy brings into play another set of factors. In [24], fuzzy logic was applied to modeling the lifetime of a wireless sensor network, though again no real-time control takes place. In [25], the problem of fading wireless channels (ones in which multi-path transmission causes mutual interference between the various versions of the received signal) was tackled with fuzzy filters to equalize the signal response according to variation of the wireless channel. 3. FLC CONGESTION CONTROL Fig. (1) is a block diagram of an FLC, with two inputs, a delay factor, df, and delay samples to form a trend. The formation of these inputs is described shortly. These inputs are converted to fuzzy form, whereby their membership of a fuzzy subset is determined by predetermined membership functions. This conversion takes place in the fuzzifier and trend analysis units of Fig. (1). The fuzzy outputs are then combined in the inference engine through fuzzy logic. Fuzzy logic is expressed as a set of rules, which take the form of linguistic expressions. These rules express experience of tuning the controller and, in the methodology, are captured in a rule base. The inference engine block is the intelligence of the controller, with the capability of emulating the human decision making process, based on fuzzy-logic, by means of the rule base, consisting of embedded rules for making those decisions. The output processing block converts inferred fuzzy control decisions from the inference engine to a crisp or precise value, which is converted to a control signal. Lastly, the rate of video is altered in the video rate adaptation unit. The compressed video bitstream is subsequently packetized prior to sending over the Internet. The FLC determines incipient congestion from one-way queuing delay in intermediate router buffers. The queuing delay is a measure of network congestion, and the ratio of the average queuing delay to the maximum queuing delay is a measure of bottleneck link buffer fullness. For each received packet indexed by i where

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 97

Video rate adaptation unit

Rule base

df Fuzzifier Delay samples

Compressed bitstream

CTRL Trend analysis

Delay trend TPCT

Output processing

Inference engine

Figure 1: FLC delay-based congestion controller.

OWDi = Tr - Ts Tr is the receive time of the current packet and Ts is the time the packet was sent. When it is appropriate, the computed OWDi updates the minimum and maximum One-Way Delays (OWDs), OWDmin and OWDmax, on a packet-by-packet basis. Subsequently, the maximum queuing delay is found as maxQD = OWDmax − OWDmin. The queuing delay over the network path, QDi is computed from the measured delay and the minimum delay: QDi = OWDi − OWDmin and an exponentially-weighted average of the queuing delay for the ith received packet is formed by avgQDi = (1

) × avgQDi 1 +

× QDi

where 1 is a forgetting constant (a constant that gradually reduces the influence of historic inputs). In tests, α was set to 0.1. A delay factor, df, is computed from the average queuing delay and the maximum queuing delay, df = avgQDi /maxQD where df ranges between [0,1] with 0 indicating no incipient congestion, 1 indicating full-blown congestion, with shades of incipient congestion between 0 and 1. df is an early notification of congestion and is the first input to the FLC. A trend analysis method is used to determine the general trend of the average delay. In each measurement epoch, a number k of queue delay samples are grouped into τ groups, where k . We use the Pairwise Comparison Test (PCT) to determine the overall trend of the queuing delay as shown in (1). I (M i TPCT

M i 1)

i 2

1

(1)

where Mi is the median of group i and I(X) is 1 if X holds and 0 otherwise. The value of TPCT is sent back to the sender, where a fuzzifier determines whether the level was increasing or not, according to membership functions. Fig. (2) shows the streaming architecture, in which fuzzy logic controls the sending bit rate. The Congestion Level Determination (CLD) unit finds the congestion state of the network from measured delay samples and delay trend made by the timer module. The congestion state data are relayed to the sender and compared with the output inter-packet gaps. FLC employs this delay information to compute a new sending rate that is a reflection of the current sending rate and the level of network congestion. The video rate

98 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

adaptation unit (either by a bitrate transcoder adapting pre-encoded video or by an encoder adapting the rate of live-video, through its quantization parameter) changes the sending rate to that computed by the fuzzy controller. We briefly explain how altering a single quantization parameter can change the rate. Video compression is achieved by encoder-decoders (codecs) that in standard codecs work on an image block-by-block basis. These are hybrid codecs [8], consisting of a number of concatenated algorithms. Block-based hybrid video codecs such as MPEG 1 & 2 and H.263 & 4 are inherently ‘lossy’. By lossy is meant that the decoded video sequence is not an exact reproduction of the input sequence but introduces variations. Because the scenes are natural, the viewer is usually unaware of what the original scene looked like, even if any one viewer can have the same view of a scene as another viewer. These codecs achieve compression not only by removing truly redundant information from the compressed bitstream but also by making small quality compromises, in ways that are intended to be barely perceptible. In particular, the quantization parameter regulates how much spatial detail is saved. When the quantization parameter is small, almost all that detail is retained. As it is increased, some of that detail is aggregated, so that the bit rate drops - but at the price of some increase in distortion and rendered quality at the video display. The current implementation of the bitrate transcoder changes the quantization level of a frequency-domain transcoder [26] for VBR video. Full decode and re-encode is prohibitively time consuming. Prior approaches relied on estimation of the error introduced by re-quantization without taking account of the impact on motion estimation by reconstructing the picture and reusing information in the bitstream [27], which still introduces delay, whereas partially (entropy) decoding and motion estimation in the transform domain is faster.

Stored video

Bitrate transcoder

Video encoder

FLC congestion controller

Video Server

CLD unit

Video decoder

Internet

Display

Client Timer unit

Figure 2: A fuzzy logic congestion controlled video server.

3.1. Fuzzy Logic Model Design In a fuzzy subset, each member is an ordered pair, with the first element of the pair being a member of a set S and the second element being the possibility, in the interval (0, 1), that the member is in the fuzzy subset. This should be compared with a Boolean subset, in which every member of a set S is a member of the subset with probability taken from the set {0, 1}. A probability of 1 represents certain membership and 0 represents non-membership. As a simple example, in a fuzzy subset of (say) ‘tall’, the possibility that a person with a given height taken from the set S of heights may be called tall is modeled by a membership function, which is the mapping between a data value and possible membership of the subset. Notice that a member of one fuzzy subset can be a member of another fuzzy subset with the same or a different possibility. Membership functions may be combined according to a set of ‘if... then’ rules to make inferences such as if x is tall and y is old then z is happy, in which tall, old and happy are membership functions of the matching fuzzy subsets and x, y, z are linguistic variables (names for known data values). In practice, the membership functions are applied to the data values to find the possibility of membership of a fuzzy subset and the possibilities are subsequently combined through de-fuzzification to provide a precise output. We have applied a semi-manual method of deriving the rules, combining human knowledge of protocol and network behavior with testing by simulator. The fuzzy model behavior itself was examined through Matlab Fuzzy Toolbox v. 2.2.4. This results in a widely applicable but static set of rules. The

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 99

FLC’s behavior can be predicted from its output surface, formed by knowledge of its rule table and the method of defuzzification. For example, Matlab’s toolbox allows a set of output data points to be calculated to a given resolution, allowing interpolation of the surface. Possible input, df, and output variables for this FLC are summarized in Table 1. Notice that though these linguistic variables are identified in Table 1, this does not imply that all of them are utilized in the implementation of the fuzzy membership functions and indeed some were found to be extraneous to the needs of the fuzzy models in the following. The input variables were fuzzified by means of triangular-shaped membership functions, which are a compromise between reduced computational-time at the expense of a sharper transition from one state to another. Choosing the number of membership functions is important, as it determines the smoothness of the bit-rate granularity. However, the number of membership functions is directly proportional to the computation time. Fig. (3) describes df’s membership functions that partition its range into four regions with different levels according to Table 1. Similarly, Fig. (4) shows the partitioning of the output, the variables for which are again listed in Table 1. Dividing the congestion levels into a manageable set, ranging from low to very high (according to delay), makes for a simple number of decision rules, as expressed in Table 2. The fuzzy inference rules are in the same form as the following examples: if df is H and T is I then S is NVH if df is L and T is D then S is PVH where S is the fuzzified output from the controller, D is a decreasing trend (T) and I is an increasing trend, while the output is taken from Table 1. The complete set of rules for the evaluation of the control output in Table 1, captured in a concise form the information contained in English sentences, which are constrained in the manner of the previous two examples. Table 1. Linguistic variables for FLC input and resulting output df L M H VH

Low Medium High Very High

Output NL NM NH NVH NEH Z PL PM PH PVH PEH

Figure 3: Delay factor membership functions.

Negative Low Negative Medium Negative High Negative Very High Negative Extremely High Zero Positive Low Positive Medium Positive High Positive Very High Positive Extremely High

100 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

Figure 4: Output membership functions. Table 2: Fuzzy-logic inference rules Delay, df Trend

L

M

H

VH

D

PVH

PM

Z

NL

I

PH

NL

NH

NEH

The FLC employs a simple Mamdani inference model [28] and center-of-gravity defuzzification method. Equation (2) maps the input to the output of the controller: M

CTRL =

S Ki

i 1 i M i

(2)

K 1 i

where M is the number of rules, Si is the value of the output for rule i, Ki is the inferred weight of the ith output membership function. More specifically, Si is the value at the middle of the range of data values that are possible members of the ith fuzzy subset. Ki is the area under the ith output membership function, clipped by the minimum possibility of membership of df in the input membership function of the ith rule. As more and more rules may apply, (2) is in the form of a weighted average of the values arising from the different rules that are applicable, with outputs of zero for those remaining fuzzy subsets for which the data value is not a member.

Figure 5: Output control surface (output from Fuzzy Toolbox).

The control signal CTRL, as specified in (2), is normalized to the range (0, 1), subject to a minimum lower bound (to avoid unacceptable low quality video output). For input bitrate Rin, the target output bitrate is Rout is given by

Rout

(1 CTRL) Rin

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 101

Fig. (5), from the Fuzzy Toolbox, shows the output control surface for this system. Intuitively, the smoothly varying surface indicates the stability of the system. 4. EVALUATION

The controller was evaluated through simulation with the well-known ns-2 network simulator (version 2.28 used) [29]. The simulated network, with a typical dumbbell topology, Fig. (7), had a tight link between two routers and all side-link bandwidths were provisioned such that congestion would only occur at the tight link. The one-way delay of the tight link was initially set to 5 ms and the side links delays were set to 1 ms. The tight-link router buffer’s queuing policy was defaulted to be FIFO (droptail) and the queue size was set to twice the bandwidth-delay product, as is normal in such experiments to avoid packet losses from too small a buffer. (The bandwidth-delay product measures the maximum amount of data that can occupy a link in one direction. A link is able to transmit in both directions; hence twice this product. A properly dimensioned buffer should be able to absorb any data while a link is cleared but not be so large that it causes delay or so small that arriving data is rejected because the link is fully occupied.) Sources in Fig. (6) provide other traffic that competes with the video stream of interest.

Video server

1 ms delay

1 ms delay FIFO buffer

Source 1 Router

Client

5 ms delay Tight link with variable capacity

100 Mbps Source n

Sink 1

Hub 100 Mbps

Sink n

Figure 6: Classic dumbbell simulation topology used.

Feedback was returned to the fuzzy controller after at least 40 ms had elapsed at the receiver, which corresponds to every frame at rate of 25 frames/s. As becomes evident in the reported tests, for larger network path delays (at a transcontinental scale), more frequent feedback messages would be needed to reduce the overall latency and improve the response. Some consideration to the stability of the control system might also be necessary in those circumstances. However, for expected streaming services within medium-sized networks, these measures are unlikely to be necessary. For example, in the congestion control system of [30] latencies beyond 120 ms were not tested and stability was apparently not an issue, which is the same assumption in this Chapter. Calibration experiments indicated that the algorithm accurately tracked various fixed capacity bottleneck bandwidths, producing a smooth flow with limited fluctuations to disturb delivered video quality. The performance of the scheme was also tested by changing the available bandwidth during a streaming session by injecting CBR background traffic at various rates. In Fig. (7), it is clear that the FLC controller responds to the changes in a timely manner, after a brief period of adjustment. The performance of the controller was also tested by varying the tight link one-way latency in order to emulate a range of end-to-end path delays. Whether the delay arises from propagation or from queuing delay, the feedback to the FLC module will be delayed. The tight link capacity was set to 700 kbit/s for the experiments reported in Fig. (8). The FLC CBR rate maintains its value, though the sending rate becomes more ‘bursty’ for delays of 100 ms and above, as feedback is itself delayed. Therefore, there is a possibility of an unsatisfactory experience for the viewer, as the received quality changes for path delays at and beyond 120 ms. However, all congestion control mechanisms will suffer from the same problem and can only reduce the problem by increasing the feedback sampling rate. In our case, this would gain at most a 40 ms reprieve, at a cost in reduced

102 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

number of samples to make the delay estimate, which itself may lead to rate oscillations. However, a delay of 120 ms is only likely to occur in a trans-national network, whereas maximum propagation delays of around 50 ms are typical of medium-sized nations such as France and Germany.

Figure 7: Tracking a varying available bandwidth.

Video quality is commonly objectively measured by the Peak Signal-to-Noise Ratio (PSNR) [8]. This is a logarithmic measure corresponding to the way that the human eye responds to a scene’s luminance. The average PSNR after streaming was found for two 32 s video clips: 1) ‘News’, consisting of a news presenter and changing background, with moderate motion; and 2) an extract from an episode of the wellknown situational comedy ‘Friends’, with greater motion. The videos were encoded using the MPEG-2 codec at an original bit-rate (before transcoding) of 1 Mbit/s. European SIF-format sequences were used (progressive, 25 frames/s, 352 × 288 pixel/frame). The pictures were divided into eighteen per row of macroblock slices, with one slice in each packet for error resilience purposes.

  (a)

20 ms.

(c) 100 ms. Figure 8: FLC rates across a 700 kbit/s bottleneck with various end-to-end delays.

(b) 60 ms.

(d) 120 ms.

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 103

Figure 9: Average PSNR for different available bandwidths when sending under FLC congestion control for ‘News’ and ‘Friends’ sequences.

Fig. (9) shows average PSNR after simulation of transmission of these clips across a link with differing available bandwidth (formed from a CBR background flow), with delay set 5 ms. Clearly, the video quality tracks available bandwidth but the quality is reduced for the more active ‘Friends’ clip. Given that PSNR is a logarithmic quantity, the bottleneck tracking is not expected to be strictly linear and, at lower bandwidths, the transcoder implementation limited the rate to around 90% of the input rate. Fig. (10) shows the timewise behavior of PSNR for the two clips under the worst of the bottlenecks. Without the impact of cross traffic, the quality, relative to the original encoded video, is reasonable, though clearly the more complex ‘Friends’ clip’s quality has been degraded more.

Figure 10: PSNR for a 400 kbps available bandwidth when sending under FLC congestion control for ‘News’ and ‘Friends’ sequences.

The ability to track a changing available bandwidth is illustrated by Fig. (11). This is the same test as previously in Fig. (7) but with the ‘News’ clip rather than CBR traffic under FLC congestion control. Also shown is the CTRL output from the FLC module, plotted against the left-hand vertical axis. Again, apart from small over-rides at the time of an abrupt upward available bandwidth change and some flattening out of the rate after a downward change, tracking accuracy is maintained. In practice, available bandwidth would not change as abruptly as happens in this test. Optimization of the fuzzy models will further adjust these small inconsistencies. A set of tests were also performed to establish whether available bandwidth tracking was maintained in typical internet conditions. Internet measurement studies [31, 32] have demonstrated a typical internet traffic mix to consist of longer term flows, ‘Tortoise’, representing file transfers, and transient HTTP connections, ‘Dragonflies’. In our set of tests, one FLC video source and ten TCP sources were passed across the link. The first five TCP sources were configured as ‘tortoise’, with an on duration of between five and twenty seconds and an off duration between one and five seconds, all also randomly generated from a uniform distribution. The remaining five TCP sources were ‘dragonflies’ with a random duration of between one and five seconds. These sources were generated from a Uniform distribution and with an off duration of between one and five seconds, also randomly generated from a Uniform distribution.

104 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

Figure 11: FLC congestion control of the ‘News’ sequence with changing available bandwidth and including the CTRL output from the FLC.

Ten experiments were conducted for a bottleneck capacity of 1 Mbit/s, with a 5 ms delay across the link. In the first experiment, only one TCP ‘tortoise’ source was present as background traffic, in the second two TCP ‘tortoise’ sources acted as background traffic and so on until the ‘dragonfly’ sources are eventually introduced, so that all ten TCP sources were on as background traffic for the tenth experiment. The video source was ‘News’ with the same characteristics as before. Fig. (12) summarizes the results, showing the correspondence between the mean over time of the bandwidth occupied by the FLC video source (plotted against the left-hand vertical axis) and the mean available bandwidth. The data points are not evenly spread out because of the larger bandwidth contribution of the ‘tortoise’ sources compared to ‘dragonflies’. Some data points, at low available bandwidth, are partially superimposed in the plot. For convergence, the data points represent the mean of twenty independent runs. From the plot, the sending rate of the FLC video is never above the available bandwidth, but tracks the available bandwidth throughout the experiments, leading to low packet losses. Consequently, the video quality (mean PSNR over time plotted on the righthand vertical axis) follows the rate trend and does not suffer any degradation in quality.

Figure 12: FLC congestion of the ‘News’ sequence with rising available bandwidth due to the presence of Web-like traffic, showing the mean bandwidth acquired by the FLC source and its corresponding video quality.

A comparison was made between the video quality delivered by FLC congestion avoidance and that by the TFRC protocol [9]. To ensure fairness the publicly available TFRC ns-2 simulator model (in the form of object tcl scripts to drive the simulator) was availed of from http://www.icir.org/tfrc/. In TFRC, the sending rate is made a function of the measured packet loss rate during a single RTT duration measured at the receiver. The sender then calculates the sending rate according to the TCP throughput equation [33]. In Figs. (13) and (14), both methods of congestion control were applied to the ‘News’ and ‘Friends’ sequences respectively. The available bandwidth at their various rates was formed by sending a CBR stream across the bottleneck link. Averages were taken over ten simulation runs. Though the advantage is not as much for FLC when controlling the ‘Friends’ sequence than for ‘News’, for all data points the delivered video quality from FLC congestion avoidance is superior to that of TFRC’s. There are a variety of reasons that one might suggest for the weaker performance of TFRC such as: the retention of a residual bandwidth probing action

Engineering Congestion Control of Internet

Artificial Intelligence Resources in Control and Automation Engineering 105

out of the need to emulate the average rate of TCP; the fact that rate decisions are taken according to the model every Round Trip Time (RTT); and use of the RTT rather than OWD as input. Unfortunately, reducing the feedback regularity is known [34] to cause TFRC to acquire more than its fair share of bandwidth, defeating the purpose of TFRC, which is to avoid congestion collapse [13].

Figure 13: FLC and TFRC: Comparison of average PSNR for a range of available bandwidths, when transporting the ‘News’ clip.

Figure 14: FLC and TFRC: Comparison of average PSNR for a range of available bandwidths, when transporting the ‘Friends’ clip.

5. CONCLUSIONS

The anticipated growth of IPTV (networked TV over the Internet) makes selection of suitable congestion controllers for video stream traffic of vital concern to the consumer market. Networked video communication is achieved by determining the available bandwidth and adapting the video rate at a live-video encoder or an intermediate bitrate transcoder. It is paramount that the network state be determined in an accurate and timely manner. In this Chapter, FLC helps optimize the response to network congestion after receiving feedback of packet delay and its delay trend. FLC, which has from its inception been extensively used for industrial and commercial control applications, is a convenient tool for handling un-modeled network congestion states. It allows the intuitive nature of congestion reduction to be captured through linguistic variables. The inherent looseness of its definition and the measurements available, together with the need for a real-time solution, all point in the direction of fuzzy logic. The fuzzy-logic models were shown to be robust under: changes in the complexity and motion content of the video stream under control; a wide range one way end-to-end link delays up to 120 ms; and variations in available bandwidth. Tests also reported that the fuzzy-logic approach compares favourably to standard TFRC congestion control. FLC is frequently efficiently implemented by means of a look-up table of quantized model output values. For a hardware congestion controller, an LUT-based approach is simple to implement, though there is a

106 Artificial Intelligence Resources in Control and Automation Engineering

Fleury et al.

range of designs for fuzzy-logic hardware. The need for a hardware implementation clearly implies that once developed the FLC models should have wide applicability without retuning. For example, the same controller should be able to cope with a range of internet path delays and with video streams with differing characteristics in terms of scene complexity, motion, and scene cuts. One problem with FLC has always been that compared to mathematically-based analytic methods, it has always been possible to object that the response to un-modeled network states is difficult to predict. A traditional, type-1 FLC is not completely fuzzy, as the boundaries of its membership functions are fixed. This implies that there may be unforeseen traffic scenarios for which the existing membership functions do not suffice to model the uncertainties in the video stream congestion control task. An interval type-2 FLC can address this problem by extending a Footprint-of-Uncertainty (FOU) on either side of an existing type1 or traditional membership function. Type-2 logic can model uncertainty in network conditions to a still greater extent, and, therefore, could increasingly find applications in video streaming over fixed and wireless networks. Type-2 logic is also open to hardware implementation. Fuzzy logic may be even more suited to resource control on wireless access networks, which now frequently form the final network hop to the end user. Transmission of higher quality video over a wireless interconnect has long been sought. However, it is important to factor in power usage and not simply regard a wireless channel as a fixed channel with the addition of errors, as mobile devices are typically battery powered. Fuzzy-logic control of Automatic Repeat Request (ARQ) is able to respond to a fixed power budget that subsequently diminishes over time. Other factors to include are packet delay deadlines, and send buffer congestion. Fuzzy-logic control, which can also take into account picture type and content, has the potential to deliver superior video quality and reduce delay over wireless networks. Therefore, fuzzylogic control represents a way forward for wireless access networks. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

[12] [13] [14]

W. Simpson, Video over IP: IPTV, Internet video, H.264, P2P, Web TV, and streaming, A complete guide to understanding the new technology, 2nd edition, Focal Press, Burlington, MA, Sept. 2008. P.A. Chou, “Streaming media on demand and live broadcast,” in P. A. Chou and M. van der Schaar (eds.) Multimedia in IP and Wireless Networks, pp. 453-501, Academic Press, Burlington, MA, 2007. J.F. Kurose, and J. M. Ross, Computer networking: A top-down approach, 5th edition, Pearson Education, Oxford, UK, Jun. 2009. M. Jain, and C. Dovrolis, “Pathload: A Measurement Tool for End-to-End Available Bandwidth,” Passive and Active Measurements Workshop, Mar. 2002. Cisco Systems, Inc., “LAN design guide for the midmarket,” San Jose, CA, 2000. G. Xie, G. Zhang, J. Yang, Y. Min, V. Issarny, and A. Conte, “Survey on traffic of metro area network with measurement on-line,” Int. Teletraffic Congress, pp. 666-677, 2007. J. Widmer, R. Denda, and M. Mauve, “A survey on TCP-friendly congestion control,” IEEE Network, vol. 15, no. 3, pp. 28-37, 2001. M. Ghanbari. Standard Codecs: Image Compression to Advanced Video Coding. IET Press, London, UK, 2003. M. Handley, S. Floyd, J. Padyhe, and J. Widmer, “TCP friendly rate control (TFRC): Protocol specification,” 2003, IETF RFC 3448. I. Rhee, V. Ozdemir, and Y. Yi. “TEAR: TCP emulation at receivers - flow control for multimedia streaming,” NCSU Technical Report, Apr. 2000. D. Sisalem, and H. Schulzrinne, “The loss-delay based adjustment algorithm: a TCP-friendly adaptation scheme,” Network and Operating System Support for Digital Audio and Video (NOSSDAV), pp. 215-226, Jul. 1998. G. Muntean, “Efficient delivery of multimedia streams over broadband networks using QOAS,” IEEE Trans. on Broadcasting, vol.52, no. 2, pp. 230-235, 2005. S. Floyd, and K. Fall, “Promoting the use of end-to-end congestion control in the Internet,” IEEE/ACM Trans. on Networking, vol. 7, no. 4, pp. 458-472, 1999. M. Voljnovic, and J.-Y. Boudec, “On the long-run behavior of equation-based rate control,” IEEE/ACM Trans. on Networking, vol. 13, no. 3, pp. 568-581, 2005.

Engineering Congestion Control of Internet

[15]

[16]

[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

[31] [32] [33] [34]

Artificial Intelligence Resources in Control and Automation Engineering 107

A. Pitsillides, and A. ekercioglu, “Congestion control,” in W. Pedrycz and A. Vasiliakos, editors, Computational Intelligence in Telecommunications Networks, pp. 109-158. CRC Press, Boca Raton, FL, September 2000. S. Ghosh, Q. Razouki, H.J. Schumacher, and A. Celmins, “A survey of recent advances in fuzzy logic in telecommunications networks and new challenges,” IEEE Trans. on Fuzzy Systems, vol. 6, no. 3, pp. 443-447, 1998 A. ekercioglu, A. Pitsillides, and A. Vasilakos, “Computional intelligence in management of ATM networks: A survey of current state of research,” Soft Computing Journal, vol. 5, no. 4, pp. 257-263, 2001. H. Kazemian, and L. Meng, “An adaptive control for video transmission over Bluetooth,” IEEE Trans. on Fuzzy Systems, vol. 14, no. 2, pp. 263-274, 2006. L. Rossides, C. Chrysostemou, A. Pitsillides, and A. Sekercioglu, “Overview of Fuzzy-RED in Diff-Serv networks,” Soft-Ware 2002, D. W. Bustard, W. Liu, and R. Sterritt, Eds., April 2002, pp. 2-14, LNCS # 2311. X. Wang, D. Ye, and Q. Wu, “Using fuzzy logic controller to implement scalable quality adaptation for stored video in DiffServ networks,” 12th Int’l Packet Video workshop, Apr. 2002. A. Leone, A. Bellini, and R. Guerrieri, “An H.261 fuzzy-controlled coder for videophone sequences,” IEEE World Conf. on Computational Intelligence, pp. 244-248, June 1994. P. M. Grant, Y.-S. Saw, and J. M. Hannah, “Fuzzy rule based MPEG video rate prediction and control,” Eurasip ECASP Conference, pp. 211-214, Jun. 1997. Q. Liang, and J.M. Mendel, “MPEG VBR video traffic modeling and classification using fuzzy technique,” IEEE Trans. on Fuzzy Systems, vol. 9, no. 1, pp. 183-193, 2001 R. Razavi, M. Fleury, and M. Ghanbari, “Fuzzy logic control of adaptive ARQ for video distribution over a Bluetooth wireless link,” Advances in Multimedia, 2007. 13 pages, online volume. Q. Liang, and J.M. Mendel, “Equalization of time-varying nonlinear channels using type-2 fuzzy adaptive filters,” IEEE Trans. on Fuzzy Systems, vol. 8, no. 5, pp. 551-563, 2000. P.A.A. Assunção, and M. Ghanbari, “A frequency domain video transcoder for dynamic bit-rate reduction of MPEG-2 bit streams,” IEEE Trans. on Circuits and Systems for Video Technol., vol. 8, no. 8, pp. 953-967, 1998. A. Vetro, C. Christopoulos, and H. Sun, “Video transcoding architectures and techniques: An overview,” IEEE Signal Processing Mag., vol. 20, no. 3, pp. 18-29, Mar. 2005. E.H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” Int. J. of Man-Machine Studies, vol. 7, no. 1, pp. 1-13, 1975. T. Issariyakul, and E. Hossain, Introduction to ns2 simulator, Springer Verlag, Berlin, 2009. Y.-G. Kim, J. W. Kim, and C.-C.J. Kuo, ”TCP-friendly Internet video with smooth and fast rate adaptation and network-aware error control,” IEEE Trans. on Circuits and Systems for Video Technol., vol. 14, no. 2, pp. 256268, Feb. 2004. N. Brownlee, and K.C. Claffy, “Understanding Internet traffic streams: Dragonflies and tortoises,” IEEE Communications Mag., vol. 40, no. 10, pp. 110-117, 2002. J. S. Marron, F. Hernandez-Campos, and F.D. Smith, “Mice and elephants visualization of Internet traffic,” 15th Conf. on Computational Statistics, Aug. 2002. J. Padyhe, V. Firoiu, D. Towsley, and J. Kurose, “Modeling TCP throughput: A simple model and its empirical validation,” in Proc. of ACM SIGCOMM, pp. 303-314, Sept. 1998. I. Rhee, and L. Xu, “Limitations of equation-based congestion control,” IEEE/ACM Trans. on Networking, vol. 15, no. 4, pp. 852-865, 2007.

108

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 108-134

CHAPTER 5 Artificial Intelligence and Electrical Drives Ben Hamed Mouna1* and Sbita Lassaâd2 1

High Institute of Industrial Systems of Gabès, University of Gabès, Tunisia and 2National Engineering School of Gabès (ENIG), University of Gabès, Tunisia Abstract: The main topic of this chapter is the application of artificial intelligence as fuzzy logic and neural network in motor drive systems. Artificial Neural Network (ANN) speed sensorless fuzzy control both in scalar and vector control of induction motor are presented and analyzed. The feasibility and effectiveness of the proposed methods are verified through experimentation. The experimental is built all around dSpace system with DS1104 controller board based on digital processor (DSP) TMS320C31.

Keywords: Artificial intelligence, Induction motor, motion control and sensorless. 1. INTRODUCTION In the past, the Direct Current (DC) motors were used extensively in areas where variable speed operations were required, since their flux and torque could be controlled easily by the field and armature current. In particular, the separately excited DC motors have been used mainly for applications where was a requirement for fast response. However, DC motors have certain disadvantages which are due to the existence of the commutator and brushes. Hence, they require periodic maintenance. Besides, they can’t be used in explosive or corrosive environments on one hand. On the other hand, they have limited commutator capability under high speed and high voltage operational conditions. These issues can be overcome by the application of AC motors, which have simple and rugged structure, high maintainability, economy, and robust. Among these various AC drive systems, those which contain the Squirrel Cage Induction Motor (SCIM) have a particular cost advantage. The SCIM is simple, rugged and is one of the cheapest machines available in a wide range of power. Due to their excellent control capabilities, variable speed drives incorporating with modern static converters and torque control can compute well with high performance four quadrant DC drives. A simple way of controlling the induction motor is to adjust the magnitude of the stator voltage proportionally to a reference frequency. This open loop method, known as the scalar control or constant voltage per hertz control, is still used in low cost frequency converters due to its important advantages. A speed sensor is not needed in this case. The knowledge of motor parameters is not necessary implying that the method is robust. However, their dynamic performances are poor [1-4]. Vector control techniques incorporating fast microprocessors and DSPs have made possible the application of induction motor drives for high performance applications. In case of vector control, the torque and the flux of the induction motors producing current components are decoupled [8, 10, 11] and [22-25]. The vector control techniques can be separated into two categories: direct and indirect flux vector orientation [38-40]. For direct method, the flux vector is obtained by using stator terminal quantities. While indirect methods use the machine slip frequency in addition to the rotor speed to achieve field orientation [36]. The overall performance of scalar and field oriented controlled induction motor drive systems depends on the performance of the used controllers [13]. Researchers have used various types of closed loop controllers for the rotor speed of the induction motor. Among these controllers, the proportional integral derivative controllers are widely used in the outer speed loop. However, the use of this type of controller is more sensitive to parameter variation. To overcome this *Address correspondence to Ben Hamed Mouna: High Institute of Industrial Systems of Gabès, University of Gabès, Tunisia; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved-© 2012 Bentham Science Publishers

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 109

problem, adaptive and robust controls were used. The adaptive control imposes a very computation burden while H robust control requires the knowledge of the limit of the disturbance [6, 7, 9]. The sliding mode control is also used in the speed loop but the worst disadvantage of this type of controller is the high switching frequency. Recently, speed controllers based on artificial intelligence techniques as fuzzy logic and neural network have been proposed [4]. Since these approaches do not require the knowledge of a mathematical machine model, the algorithm would remain robust despite of parameter deviations and noise measurements. All high performance of scalar and vector controlled induction motor drives requires accurate rotational speed information for the feedback control loop. This information is provided by an incremental encoder. The use of this sensor implies more electronic components, higher cost, lower reliability, difficulty in mounting in some cases such as motor drives in harsh environment, increase in weight, increase in size and increase electrical susceptibility. To overcome these problems, in recent years, the elimination of those transducers has been considered as an attractive prospect. Numerous approaches have been proposed to reconstruct the rotor speed from machine terminal properties such as stator current or voltage. Due to the advantage of the artificial intelligence techniques, in this chapter, a fuzzy speed controller and Artificial Neural Network (ANN) observer to reconstruct the rotor speed in both scalar and vector control of the induction motor are described. Also, experimental results are presented and discussed. 2. ARTIFICIAL INTELLIGENCE (AI) AI is basically computer emulation of human thinking (called computational intelligence). The human brain is the most complex machine on earth. Neurobiologists have taken a bottom-up approach to understand the brain structure and its working. The psychologists and psychiatrists have taken the top-down approach to understand the human thinking process. However, our understanding of the brain and its behavior has been extremely inadequate. The goal of AI is to mimic human intelligence so that a computer can think like a human being. However, due to the complexity of the human thought process, there is no denying the fact that computers have adequate intelligence to help solve problems that are difficult to solve by traditional methods. AI techniques are principally classified into three different areas: the fuzzy logic, neural network and genetic algorithms [26-37]. Today, the AI techniques are used in many areas that include power electronics and motor drives. In the following section we are limited to the fuzzy logic and the neural network. 2.1. Fuzzy Logic With fuzzy logic, the controlled process is translated in linguistic terms by the fuzzyfication procedure and the control actions. These two are linguistic rules based on the experience of the designer. The linguistic expressions are not entirely true or not entirely false but live with certain degree of truth given by the membership functions. They are many types of fuzzy logic controller. The most used are sugeno, and mamdani. But, for controllers, the fuzzy mamdani type is used. As shown in Fig. (1), in general, this type of fuzzy logic controller contains four parts [29, 33]: Fuzzyfication, Knowledge base, Inference engine, Deffuzzification. The fuzzification means that the measured signals are transformed into fuzzy quantities which are also referred to as linguistic variables in the literature. This transformation is performed by using membership functions. In a conventional fuzzy logic controller, the number of membership functions and shapes are

110 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

initially determined by the user. A membership function has a value between 0 and 1. It indicates the degree of belongingness of a quantity to a fuzzy set. If it is absolutely certain that this quantity belongs to the fuzzy set, then its value is 1 (it is 100% certain that this quantity belongs to this fuzzy set), but, if it is absolutely certain that this quantity does not belong to the fuzzy set, then its value is 0. Similarly, for example, the quantity belongs to the fuzzy set to an extent of 50% and then the membership function is 0.5. The membership function can take many forms including triangular, Gaussian, trapezoidal, etc. The knowledge base consists of the data base and the linguistic control rule base. The data base provides the information linguistic control rule and the fuzzy data manipulation in the fuzzy logic controller. The rule base (expert rules) specify the control goal actions by means of a set of linguistic control rules. In other words, the rule base contains an expert rule. The fuzzy logic controller looks at the input signals and up on the expert rules determines the appropriate output signals (control actions). The rule base contains a set of “if-then rules”. The main methods of developing the rule base are: Using the experience and the knowledge of an expert for the application and control goals, Modeling the control actions of the operator, Modeling the process, Using a self organized fuzzy controller, Using ANN. The inference engine is the kernel of a fuzzy logic controller and has the capability both of simulating human decision-making based on fuzzy concepts and of inferring fuzzy control actions by using implication and fuzzy logic rules of inference. In other words, once all the monitored input variables are transformed into their respective linguistic variables by fuzzyfication, the inference engine evaluates the set of if-then rules (given by the rule base) and thus as a result is obtained which is again a linguistic value for a linguistic variable. The linguistic result has then to be transformed into a real output value of the fuzzy logic controller and this is why a second transformation in a fuzzy logic controller is needed. The second transformation is performed by defuzzification. It yields a non fuzzy, real control action from the inferred fuzzy control action by using membership functions. There are many defuzzification techniques. But, due to the simplicity of its implementation and simpler training algorithms, the gravity center method is generally adopted. Physically, this corresponds to tacking a weighted average of the control action contributions from each various fuzzy rules. When a classical controller is used, then the controller input is the error signal. For example, for a proportional and integral (PI speed) controller, the input is the speed error, which is the difference between the reference speed and the actual speed. However, when a fuzzy logic controller is used, there is more than one input to the controller. In the most frequently used fuzzy logic controller, there are two inputs. These are the error (E) and the Change of Error (CE). As discussed above, in the heart of the fuzzy logic controller, there is a rule base and certain individual rules (sub rules). In general, these linguistic rules are in the following form of “If-Then” rules and can take the following form: If (E is A and CE is B) Then (CU is C) Where A, B and C are fuzzy subsets for the universe of discourse of the error, change of error and change of the output respectively.

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 111

Figure 1: Mamdani type of fuzzy logic controller.

2.2. Artificial Neural network (ANN) 2.2.1. Basic Principle ANN is powerful modeling tool that is able to capture and represent complex input/output relationships. Important feature of ANN is that it normally requires supervised training (or learning) by input-output example data sets unlike conventional programming of digital computer [15-17]. An ANN consists of a number of interconnected artificial neurons. The structure of an artificial neuron is inspired by the concept of a biological neuron. A neuron is the basic processing element in the nervous system of the brain that receives and combines signals from other similar neurons through thousands of input paths called dendrites. Each input signal (which is electrical in nature), flowing through a dendrite, passes through a synapse or synaptic junction. The junction gap is filled with neurotransmitter fluid, which either accelerates or delays the flow of the signal. These signals are then summed up in the nucleus, nonlinearly modified at the output before flowing to other neurons through the branches of an axon. Each input signal flows through a gain or weight (called a synaptic weight) that can be positive or negative, integer or non integer. The summing node that accumulates the weighted input signals also receive a weighted bias signal and then passes to the output through the nonlinear (or linear) transfer or activation function. Several common-type activation or transfer functions are linear, threshold, sigmoid (or log-sigmoid), hyperbolic-tan, Gaussian, etc. The magnitudes of these functions vary between 0 and 1 or -1 to +1. The linear function can be unipolar or bipolar. All of these functions are characterized as squashing functions because they limit the neuron response between the asymptotic values. The ANNs can be classified as feed forward and feedback or recurrent networks. In the former type, the signals flow only in the forward direction, whereas in a recurrent network, the signals can flow forward, backward, or laterally. For static mapping, the feed forward networks are important, whereas for dynamic or temporal mapping, the recurrent networks are important. The type of the ANN used in power electronics applications is the feed forward multilayer back-propagation algorithm. ANN is based on learning process. It is defined as changing the synaptic weights of each interconnection in the network to update it until the target error is used for adjusting the neural network weights and biases during the training phase [17]. 2.2.2. Back-Propagation Algorithm When the back-propagation technique is used, the main task to configure the weights and biases is such a way that the squared output (between the desired and the actual output) of the ANN should be minimal. Initially, the weights in the neural network are randomly selected and therefore, the output signals of the neural network will not be equal to the desired output. However, during training, the actual output signals are compared to the desired output signals (output pattern) and the weights are adjusted (iteratively by back-propagation training algorithm), until the error becomes smaller then a preset threshold value. During training, when the input patterns are applied, the total output square error (Esc) is the sum of the squared output error for all output layer neurons ( Escp ), thus P

Esc

Escp p 1

(1)

112 Artificial Intelligence Resources in Control and Automation Engineering

Where Escp

0.5 d p

Mouna and Lassaâd

yp ²

Thus

Esc

P

1 2

Ep

p 1

P

K

d pk

y pk ²

(2)

p 1k 1

In (2), d pk is the desired output vetcor of the k th output neuron (in the output layer) for input pattern P ( p = 1, 2... P ). Here P is the number of training patterns

y pk is the actual output of the k th output neuron (in the output layer) for Input patterns P and K is the number of output node (in the output layer). With a successful learning process for the neural network, after a large number of exposures to the input and output data, the ANN can found the required relationship between the input and output data sets and configures the weights and biases. This training process is then followed by supplying the trained ANN with the new input data and the ANN then outputs the required data. The procedure of “back-propagation” training algorithm is as follow [12]: Step#1: initially randomize the weights from -0.5 to 0.5, Step#2: obtain the input-output example data patterns from the experimental results or from simulation results if simulation is possible with the mathematical model of the plant, Step#3: calculate the error, Step#4: adjust the weights and biases of the ANN, Step#5: calculate the output of the ANN, Step#6: repeat step1 until the stipulated error is reached. 3. ANN SPEED SENSORLESS FUZZY LOGIC CONTROL IN SCALAR CONTROLLED INDUCTION MOTOR 3.1. Scalar Controlled Induction Motor: Basic Principle

In steady state operation, the induction motor flux is approximately equal to the ratio vs f s [6]. The correct utilization of the machine magnetic characteristic is done by maintaining the constant flux below the base speed [1, 2, 6]. Based on the mathematical equations governing electrical dynamic of an induction motor in a synchronous rotating frame in the steady state, we obtain:

vds

rs ids

s

qs

(3)

vqs

rs iqs

s

ds

(4)

vdr

rr idr

(

vqr

rr iqr

(

s

s

) )

qr

dr

(5) (6)

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 113

The d and q axis can be referred in a space vector if they are respectively placed at real and imaginary axis. Hence,

vs

vds

jvqs

is

ids

jiqs

(8)

ir

idr

jiqr

(9)

(7)

s

ds

j

qs

(10)

r

dr

j

qr

(11)

Employing (3) and (4) in (7) yields:

vs

rs is

j

s

(12)

s

Similarly, the rotor voltage is defined as: vr

rr ir

j

r

(13)

r

The stator and rotor flux are: ds

Ls ids

M idr

(14)

qs

Ls iqs

M iqr

(15)

dr

Lr idr

M ids

(16)

qr

Lr iqr

M iqs

(17)

Based on the equation system (3-6) combined with equations (7-10), the stator and rotor fluxes in space vector are defined by: s

Ls is

M ir

(18)

r

Lr ir

M is

(19)

By replacing the flux with their expressions, (12) and (13) become:

vs 0

rs is rr ir

j s [ Ls is j

r

[ Lr ir

M ir ] M is ]

(20) (21)

In the further section, we shall use the well known equivalent single phase model transformed to the stator where are considered the magnetic leakages as totalized and grouped to the rotor and designed by N e s [2]. Fig. (2) shows this model.

114 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

R'r /g

Vs

Figure 2: Single phase equivalent circuit of the induction machine.

Where Rr ' and Ne represent respectively the rotor resistance and total leakage inductance located in the rotor. The evolution of the stator synchronous field round the rotor produces an electromagnetic power which will be transmitted to the rotor at synchronous speed. The electromagnetic power is defined as [1-4]:

Pem

Tem

2 s

3R 'r V

s

1

2

R 'r g g

2

Ne

(22)

s

By assumption, we neglect the stator resistance. Then, we get:

Tem

6

2 s

R 'r f r

R 'r fr

1

2

Ne 2

2

(23)

Here f r is the slip frequency. The mechanical dynamics of the induction motor is expressed as:

J

d dt

n p ( Tem TL )

(24)

If we give the zero value to the load torque (TL ) and we neglect 2 N e , the transfer function between the rotor speed and synchronous speed s is given as: 1 s

3 p²

s

² R 'r Js

R 'r f

3n p ²

s

²

1

k 1

s

1

Here np is the number of poles pair, f is the viscous coefficient, gain of the system.

(25)

is the time constant and k is the static

It can be seen from equation (23) that the rotor speed is controlled through the synchronous angular speed. Therefore, to compensate the slip angular speed when a disturbance occurred, a speed controller must be added. Compared to conventional scalar control, this new scalar strategy compensates the frequency slip calculation loop leading to a reduced calculation time.

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 115

3.2. ANN Speed Observer

The most significant point to keep in mind when defining the structure and operation of neural net are mainly the choice for the inputs and the outputs. Some inputs should be chosen that determinate completely the rotor speed of the induction motor. The inputs in the motor must be easy to measure so that the hardware to control the machine will be simplified. im

vs' Lm

1

(26)

s

By application of the Kirchhoff’s voltage law, (26) becomes:

im

vs

1

rs is Lm

(27)

s

The voltage drop caused by the stator resistance is in general neglected. Therefore, (27) can be written: im

vs Lm

1

(28)

s

This can be expressed as: im

vs f s

1

1

2 Lm

(29)

If the ratio vs f s 1 is maintained constant, the current im is also constant. Based on the Kirchhoff’s current law, the stator current is expressed as:

is

im ir

(30)

The application of the Kirchhoff’s voltage law deals to: ir

vs r ' r

jNe

1

(31)

s

Based on (30), the square magnitude of the stator current can be expressed as: i²s

i²m

vs f s

1 2

4 ² r 'r

1 s

1

² Ne²

(32)

With the scalar control, the I m and the ratio vs f s 1 are constants. Therefore, varies with I s and s according to a non linear function. Therefore, the inputs which determine completely the rotor speed are I s and s . The magnitude value of I s is expressed as:

Is

4 / 3 ias ² ibs ias ibs ²

(33)

where ias and ibs are the measured stator currents. It is clear that to calculate the current I s , we need two current sensors [24, 25]. In this paper, we propose a simple and new method to calculate the current I s by using only one current sensor. It is well known that ias and ibs are illustrated by these equations:

116 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

ias

I as sin( s t )

(34)

ibs

I bs sin( s t 2 / 3)

(35)

Here, we suppose that three stator phases are in equilibrium. 1

By looking ias and ibs expressions, we note that ibs has the value of ias with a delay of 2 3 s . Therefore, to obtain the value of ibs , we can measure the ias value. ibs value can be obtained from the 1 2 3 s delayed ias value. The validity of this method is tested in real time by using a DS1104 board layout. The validity results are shown in Fig. (3).

Figure 3: Measured ias and computed ibs .

Comparing to other works [5, 6, 8], this method reduce the number of sensors used to achieve this aim as only one current sensor is used. Our goal is to obtain a neural network speed observer which estimates the full range of speeds (from negative to positive values). According to the length of training data, we notice that they are very huge and the neural network observer finds many training problems as these informations are very huge to be learnt by the neural network. Many solutions are proposed [14, 16]. We can increase the number of layers and neurons. However, this creates a problem of computation time and memory capacity. We propose a simple and easy solution which consists of learn only the range of the positive speed. It is well known that the relation between the positive and negative speeds is a minus mark in the command issue. How to detect the negative speeds? If the reference speed becomes negative, the speed becomes also negative and vice versa. To make the neural network available in negative speeds, an absolute value is added to the control voltage and a sign function is implemented. The output of this function is (+1) if the speed is positive and (-1) if the speed is negative. By the use of this technique, we reduce the time, memory capacity and we observe the speed in the whole range (from positive to negative). Based on all these considerations, the neural network observer will have the phase current magnitude and the control voltage (u) as the inputs and the speed as the output [1, 2, 18]. The final structure of the neural network used is a multilayer net with a three layers. The first is formed by two neurons (input control voltage and stator current magnitude). The second, made of two hidden layers (the first hidden layer is formed with four neurons and the second is formed with two neurons) are used to reach the objective of the target error (10-6). The third one is formed with one neuron to give the speed output. The sigmoid function is used at the hidden and the output layers. A linear function is used at the input layer. The sigmoid function has an output signal varying between 0 and 1. Hence, we adopt the signals by dividing the output by its nominal value. The way of training the neural network consists of tacking training data corresponding to the positive speed and we present these informations to the back propagation algorithm. The data base must have the significant informations. Therefore, it consists of variables speeds steps (Fig 4 and 5). For each step, different values of load are applied. It is kept in time and then eliminated.

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 117

2500

Speeds (rpm)

2000 1500 1000 500 0 -500 0

100

200

300

400

Time (s)

Target speed Real speed 500 600 700

Figure 4: Rotor speed for various steps and load values.

Figure 5: Control voltage (u) for various steps and load values (Is).

The used training algorithm of the neural network speed observer is as follows [19-21]: Step#1: initially randomize the weights from -0.5 to 0.5, Step#2: compute the control voltage (u) from the fuzzy logic controller and stator current (Is) from current sensor (vector data is saved in closed loop), Step#3: compute the error between the real and the observed speed, Step#4: adjust the weights of the neural network, Step#5: calculate the output of the neural network, Step#6: repeat 2nd step until the stipulated error will be reached. The internal structure of the neural network observer is shown in Fig. (6). 3.3. Fuzzy Logic Speed Controller

Due to its advantages, a fuzzy logic controller is used in the feedback loop of ANN speed observer. The used controller is based on rules and it is normalized which can be adapted to different machines easily [20]. As shown in Fig. (1), the core of the system drives is the artificial neural network and the fuzzy logic controller. As it is shown in Fig. (1), first the control voltage and the stator current are used by the artificial neural network to obtain the speed observer. Next, the observed speed is compared to its target value. After that, this error and its change are normalized and fed the fuzzy logic controller to provide the change of the control voltage. Hence, response time of the system can be improved. Moreover, the setting time of the system is adjusted by this gain G.

118 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

Figure 6: The internal structure of the neural network speed observer.

E (k )

ref

ANN

(k )

(36)

E ( k ) E ( k 1) Te 1

CE ( k )

Where

(k )

ref

is the target speed,

(37) ANN

is the ANN observed rotor speed and Te is the sample time.

The control voltage that is applied to scalar control system is defined by the recurrent equation: u (k )

u (k 1)

u (k )

(38)

In the first stage, the real variables E (k ) and CE (k ) are converted into fuzzy variables.

NB

NM

EZ

NS

PS

PM

PB

DeMEmbership grade

Membership grade

The fuzzyfication maps the error and the error variation to linguistic labels: NB (Negative Big), NM (Negative Medium), NS (Negative Small), ZE (Zero Equal), PS (Positive Small), PM (Positive Medium) and PB (Positive Big). Each fuzzy label has an associated membership function. The membership function of triangular type and the control surface are shown in Fig. 7. Knowledge base involves defining the rules represented as statements governing the relationship between input and output variables in the term of the membership functions. The control rules are represented as a set of if-then rules. The fuzzy rules of the proposed controller for sensorless speed control of IM are detailed in Table 1.

1 0.5 0 -1

-0.5

0

E(k)

0.5

1

NB

NM

NS

0 -1

NS

EZ

PM

PS

PB

-0.5

0

CE(k)

0.5

1

PB

1

0.5

0.5 0 -1

PM

(b)

u(k)

Membership grade

NM

PS

0.5

(a) NB

EZ

1

0 -0.5 1

-0.5

0 u(k)

(c)

0.5

1

0

CE( k)

-1 -1

0 E(k)

(d)

Figure 7: The memberships of the a-error, b-error variation, c-command variation and d-control surface.

1

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 119

Table 1: Control rule base E(k) CE(k)

NB

NM

NS

ZE

PS

PM

PB

NB

NM

NS

ZE

PS

PM

PB

PS

NM

NS

ZE

PS

PS

PM

PB

PM

NS

ZE

PS

PM

PB

PB

PB

ZE

ZE

NB

NM

NS

ZE

PS

PM

PB

PS

NM

NS

ZE

PS

PS

PM

PB

PM

NS

ZE

PS

PM

PM

PM

PB

PB

ZE

PS

PM

PB

PB

PB

PB

3.4. Implementation of the Drive System

The experimental set up is shown in Fig. (8). It is constructed to investigate the real time implementation and effectiveness of the proposed algorithm. The Space Vector Pulse Width Modulation (SVPWM) method is applied to the Voltage Source Inverter (VSI) to drive the motor [28]. The A/D converter for the current measurements has 16 bits resolution. The 1024pulses/revolution rotary encoder is used to validate the ANN speed observer. A 1kw Direct Current Generator (DCG) supplying a resistor bank is used as a variable load. The control algorithms are implemented in a Matlab/Simulink package, compiled to machine language and downloaded on a Real Time Interface Ds1104 Fig. (9). The used speed sampling time for the scheme implementation is of 1ms. The power circuit part is composed with Intelligent Power Modules (IPMS). IPMS are based on the Insolated Gate Bipolar Transistors (IGBTs). To control the power modules, the Pulse Width Modulations (PWM) are generated by a scalar strategy PWM card.

Figure 8: View of the experimental set up.

120 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

Figure 9: IM speed sensorless implementation using Dspace 1104 RTI.

3.5. Experimental Results

Experiments were carried out on the various operating conditions to verify the performance of the proposed algorithm. Fig. (10) shows the speeds and control voltage at constant target speed. From this figure, it is shown that the proposed sensorless drive has good observation and high performance control characteristics at rated speed. Fig. (11) gives the variable speed control performance at acceleration and deceleration reference trajectory speed and in the field weakening region. Hence, high speeds require rather large input voltages. In practice, the voltage must be kept within the inverter ceiling limits [29, 30] so that the flux is decreased Fig. (12) from the rated as the speed increases above rated one (scalar law strategy at constant power). This method of reducing the flux at high speeds is called "field weakening operation". These results show that the real speed and ANN's speed are in close agreement with a small difference in dynamic state. Fig. 13 highlights the speed sensorless control performance where various values of load were applied by using the DC generator which fed a resistive bank load. At positive speeds, a resistive load of 600w and 400w are applied at times 64s and 73.5s respectively. These values of loads are eliminated at times 70s and 78.5s respectively. At reverse speed operation, resistive loads of 600w, 400w, 400w and 200w are applied at times 172s, 193s, 211s and 220s respectively. These values of loads are eliminated at times 180s, 203s, 221s and 240s respectively. As it is given in Fig. (14), the ANN's observed speed coincides with the real speed although the various values of loads with a tiny error. To investigate the dynamic performances of the ANN's observed speed, a load of 600w is applied and eliminated when the induction motor decelerates. Despite of these disturbances, the ANN's observed speed follows the actual IM speed. 4. ANN SPEED SENSORLESS FUZZY LOGIC CONTROL IN VECTOR CONTROLLED INDUCTION MOTOR 4.1. Fundamental of Vector Controlled Induction Motor

The field oriented control, also known as vector control, is published by Blaschke in 1972, is a powerful control strategy that allows the achievement of high performance control with an induction motor. Its main

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 121 5

1500

Control voltage (v)

Speeds (rpm)

4 1400.5 1400 1399.5

1000

140

140.5

500

0 0

50

100

150 Time (s)

ANN observed speed Target speed Real speed 200 250 300

3 2 1 0 -1 0

50

100

(a)

150 Time (s)

200

250

300

(b)

Figure 10: a-Measured, ANN's observed speeds and b-Control voltage under constant target speed.

5

Control voltage (v)

Speeds (rpm)

10

Real speed ANN observed speed Target speed

2000 1000 0 -1000

0

-5

-2000 0

50

100 Time (s)

-10 0

150

50

(a)

100 Time (s)

150

(b)

Rotor speed (rpm)

Figure 11: a-Measured, ANN's observed speeds and b-Control voltage at reverse speed in the field weakening region.

3000 2000

b) (w nt e n 0 po m co x flu

-1

1000 -1

-0.5

0

0.5

Reverse flux compon

1

ent (wb)

1 ct re Di

Figure 12: Stator flux space vector versus rotor speed. 6

2000 (b)(d) (a) (c)

Real speed

4

0

Control voltage (v)

Speeds (rpm)

1000

Target speed (e)

-1000

(f)

(g)

-2000 0

ANN observed speed 50 100 150 Time (s)

(a)

(h)

(k) (n) (m) (r)

(s)

200

250

2 0 -2 -4

300

-6 0

50

100

150 Time (s)

(b)

Figure 13: a-Measured, ANN's observed speeds and b-Control voltage under load applied.

200

250

300

122 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

objective is, as a separately dc machine, to independently control the produced torque and flux. This control strategy is based on the orientation of the stator or rotor flux on the direct axis. Vector control techniques can be separated into two categories: direct and indirect flux vector orientation. In Direct Field Oriented Control (DFOC) strategy, both the instantaneous magnitude and the position of the rotor flux are supposed to be available and known with high precision: directly measured or observed. On the other hand, the position of the flux is obtained analytically in Indirect Field Oriented Control (IFOC) strategy. IFOC is much easier to implement than the DFOC, but the slip speed calculation involves the rotor time constant, which is known to vary with frequency and temperature. To maintain the flux orientation, the variations of this parameter should be tuned on line and its actual value supplied in real time to the speed controller and to the slip calculation value [25]. In this chapter, we are limited to an improved version of the Direct Rotor Field Oriented Control (DRFOC). 4.2. Dynamic Induction Motor Model

Assuming linear magnetic circuits, equal mutual inductances and neglecting iron losses, the induction motor mathematical model in the stationary frame is formulated as [10]: v

rs i

s

d

s

dt

1

s

v

rs i

s

d

s

dt

1

s

0

rr i

d

r

dt

1

r

0

rr i

d

r

dt

1

r

(39) r r

The stator and rotor winding flux linkages are expressed as: s

Ls i

s

Ls i

r

Lr i

r

Lr i

i s , i s, v s

,

s

s

,

s

Mi

r

s

Mi

r

r

Mi

s

r

Mi

s

and v

s

r

and

(40)

are respectively the stator currents and voltages components, r

are respectively the stator and rotor fluxes components.

rs and rr are respectively the stator and the rotor resistances Ls , Lr and M are respectively the stator self, the rotor self and the mutual inductances. is the leakage coefficient and is the rotor speed. The electromagnetic torque developed by the motor is expressed in terms of rotor flux and stator currents as: Te

p

r

is

(41)

4.3. Proposed Scheme of the Drive System

The bloc diagram of the proposed induction motor drive system is shown in Fig. (14). The closed loop control scheme consists of an inner currents control loops and an outer speed and flux control loops. The feedback signals for the outer control loops are estimated using an on line data of motor terminals in terms of stator voltages and currents. The stator’s voltages and currents are sensed using Hall Effect voltage and current sensors. The signals corresponding to voltage and current of the stator are fed to the processor through the dSpace system with DS1104 controller board. Thereafter, the rotor speed and the rotor flux are

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 123

estimated inside the processor using the sensed values of stator terminals (Fig. 15). The estimated speed ref (k ) to compute the speed error, ANN ( k ) using the artificial neural network is used with the reference which is processed in a fuzzy logic controller. The output of the speed controller which represents the electromagnetic torque target is used to compute the reverse stator current iqsref target. The later is applied to a current limiter which sets a limit on this reference current. This limit on the target reverse current is desirable to operate the devices of the inverter circuit in their safe range of current. The current signals iqs and iqsref are processed in a PI controller to generate the reverse stator voltage vqs . The estimated rotor flux is used with the reference flux dr ref to compute the flux error, which is processed in a PI controller. The output of the flux controller which represents the target direct stator current idsref is applied to a current limiter which sets a limit on this reference current. The two current signals ids and idsref are processed in a PI controller to generate the direct stator voltage vds . The estimated slip speed using the target rotor flux and the target reverse stator current is added to estimated rotor speed to get the synchronous one s . The obtained vds , vqs and s are fed to the d-q a - b - c bloc to get the reference target stator voltages vasref , vbsref and vcsref . The target stator voltages are processed in the PWM bloc to provide appropriate switching patterns to the devices of the fed inverter.

Rectifier + Filter

Inverter

Direct Voltage Bus

RF

CF

sa

Half bridge IGBT

sb

a1

3~ AC-supply

CF

RF

a2

c1

sb

b2

A B C

C

B

A

sa

sc

b1

sc

SCIM 3~

c2 --------Enco deur

dSpace card 1104

sa sa sb sb

sc sc PWM card

G

5 Current card

Voltage card

Speed card

CP1104 PC + DS 1104 Evironment

---

Resistor bank Acquisition and control set

Figure 14: The bloc diagram of the proposed induction motor drive system.

4.3.1. Direct Rotor Field Oriented Control Scheme

For the Direct Rotor Field Oriented Control (DRFOC), the rotor flux vector is aligned with d axis and 0. With setting the rotor flux to be constant equal to the rated one which means dr qr r and respect to this condition, the estimated rotor flux and the slip speed are given as: dre

sl

With

r

M 1

r

Miqsref

r

s

1

(42)

idsref 1

drref

Lr is the rotor time constant. rr

(43)

124 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

Figure 15: DRFOC scheme of induction motor.

4.3.2. Neural Network Speed Observer

By replacing stator flux with its expression and eliminating the rotor current in (39), we obtain: v

rs i

s

d

s

dt

1

s

v

rs i

s

d

s

dt

1

s

0

rr i

d

r

dt

1

r

0

rr i

d

r

dt

1

r

(44) r r

Based on these equations, we recognize the well known models: the Voltage Model (VM) and the Current Model (CM). The equality between the rotor fluxes deduced from the models, we obtain [23]: Lr M

1

Lr M

1

v v

rs

s

rs

s

Ls s i Ls s i

s s

M M

Multiplying the first equation by Lr M

1

v

s

r

rs

Ls s i

r

s

1 r

i

1 s

r

1 r

i

r

r

r

r

s

r

and the second one by r

(45)

1

v

s

r

rs

Ls s

r

, we establish: r

i

s

M

1 r

r

i

s

r

i

2 s

r

(46)

In the vector control, varies with respect to v s , v s , i s and i s . r are constants. Therefore, r and Hence, the significant inputs which determine completely the rotor speed are v s , v s , i s and i s . It is better to obtain a neural network speeds observer which observes the whole range of speeds (from negative to positive values). By looking at extent training data, we find them very huge and the neural network observer finds many training problems because of the amount of information to be learnt by the neural network. Many solutions are proposed [5, 7]. For example, we can increase the number of layers and neurons. However, this creates a problem of computation time and memory capacity. A simple and easy solution is to learn only the range of the positive speed. It is known that the relation between positive and negative speeds is a minus mark in the command issue. How to detect the negative speeds? If the reference speed becomes negative, the speed becomes also negative and vice versa. To make the neural network available in negative speeds, an absolute value is added to the bipolar inputs of the neural network and a sign function is implemented. Using this technique, we save time, memory capacity and we observe the speed in the whole range (from positive to negative). The final structure of the neural network used is a multilayer net with the three layers. The first one contains four neuron inputs v s , v s , i s and i s , the second one has two hidden layers and the third one by one neuron to give observed speed. This final structure is chosen by trial and error method. The sigmoid function has an output signal varying between 0 and 1. Therefore, we adopt the signals by dividing the output by its nominal value. The way of training the

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 125

neural network consists of sampling the training data corresponding to the positive speed and presenting these data base to the back propagation algorithm [18]. The training algorithm of the neural network speed observer is as follows: Step#1: initially randomize the weights from -0.5 to 0.5, Step#2: obtain the stator currents and voltages, Step#3: calculate the error between real and observed speeds, Step#4: adjust the weights of the neural network, Step#5: calculate the output of the neural network, Step#6: repeat 2nd step until the stipulated error is reached. The internal structure of the neural network speed observer is shown in Fig. (16).

Figure 16: The internal structure of the neuronal network speed observer.

4.3.3. Fuzzy Logic Speed Controller The structure of a standard fuzzy controller is presented in Fig. 17.

Figure 17: Structure of fuzzy controller.

Consider the fuzzy speed control system of an induction motor drive with direct vector control where E and CE are the signals from the speed loop and U is the crisp output signal. The U signal after integration constitutes the target electromagnetic torque command Teref for the DRFOC drive. Fig. 18 shows the fuzzy sets with triangular MF set of each signal and input output control surface. The universe of discourse of each variable is expressed in pu values. All the MFs are symmetrical in nature. There are five MFs for each input and output variables. Table 2 shows the rule matrix which contains 5X5 = 25rules. The design of fuzzy controller is

126 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

essentially the knowledge base design that consists of formulation of MFs and the rule matrix [5]. This design is often based on trial-and-error approach based on performance experience about the plant. The torque command is then computed (47). Te k

(47)

Te ( k 1) G Te ( k )

With G is an tuned gain. For this control law, only at steady state, the speed error goes to zero, however, at dynamic state, the tracking error is significant. To minimize the error at dynamic state, a new control law is proposed. It is defined as: Te k

(48)

Te (k 1) G Te ( k ) G1 Te ( k 1)

Here G1 is also tuned gain. Table 2: Rule matrix for fuzzy logic speed controller

CE

u (k ) PN

Z

PP

GP

GN

GN

GN

PN

PN

Z

PN

GN

PN

PN

Z

PP

Z

PN

PN

Z

PP

PP

PP

PN

Z

PP

PP

GP

GP

Z

PP

PP

GP

GP

GN

1

Z

PN

PP

GN

GP

Membership grade

Membership grade

E

GN

0.5

PN

Z

PP

-0.5

0 e(k)

0.5

0.5

0

0 -1

-0.5

0 e(k)

0.5

-1

1

(a) GN

PN

1

(b) Z

PP

GP

1

0.5 u(k)

Membership grade

GP

1

0.5

0 -0.5 1

0 -1

0 -0.5

0 u(k)

(c)

0.5

1

e(k )

-1

-0.5

-1

0 e(k)

(d)

Figure 18: The memberships of the: a-Error, b-Error variation, c-Command variation, d-Control surface.

0.5

1

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 127

4.4. Implementation of the Drive System

We have tested the neural network for fuzzy controlled speed sensorless direct field oriented control of induction motor drive at different speed values under no load and with load applied. Fig. (19) shows the experimental set up drive system of the used configuration.

Figure 19: A photo of the experimental set up.

It consists of an appropriate hardware and its software components. The major parts of the drive system are: a)

Neural network speed observer,

b)

Fuzzy logic speed controller,

c)

Current controllers,

d)

Rotor flux estimator,

e)

Rotor flux controller,

f)

IGBT’s Gate drivers,

g)

Voltage source inverter (vsi) based on IGBT transistors,

h)

Direct current voltage bus,

i)

DSpace controller board DS1104 and its connector panel,

j)

Voltage, current and speed sensors.

128 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

Some of them are implemented through software and they are mainly speed observer, speed controller, current controllers, rotor flux estimator and rotor flux controller. The experimentation has been achieved with the help of Matlab/Simulink package and dSpace system with DS1104 controller board based on digital processors (DSP). The voltage source inverter utilizes a diode rectifier half bridge with dc bus voltage feeding the three IGBTs. The power circuit part is composed of intelligent power modules with rated 75A, 1200V to drive the induction motor. Intelligent power modules are conducted with insulated gate bipolar transistors working at a frequency up to 20KHZ with a dead fixed time of 3.25µs as it is shown in Fig. 21. (b). The pulse width modulation (PWM) signals to control the power modules are generated by dSpace system. An optical isolation and an amplification of the switching signals are provided through on optocoupler PC900V. After that the obtained signals are updated using three drivers SKHI22A (Fig. 21. (a)). The sampling period of 1ms is selected since the computation time of the algorithm is about 0.1ms. We measure two stator current using Hall type sensors LM LA 100-P through 16bits analogical-digital converter. An incremental sensor encoder delivering 1024 pulses per revolution is mounted on the rotor shaft only for comparison of the observed and real speed of the induction motor. A 1kw Direct Current Generator (DCG) supplying a variable resistor bank is used as variable load for 1kw induction motor. The control and observation algorithms are implemented in a Matlab/Simulink package, compiled to machine language and downloaded on a Real Time Interface dSpace DS1104 (Fig. 20).

Figure 20: SCIM speed sensorless digital implementation using dSpace 1104 RTI-Simulink.

4.5. Experimental Results

Many experiments were carried out under various operating conditions to verify the performances of the proposed neural network peed sensorless for a fuzzy controlled s direct field oriented SCMI drives both with and without load torque appliance. Figs. 22 to 35 illustrate the experimental results. The obtained results at variable target speed under no load are presented in Figs. 22 to 27. From Fig. 22, it is shown that the fuzzy logic controlled speed is following the measured one. The maximum observation error is 35rpm (3.5%) as it is shown in Fig. 23. In the same way, with the proposed neural network observer, the measured and observed

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 129

speeds follow the target one. In Fig. 26 is presented the direct stator currents. The real direct stator current follows the target one indicating that the decoupling of the induction motor is well established.

(a)

(b)

Figure 21: (a) Switching signals drivers’ circuit of the inverter (b) switching signals of IGBT’s half bridge with dead time of 3.25 s.

In Figs. (28) to (35), a DC generator supplying a variable resistive bank has been connected to the motor as a load. In Fig. (28), the machine has been initially set to operate at 1000 rpm in steady state. A sudden resistive load has been then applied from 28 to 36 s to the motor shaft. The maximum speed error is 28 rpm (2.8%) Fig. (29). In this case, as it can be seen from the Figs. (31) and (35), the machine needs more current. The reverse stator current increase as it is directly proportional to the electromagnetic torque. The direct stator current remains constant indicating the decoupling is guaranteed. The neural network observed speed and the measured one follow the target indicating the high performance of the proposed fuzzy logic controller. As it is seen from the experimental results the proposed neural network for fuzzy logic controlled speed sensorless direct field oriented induction motor drives has good performances. Results without Load 1200 1000 Speeds (rpm)

800 600 400 200 0 -200 0

20

Target rotor speed Real rotor speed ANN observed rotor speed 40 60 80 Time (s)

Figure 22: Measured, ANN's observed speeds at variable target speeds under load torque appliance in experimentation.

Speed observation error (rpm)

40 20 0 -20 -40 -60 -80 0

20

40 Time (s)

60

80

Figure 23: Speed observation error at variable target speeds under no load in experimentation.

Target electromagnetic torque (Nm)

130 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 0

20

40 Time (s)

60

80

Figure 24: Target electromagnetic torque at variable target speeds under no load in experimentation.

Reverse stator current (A)

0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 0

20

40 Time (s)

60

80

Figure 25: Reverse stator current at variable target speeds under no load in experimentation. 1.2 Direct stator Currents and tracking error (A)

1 0.8 0.6

Real direct stator current Target direct stator current Tracking error

0.4 0.2 0

-0.2 0

20

40 Time (s)

60

80

Figure 26: Real and target direct stator currents and tracking error at variable target speeds under no load in experimentation. Direct and reverse reference stator voltages (v)

100

vdsref vqsref

80 60 40 20 0

-20 0

20

40 Time (s)

60

80

Figure 27: Direct and reverse stator voltage at variable target speeds under no load in experimentation.

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 131

Results with Load Applied 1200 1000 Speeds (rpm)

800 600 400 200 0 -200 0

20

Real rotor speed ANN observed rotor speed Target rotor speed 40 60 80 Time (s)

Figure 28: Measured, ANN's observed speeds at variable target speeds under load torque appliance in

Rotor speed observation error (rpm)

experimentation. 40 20 0 -20 -40 -60 -80 -100 0

20

40 Time (s)

60

80

Figure 29: Speed observation error at variable target speeds under load torque appliance in experimentation.

Target electromagnetic torque (Nm)

7 6 5 4 3 2 1 0 0

20

40 Time (s)

60

80

Figure 30: Target electromagnetic torque at variable target speeds under load torque appliance in experimentation.

Reverse stator current (A)

1.2 1 0.8 0.6 0.4 0.2 0 -0.2 0

20

40 Time (s)

60

80

Figure 31: Reverse stator current at variable target speeds under load torque appliance in experimentation.

132 Artificial Intelligence Resources in Control and Automation Engineering

Mouna and Lassaâd

1.2

Direct stator currents and tracking errors (A)

1 0.8 0.6 Real direct stator current Target direct stator current Tracking error

0.4 0.2 0 -0.2 0

20

40 Time (s)

60

80

Direct and reverse stator voltage (v)

Figure 32: Real and target direct stator currents and tracking error at variable target speeds under load torque appliance in experimentation. 200

vdsref vqsref

150 100 50 0 -50 -100 0

20

40 Time (s)

60

80

Figure 33: Direct and reverse stator voltage at variable target speeds under load torque appliance in experimentation.

Rotor flux posistion (modulo 2pi)

20

5 0 15

15.5

16

16.5

17

28.5

29

29.5

30

60.5

61

61.5

62

15

5 0 28 10 5 0 60 5

0 0

20

40 Time (s)

60

80

Figure 34: Rotor flux position at variable target speeds under load torque appliance in experimentation.

Phase stator current (A)

8 6 4 2

1 0 -1 15 1 0 -1 30 1 0 -1 60

15.5

16

16.5

17

30.5

31

31.5

32

60.5

61

61.5

62

0 0

20

40 Time (s)

60

80

Figure 35: One phase stator current at variable target speeds under load torque appliance in experimentation.

Artificial Intelligence and Electrical Drives

Artificial Intelligence Resources in Control and Automation Engineering 133

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]

Ben Hamed M., Sbita L. Internal model controller of an ANN speed sensorless controlled induction motor drives. J. App. Sc., 7, 2007, 1456-1466. Sbita L., Ben Hamed M. Internal Model Controller for a Scalar Controlled Induction Motor Drive: Design and Experiments. J. Elec. Sys., 3, 2007, 73-87. M. Hinkkanen. PhD Thesis Flux estimators for speed sensorless induction motor drives, Helsinki University of Technology, 2004. I. Boldea, S.A. Nasar. Electric Drives, Taylor and Francis Group, France 2005. J. Campbell, M. Summer. Practical sensorless induction motor drive employing an artificial neural network for online parameter adaptation, Proceedings of IEEE Electric. Power Application, 2002, 255-260. A. Goedtel, I.N.D. Silva and P.J.A. Serni. Neural network based estimation of torque in induction motors for real time applications, Proc. of IEEE Electric components and system, 2005, 363-387. C. Kubota. DSP Based Speed Adaptative Flux Observer of Induction Motor. IEEE Trans. Ind. Applicat, 29, 1993, 344-348. G. Henneberger, B.J. Bransbash and T. Klepsh. Field Oriented Control of Synchronous and Asynchronous Drives Without Mechanical Sensors Using a Kalman Filter. IEEE trans. Ind. Electronics, 2006, 53, 96-119. M. Simoes, and Bose. Neural Network Based Estimation of Feedback Signals for a Vector Controlled Induction Motor Drive. IEEE Trans.Ind. Applicat, 29, 1995, 344-348. P. vas. Vector control of AC machines. Oxford. U. K,charendon 1992. J.Heredia, F. Hidalgo, and J. Duran. Sensorless Control of Induction Motors by Artificial Neural Network. IEEE Trans. On Ind. Applicat., 48, 2001, 1038-1040. S. Hwan and al. Speed Sensorless Vector Control of An Induction Motor Using Neural Network Speed Estimation. IEEE Trans on Ind. Applicat., 48, 2001, 609-614. B. Badsi, A. Elguermazi and A. Masmoudi. On the comparison between different space vector PWM strategies implemented in FSTPI-fed induction motor drives. J. Comp, Mat. Elec. Electronic. Eng., 26, 2007, 127-147. M. S. Huang and C. M. Liaw. On the control of a field -weakened induction motor having improved transient and static performances, Taylor and Francis, Electric power and systems. 32, 2004, 587-609. M. Caudili, C. Millier. Understanding Neural Networks. Massachusetts, the MIT Press. P. G. J. Lisboa, Caudili M., Millier C. Neural Networks: Current Applications. London, Chapman & Hall. Ben Hamed M., Sbita L., Abboud W. ANN Speed Sensorless Fuzzy Control of DRFOC Induction Motor Drives, Leo. Elec. J. Prac. Techno., 16, 2010, 129-150. Ben Hamed M. PhD thesis. Contribution à la Commande Numérique et Synthèse Multi Algorithmiques d'observation du flux et de la vitesse d'un Actionneur à Induction, University of Gabes Tunisia, 2009. Sbita L., Ben Hamed M. Fuzzy controller and ANN speed estimation for induction motor drives, Proc. of the 4th IEEE Intern. Conf. on system, signals and devices, 2007. Teranp T., Asai K. Fuzzy theory and its applications. NewYork, the Academic press Ltd. Dreylus C. and al. Neural network: Methodologies and Applications. France. Hwan S. and al. Speed Sensorless Vector Control of an Induction Motor Using Neural Network Speed Estimation. IEEE Trans. Ind. Applicat. 48, 2001, p. 609-614. Ben Hamed M., Sbita L., Sensorless indirect stator field oriented control of induction motor based on Luenberger observer, Proc. of IEEE Intern. Symp. On. Ind. Electron, 2006, 2473-2478. Ben Hamed M., Sbita L. Speed sensorless direct stator field oriented control of induction, Proc. of IEEE Intern. Conf. Ind. Techno, 2006. 961-966. Sbita L., Ben Hamed M. An MRAS-Based Adaptative full order Luenberger observer for sensorless DRFOC of induction motors. J. Auto. Contr. Sys. Eng, 7, 2007, 11-20. Wishart M.T., Harley R.G. Identification and control of induction machines using artificial neural networks. IEEE Trans. Ind. Applicat, vol. 31, 1995, 612- 619. Simoes M.G., Bose B. K. Neural network based estimation of feedback signals for a vector controlled induction motor drive. IEEE Trans on Ind Applicat.,31, 1995, 620- 629. Marino P., Milano M.: Robust neural network observer for induction motor control, Proc. of the IEEE. Conf. on Power Electron. 1997. Vas P. Artificial intelligence based electrical machines and drives-Application of fuzzy, neural, fuzzy-neural and genetic algorithm based techniques. Oxford university press.

134 Artificial Intelligence Resources in Control and Automation Engineering

[30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40]

Mouna and Lassaâd

Pinto J., Bode B.K., Borges L.E., Kazmierkowski M.P. A neuronal network based space vector PWM controller for voltage fed inverter induction motor drive, IEEE Trans on Ind. Applicat., 36, 2000, 1628 -1636. Sbita L. dissertation of HDR. Contribution in digital control of systems: Application to digital control of sensorless induction motor drive, University of Sfax Tunisia, 2008. Mondal S.K., Pinto J.O.P., Bose B. K. A neural network based space vector PWM controller for a three-level voltage-fed inverter induction motor drive. IEEE Trans on Ind. Elec. Applicat., 38, 2002, 660-669. Tsoukalas L. H., Uhrig R.E. Fuzzy and neural approaches in engineering, New York Wiley. Sousa G.C.D., Bose B.K. A fuzzy set theory based control of a phase-controlled converter dc drive. IEEE Trans on Ind. Elect. Applicat., 30,1994, 34-44. Sousa G.C.D., Bose B.K., Cleland J. G. Fuzzy logic based on-line efficiency optimization control of an indirect vector controlled induction motor drive. IEEE Trans. Ind. Elect., 42, 1995, 192-198. Simoes M.G., Bose B.K., Spiegel R. J. Design and performance evaluation of a fuzzy logic based variable speed wind generation system. IEEE Trans. Ind. Applicat., 33, 1997, 956-965. Ben Hamed M., Sbita L., Abboud W. Neural Networks for controlled Speed Sensorless Direct Field Oriented Induction Motor Drives, J. Elec. Eng., 2008, 8, 84-90. Ben Hamed M., Sbita L. Fractional order speed observer for sensorless induction motor drives, R. Elec. Eng.,3, 2008. Mohanty K.B. Sensorless Control of a Linearized Induction Motor Drive, International R. Elec., 2, 2007, 386397. Messaoudi M., Kraiem H., Ben Hamed M., Sbita L., Abdelkrim M. N. A Robust sensorless direct torque control of induction motor based on MRAS and extended Kalman filter. Leo. J. Sc, 12, 2008, 35-56.

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 135-158

135

CHAPTER 6 Mobile Manipulator with Resolved Acceleration and Knowledge-Based Fuzzy Active Force Control M. Mailah1*, E. Pitowarno2 and A. Noshadi1 1

Department of System Dynamics and Control, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia and 2Electronic Engineering Polytechnic Institute of Surabaya, ITS Sukolilo, Surabaya 60111, Indonesia Abstract: Perfect motion control of a mobile robotic system combining both the kinematic and dynamic aspects is still regarded as a challenging and complex problem to deal with. The proposed research study is aimed towards realizing the solution through the application of a novel and robust intelligent Active Force Control (AFC) based strategy to control a differentially-driven wheeled Mobile Manipulator (MM) system with nonholonomic constraint. The scheme incorporates an intelligent mechanism using a Knowledge-Based Fuzzy (KBF) algorithm to compute the essential estimated parameter in the AFC loop to trigger the compensation effect. A set of knowledge is investigated based on a priori knowledge with respect to a hypothesis that there exists a close relationship between the signal patterns of the generated tracking error with the actual velocity and the estimated inertial parameters of the MM system. The feasibility of implementing a Resolved Acceleration Control (RAC) technique as a kinematic-based feedback controller for the MM is first explored. The system is further consolidated with the inclusion of an intelligent AFC with KBF element that is directly embedded in cascaded form with the RAC part, serving as a dynamic-based scheme for the enhancement of the overall control scheme. The robustness of the proposed AFC-based scheme is rigorously tested with the application of the introduced disturbances in the form of constant braking torques, impact and vibratory excitations. The robust and accurate trajectory tracking performance of the system is particularly highlighted in the study to illustrate the practical viability of the proposed scheme.

Keywords: Mobile manipulator, knowledge-based fuzzy active force control. 1. INTRODUCTION A mobile manipulator is basically a conventional robotic arm mounted on a moving base. It can be compared to a human being considering the body (with legs) as the mobile base while the arm represents the robot manipulator in which it must be effectively controlled when performing a specific task. As an example, a painter carrying out a task needs to coordinate or control simultaneously and continuously both his arm and body movements together with the appropriate handling of the brush so that a desirable goal could be achieved from executing the task effectively in a given time frame. It is indeed more challenging when the human operators are replaced by robots or automated machines in performing tasks that are particularly repetitive, boring, dangerous and hazardous in nature. A comprehensive study on the coordinated motion control of the MM system involving its kinematics and dynamics should be rigorously explored to develop a robust and effective scheme that can produce results comparable to those executed by human operators. One of the research areas that is actively being investigated is on the dynamics and control of mobile manipulators which have been associated with many useful real-world applications. Mobile manipulators are increasingly being employed in many applications such as in bomb disposal robots, robotic space vehicles, mobile transporters, hazardous materials handling systems and robotic maids. The level of complexities of the systems largely depends on the specific design requirements and the methods employed to control them effectively. *Address correspondence to M. Mailah: Department of System Dynamics and Control, Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved-© 2012 Bentham Science Publishers

136 Artificial Intelligence Resources in Control and Automation Engineering

Mailah et al.

In recent years, there has been a great deal of research interest and enthusiasm in studying the mobile manipulator systems [1-5]. The study of mobile manipulator is mostly directed towards a central question: how to move or navigate the MM effectively from one location to another in a structured or unstructured environment. It mainly focuses on two important aspects related to the motion of the MM, i.e., the system kinematics and the dynamics. The kinematic analysis is particularly useful to describe the robot’s workspace and motion path planning tasks including obstacles avoidance, collision free moving capability and manoeuvrability, while the dynamic analysis is typically related to the system stability and robustness. There are a number of extensive works that can be found in literature related to the kinematic control of the mobile manipulator [6-11]. The works mostly focus on the methods to solve the redundancy problems with the dynamics not specifically addressed. A number of nonholonomic mobile robot tracking control methods was proposed, such as the velocity and heading angle (v, ) control [12], intelligent steering control and path planning using genetic algorithm [13] and an improved (v, ) control with exponential stabilization using Lyapunov’s stability technique [14]. The models used in the cited works are more concerned about the kinematics and the studies mostly relate to establishing the mobile robot’s stability under varied initial conditions and trajectory input functions. Other researchers focus on the robust motion control approaches via backstepping kinematics to dynamic method [15], (v, ) control with conversion to torque control with neural network method [16] and adaptive control [17]. In actual implementation pertaining to robot’s motion, it is also typical to address the control problem involving the robot’s dynamic. At this juncture, designing appropriate controller can lead to significant improvement in performances [18]. Combining both the extensive kinematic and dynamic aspects for a perfectly motion control of any dynamical system still remains a complex and challenging problem. In recent years, several researchers have contributed to solving this problem using a number of methods such as those related to adaptive [19], optimal [20], neural network [21], fuzzy [22] and model-based [23]. Active Force Control (AFC) combined with a Resolved Acceleration Control (RAC) is yet another method to control effectively a mobile manipulator which is central to the proposed study. The control system combines both the kinematic and dynamic aspects seamlessly to yield a powerful two Degree-of-Freedom (DOF) controller that has been shown to perform very robustly using simple algorithms. The AFC technique that was pioneered by Hewit and Burdess [24] is one of the potential force control schemes. The main feature of AFC is that it can be practically implemented to the control of general dynamical systems including robots. The AFC method involves a direct measurement of the acceleration and force quantities plus the appropriate estimation of the inertia matrix to set off its control strategy. The RAC part that was first proposed by Luh et al. [25] is a powerful acceleration mode control method that is still considered as one of the best control options due to its simplicity in real-time implementation and that it could improve the performance of the existing conventional servo control as reported in a number of studies [26]. In the proposed research, the RAC was designed as the explicit kinematic-based controller while the AFC was applied as the dynamic controller. A simplified coordinate (x, y) and heading angle ( ) of a nonholonomic MM motion control using RAC combined with an intelligent AFC-based scheme is thus proposed. By using this RAC-based x and y control, the scheme would have a more flexible position, speed and acceleration control. This flexibility is gained by the use of simultaneous input reference positions, velocities and accelerations. To tackle the robot’s dynamic problem particularly those involving disturbances and uncertainties, the AFC element was directly combined in series with the RAC part to form a RACAFC system [27]. A novel value-added approach employing a Knowledge-Based Fuzzy (KBF) logic is embedded into the AFC loop to produce a more robust and precise operation of the mobile manipulator in tracking a given trajectory. The overall proposed system to be known as RACKBFAFC scheme, primarily uses a fuzzy logic method and a knowledge-based inference mechanism as described in [28] to estimate the appropriate inertia matrix of the system necessary for the AFC loop to compensate for any disturbances and uncertainties during the robot’s operation. The disturbances are modelled as braking, impact and vibratory forces to test the system performance in terms of robustness and effectiveness when the MM is performing trajectory tracking tasks. The underlying principles pertaining to the important elements of the proposed control system and their implementation are systematically explained in the respective sections of this chapter.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 137

2. MOBILE MANIPULATOR MODEL The mobile manipulator considered in the study can be represented as shown in Fig. (1).

(xE, yE)

m 2 , I2 Y

E ©

m1, I1

r

l2 l22

2

1

©

F (xF, yF)

l1

G © m 0 , I0

2b y

l11

x

d X

Figure 1: A mobile manipulator.

For the manipulator serially mounted on board the platform at point F, its forward kinematics can be described using equations (1) to (6) as follows: xE yE

xF yF

cos sin

cos sin

sin cos

J11 J 21

sin cos

J12 J 22

1

…

(1)

2

where

xF yF

J11

l1 sin

J12

l2 sin(

J 21

l1 cos

J 22

l2 cos(

J12

1

1

l2 sin(

2

1

l1 cos

J 22

l2 cos(

1

and

R

L

2

2

2

2

1

2

r 2 d r 2b

L

…

(2)

R

)

)

…

(3)

) )…

l2 cos(

1

1

)

l2 cos(

1

J 21

where

l2 sin(

1

r 2 d r 2b

1

(4) 2

)…

)…

(5) (6)

are the angular velocities of the left and right wheels, respectively.

A MM dynamic equation can be obtained using the Lagrangian approach [18, 21] in the form expressed by equation (7):

138 Artificial Intelligence Resources in Control and Automation Engineering

M (q)q C (q, q)q F (q, q) AT (q)

Mailah et al.

B( q ) …

d

(7)

where, q is a generalized coordinate, M(q) is a symmetric and positive definite inertia matrix, C (q, q) is the centripetal and Corioli’s matrix, F (q, q ) is a friction and gravitational vector, A(q) is a constraint matrix, is a Lagrange multiplier which denotes the vector of constraint forces, d is a bounded unknown disturbance vector including the unstructured dynamics, B(q) is the input transformation matrix and is a torque input vector. 3. PROPOSED CONTROLLER The proposed scheme as shown in Fig. (2) is made up of two main controllers constituting a two DOF controller, i.e., RAC and KBFAFC that can be theoretically designed independently. RAC

qref

+

Q

AFC Section

qcom

+

ref

coordinate transformation

act

IN/Ktn

Ktn

Mobile Manipulator

act

1 s

act

1 s

act

+

+

KBF 1/Ktn

Q*

×

IN

Kp

qref qref

qact

-

+

+

INKBF

KBFAFC

Kd

coordinate transformation

qact

-

coordinate transformation

Figure 2: Proposed RACKBFAFC scheme.

In Fig. (2), the subscripts of ref, com and act denote the reference, command and actual respectively. Q indicates the bounded (known or unknown) disturbances, Ktn are the torque constants for the actuating motors (left and right wheels of the platform and joint-1 and joint-2 of the manipulator), INKBF is the estimated inertia matrix from the KBF system, and Q* is the estimated disturbance calculated by the KBFAFC algorithm. The IN contains in the block just outside the AFC section (left side of the Fig.) is the estimated IN that is based on the optimum IN obtained from the RACAFC scheme. It should be noted that the input of the INKBF function is the angular velocity of the joints and wheels. 3.1. Resolved Acceleration Control (RAC) The RAC method is attributed to works pioneered by Luh et al. [25]. In the proposed study, it is specifically designed to handle the entire kinematic problem of the MM while the KBFAFC that is incorporated serially to the RAC deals with the dynamic aspect. For convenience, the important RAC output equations are rewritten in this section as follows:

xFcom

xFref

Kd ( xFref

yFcom

yFref

Kd ( yFref

Fcom

ref

xEcom

xEref

Kd (

ref

Kd ( xEref

xFact ) K p ( xFref

xFact ) …

yFact ) K p ( yFref act

) Kp (

ref

xEact ) K p ( xEref

yFact ) … act

)…

xEact ) …

(8) (9) (10) (11)

Mobile Manipulator with Resolved Acceleration

yEcom

yEref

Kd ( yEref

yEact ) K p ( yEref

Artificial Intelligence Resources in Control and Automation Engineering 139

yEact ) …

(12)

The subscripts ref, com, act and e refer to the input reference, command, actual output and error respectively. Kp and Kd are the proportional and derivative gains respectively. The sub-indexes E and F in the above equations refer to the specific locations on the mobile manipulator model as defined in Fig. (1). The gains were heuristically tuned and assumed to have appropriate values for the proposed scheme. All controller output equations, i.e., equations (8) to (12) have negative feedback elements that contribute to the generation of relevant error signals that are subsequently coupled with the respective controller gains. In the global MM motion control, the controller equations can be considered as separated controls but are to be executed simultaneously in real-time. 3.2. Active Force Control (AFC) The research on Active Force Control (AFC) is initiated by Johnson (1971) and later Davison (1976) based on the principle of invariance and the classic Newton’s second law of motion [24]. It has been demonstrated that it is possible to design a feedback controller that will ensure the system setpoint remains unchanged even in the presence of the disturbances or adverse operating and loading conditions provided that the actual disturbances can be modelled effectively. Hewit and Burdess (1981) proposed a more complete package of the system such that the nature of disturbances is oblivious to the system and that it is readily applied to multi-degree of freedom dynamic systems [24]. Thus, an effective method has been established to facilitate robust motion control of dynamical systems in the presence of disturbances, parametric uncertainties and changes that are commonly prevalent in the real-world environment. Mailah and coworkers extended the usefulness of the method by introducing intelligent mechanisms to approximate the mass or inertia matrix of the dynamic system to trigger the compensation effect of the controller [29-34]. The AFC method is a technique that relies on the appropriate estimation of the inertial or mass parameters of the dynamic system and the measurements of the acceleration and force signals induced by the system if practical implementation is ever considered. For theoretical simulation, it is normal that perfect modeling of the sensors is assumed and that noises in the sensors are totally neglected. In AFC, it is shown that the system subjected to a number of disturbances remains stable and robust via the compensating action of the control strategy. A more detailed description on the mathematical treatment related to the derivation of important equations and stability criterion, can be found in [24, 35]. For brevity, the underlying concept of AFC applied to a dynamic rotational system is presented with reference to Fig. (3). Disturbances

Q PD controller

Desired position +

Gc(s)

d

-

Actuator +

KGa(s)

+

T +

Dynamic system

1 s2

G(s)

+ Torque sensor

Measured acceleration

Accelerometer

'

W(s) K

I' Measured torque

T' +

Estimated disturbance

H(s) Position sensor

Figure 3. A schematic diagram of an AFC scheme.

The notations used in Fig. (3) are as follows:

Q'

-

Estimated inertia

Actual position

140 Artificial Intelligence Resources in Control and Automation Engineering

:

desired joint position

:

actual joint position

K

:

constant gain

G(s)

:

dynamic system transfer function

Ga(s)

:

actuator transfer function

Gc(s)

:

outer loop controller

H(s)

:

sensor transfer function

W(s)

:

weighting function

Q

:

disturbances

T

:

applied torque

I

:

mass moment of inertia

:

angular acceleration

d

Mailah et al.

The computed variable Q’ often known as the estimated disturbance is obtained by considering the following expression: Q’ = T’-I’ ’…

(13)

where the superscript ’ in equation (13) denotes a measured, computed or estimated quantity. T’ can be readily measured by means of a torque sensor and ’ using an accelerometer. I’ may be obtained by assuming a perfect model, crude approximation or intelligent methods [30]. Q’ is then passed through a weighting function W(s) to give the ultimate AFC signal command to be embedded with an outer control loop. This creates a two DOF controller that could provide excellent overall system performance provided that the measurement and estimated parameters were appropriately acquired. The outer control loop can be a Proportional-Integral-Derivative (PID) controller, Resolved Acceleration Controller (RAC), intelligent controller or others deemed suitable. It is apparent that a suitable choice of W(s) needs to be obtained that can cause the output invariant with respect to the disturbances Q such that: Ga(s)W(s) = 1…

to be made (14)

In other words, if W(s) in equation (14) is chosen as the inverse of Ga(s) with Q’= Q, then perfect force control should be possible [24]. A set of outer control loop control is applied to the above open loop system, by first generating the world coordinate error vector, e = ( d- ) which would then be processed through a controller function, Gc(s), typically a classic Proportional-Derivative (PD) controller that can be represented by:

u( s) Gc (s)e(s) ( Kp

Kd s)e(s) …

where u(s)

:

control signal

(15)

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 141

e(s)

:

error signal

Kp

:

proportional gain

Kd

:

derivative gain

It is common that the gains in equation (15) can be acquired using techniques such as Ziegler-Nichols, root locus or pole placement methods apart from heuristic means. Note that the proposed study utilizes a RAC with PD element. The main computational burden in AFC is the multiplication of the estimated inertial parameter with the angular acceleration of the dynamic component before being fed into the AFC feedforward loop. Mailah et al. [29], Mailah [30] and Pitowarno et al. [27, 28] have demonstrated the effectiveness of the AFC scheme applied to rigid robot arms. Gigih et al. have equally shown a robust intelligent AFC method that is capable of controlling a vehicle suspension system and effectively suppressing the introduced disturbances [33, 36]. 3.3. Knowledge-Based Fuzzy (KBF) The phrase ‘knowledge-based fuzzy control’ which was first quoted in Rhee et al. [37] is comprised of two parts, i.e., knowledge-based system and fuzzy control. The former can be deduced as systems or methods that employ human expertise to derive its explanations, procedures, algorithms and its concluded rules that will be applied. Rhee et al. rigorously described how to implement a KBF technique in control systems. A method for fuzzy control of system based on a concept of human thinking was investigated. The fuzzy controller consists of a knowledge-based containing a number of process time responses. The basic elements employed were cells in which an input and corresponding output of system were stored. The cells were organized according to different types of relations and that the result was defined as the knowledge structure. The control design was distinguished in two phases. The first phase is the learning process (i.e., knowledge investigation and representation) in which the relations between input and corresponding output are investigated. In this phase the knowledge structure is constructed. Then, the second phase is on the implementation of the knowledge structure to control the process. In this research project, a similar way of KBF control incorporated to AFC scheme is proposed in order to design a robust motion control of a mobile manipulator. The application of the KBF logic mentioned above to feedback control is rarely found in literatures. Most of the implementations are in data retrieval and image segmentation/processing that is very useful in medical diagnosis system. An investigation on KBF method that used genetic algorithm to refine the knowledge representation and acquisition can be seen in [38] where a fuzzy petri-net to perform the fuzzy reasoning was incorporated. Nanayakkara and Samarabandu implemented a class of KBF to automatic model-based image segmentation system in medical diagnosis system [39]. The implementation on ultrasound image of prostate was successfully demonstrated. Tsai et al. proposed a multi-layer of fuzzy systems to a robot manipulator control [40]. They provided the rule-base in the form of “IF situation THEN the control input” rather than “IF situation THEN the value of some nonlinear function of the robot”. Although the fuzzy system was not described as a KBF, it is clear that this fuzzy system was clearly derived from the knowledge of the robot operation in several cases. Hildebrand and Fathi introduced an approach for nondestructive quality testing by using a KBF method [41]. The colour information of the welding joints was used as the knowledge-base. The consideration was the heat applied during the welding process causes a characteristic change of the color of the affected steel. Based on this, a proper fuzzy inference mechanism that would be included to the fuzzy system was designed. An application of a KBF control can be found in reference [42]. The contribution was about tuning algorithm and rule-base reduction through knowledge-based investigation. An algorithm that computed the inconsistencies and redundancies in the overall rule set was used based on the newly proposed measure of equality of the individual fuzzy sets. The algorithm was successfully tested experimentally for the control of a commercial household vacuum cleaner. In the proposed research, the KBF part is principally embedded into the AFC scheme (loop) such that the estimated inertia IN of Fig. (4) is achieved via a KBF mechanism.

142 Artificial Intelligence Resources in Control and Automation Engineering

.. ref

IN Ktn

+

+

Mailah et al.

Q

.. act

Mobile Manipulator

Ktn +

1 s Knowledge-Based Fuzzy

' +

1 Ktn

Q'

.

-

act

IN

Figure 4: Proposed KBFAFC applied to the manipulator.

Recalling the output equation of the AFC algorithm as in equation (13) and with reference to Fig. (3), the actuated torque can be expressed as shown in equations (16) and (17) [27]:

IN

ref

I m K tn …

act

(16)

or rewritten as: IN

IN

ref

I m K tn …

act

(17)

where I’m is the measured armature current of the torque motor and Ktn is the motor torque constant. In Fig. (2), the adaptation through the KBF algorithm is imposed to IN within the AFC section denoted by INKBF such that the KBFAFC output equation can be written as: IN F

IN KBF

ref

I m K tn …

act

(18)

and the simplified dynamic equation of the system is: act

IN F

ref

IN KBF

act

I m K tn

Q…

(19)

with IN KBF

f KBF (

act

)…

(20)

where INF is the fixed IN that was obtained as the optimum IN of the existing RACAFC and INKBF is the variable or adaptive IN that should be computed by the KBF algorithm (fKBF) based on the actual velocity in equations (18) and (19) denotes an estimated or act as described in equation (20). The superscript measured quantity. The angular velocity with respect to the subsystem to be controlled (at each joint and wheel) is employed as the respective input function of fKBF. The proposed KBF design related to the knowledge-based reasoning (as a basis for the design of the fuzzy inference mechanism), knowledge investigation and representation, and knowledge acquisition and processing will be presented in the following subsections. 3.3.1. Knowledge Investigation and Representation The first procedure to implement the KBF system is knowledge investigation. The objective is to collect knowledge for the purpose of reasoning of the fuzzy system that will be applied to the proposed KBFAFC.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 143

In a standard knowledge-based system, the knowledge can be the information that is captured from the system. In a global point of view, the knowledge on MM systems and its environments including task specifications, control system characteristics and its responses, and the global constraints (kinematics and dynamics) of the robot world can be illustrated as shown in Fig. (5). They are represented within the respective circles or nodes. Physical MM

Global Constraints

MM’s Control

MM’s Task

MM’s Environment

Global Responses Note:

is relationship

Figure 5: An illustration of the global knowledge of mobile manipulators.

In principle, knowledge from any node in Fig. (5) can be initially investigated. The arrows are used to relate the knowledge being captured to a more concerned view of the knowledge in the next node. In this study, an investigation was designed and carried out based on Fig. (6) that shows the flow of the signals to or from the nodes. Physical MM

2 MM’s Task

1

Global Constraints

MM’s Control

MM’s Environment

Global Responses

Figure 6: Selected semantic networks of the MM’s knowledge structure.

Fig. (6) basically consists of two standard semantic networks. The first network follows a flow that is serially conFig.d as steps or sequence of relationships: Physical MM MM’s Task MM’s Environment MM’s Control Global Responses. The second flow can be described as follows: Physical MM Global Constraints MM’s Control Global Responses. At this juncture, the two procedural knowledge investigations are performed with the same most concerned views that are related to global responses. The node MM’s Control is used as an overlapping viewpoint that can be more qualitatively investigated. Following similar steps as proposed in [41] and [43], the viewpoint of node MM’s Control can be expressed as: Vi

{NcMM ' s _ Control ,{

R}, STEP} …

(21)

where Vi is viewpoint, Nc is current node, { R} is a set of labels, STEP is a qualitative investigation as described in equation (21). In this study, a qualitative knowledge investigation was conducted that includes essential elements in the proposed control scheme, the robot’s task and the existence of disturbances (with or without disturbances). Fig. (7) shows the qualitative investigation in a semantic network.

144 Artificial Intelligence Resources in Control and Automation Engineering Robot Task

specific speed

Mailah et al.

Robot Structure

Holonomic constraint

Robot Environment

Nonholonomic constraint

Mobile Platform

Manipulator No disturbances

Control

with specific disturbances

Control

Control

Control

Responses

Figure 7: Qualitative investigation in a semantic network.

The nodes of responses in Fig. (7) are used as qualitative measurements in which each of the prior nodes can be inferred to it. Some specified input functions are then implemented in both the simulation and experimental works so that the MM can be programmed to perform specific trajectory tracking task. The common control scheme used is the RAC with basic AFC (RACAFC scheme using fixed inertia matrix estimator). Note that the scheme is applied prior to the development of the proposed RACKBFAFC scheme. Once the knowledge is fully acquired from the knowledge investigation procedure, it is then implemented into the design of the proposed scheme. Illustrations of the Features or Knowledge Extraction Procedure in Knowledge Investigation are shown in Figs. (8) to (10). The Figs. illustrate how the knowledge required by the proposed system is investigated. Fig. (8) depicts the movement of the MM in which it can be seen that the manipulator’s tip end position produces a curvy path in the direction of the robot’s forward movement. Fig. (9) shows the error signal produced from the simulation work while Fig. (10) exhibits the corresponding error based from an experimental study. It is obvious that the error patterns for both studies are repetitive in nature. Also, it is found that the same input function that is used in the simulation study which when implemented to the experimental robot as shown in Fig. (11), yields similar error pattern over a period of time.

Figure 8: Trajectory tracking of the mobile manipulator.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 145

  Simulation: RACAFC

Experiment: RACAFC scheme error at arm

(mm)

repeating sequences

error at body

repeating sequences

1 cycle

1 cycle

1 cycle

1 cycle

1 cycle

Figure 9: Track error at the tip end position for five cycles of repeating tasks (simulation).

1 cycle

1 cycle

1 cycle

1 cycle

Figure 10: Track error at the tip end position for four cycles of repeating tasks (experiment).

Figure 11: The experimental mobile manipulator.

Thus, some essential features of the track error signal patterns have been investigated and identified. This information provides the required ‘knowledge’ for the subsequent implementation of the overall control scheme. It is evident that the error changes (increases or decreases) continuously according to specific positions of the robot system during the tracking operation. Based on the knowledge investigation procedure, a number of hypotheses can be deduced as follows: There exists a correlation between the track error pattern and the nonlinearity of the system dynamics specifically related to the robot motion. In this context, the inertia matrix IN of the manipulator can be considered as the non-linear element of interest. The ripples, spikes, and other features of the error pattern show the ‘intensity’ of the non linearity of the system that occur at specific locations and times. Some repeating error signal patterns produced at certain robot motion event could specifically imply the ‘knowledge’ that could provide a means to improve the control method. Hence, it is deemed to be a wise decision if we consider only locations where ‘positive’ definite error patterns are shown for an effective robot control action without having to take into account the full trajectory of the robot motion. This directly implies that the necessary good or essential knowledge features have been acquired.

146 Artificial Intelligence Resources in Control and Automation Engineering

Mailah et al.

Figs. (12) to (14) show the responses in relation to the respective error signal patterns generated by the MM motion subject to specific loading conditions, i.e., through the application of constant braking torque, impact and vibration disturbances. In the figures, the blue and green arrows indicate that there is a strong relationship between the actual velocities signal and the error signal pattern at the tip (arm) position. It can also be seen that the instant error signal patterns at specific times denoted by the arrows are unique and specific with respect to the corresponding actual velocities at the joints and the nature of the applied disturbances. Based on this, it is then concluded that each response can contribute to the good ‘behaviour’ of the control system. In other words, such ‘behaviour’ is considered as the captured knowledge.

Figure 12: Angular velocity and TTE relationship for RACAFC with constant torque disturbance.

Figure 13: Angular velocity and TTE relationship for RACAFC with impact disturbance.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 147

Figure 14: Angular velocity and TTE relationship for RACAFC with vibration.

Table 1 shows the representation of knowledge that has been captured through the investigation. Table 1: The knowledge representation Prior knowledge

Related knowledge

Relation descriptions

Specific responses

Empirical hypothesis/ suggestion

Robot subsystems (joints and wheels)

Partial control (holonomic or nonholonomic)

Each subsystem is partially controlled

Error of each subsystem is unique

Error of each subsystem can be partially refined

Inertia of each subsystem

Uncertainties (related to the environment and task)

The uncertainties specifically affect each subsystem

Error of each subsystem is unique

Each of the estimated inertia can be specifically refined

Robot specific task

Actual (angular) velocity of each subsystem

Specific task implies the specific actual velocity of each subsystem

Case 1: When the actual velocity is decreasing, the error is increasing. Case2: When the actual velocity is increasing, the error is decreasing.

The increased error implies that the actual inertia of subsystem is increased or decreased The estimated inertia value should be increased or decreased according to the ‘behaviour’ of the actual velocity

From Table 1, the inertia matrix estimation or adaptation can be deduced such that the increased error can be inferred to as the condition in which the actual estimated inertia matrix applied to the AFC is going to cause a mismatch. Thus, the applied estimated inertia matrix should adaptively be increased or decreased according to the amount of error produced. The decision to increase or decrease the applied estimated inertia matrix depends on the vector (or direction) of the actual velocity. 3.3.2. Knowledge Acquisition and Processing From the hypotheses deduced, an inference mechanism can be derived. In this study, the angular velocity of the robot arm is chosen as the indicator (input function) to describe the relationship between the produced

148 Artificial Intelligence Resources in Control and Automation Engineering

Mailah et al.

error and the actual velocity. The output variable to be computed is the estimated inertia matrix, IN of the system that is necessary for the AFC mechanism. Table 2 shows the derived inference mechanism. Table 2: The inference mechanism

Case Part of velocity signal pattern

Related part of error signal pattern

Actions to be taken

1

set IN pattern as top-bottom-top direction

2

set IN pattern as top-bottom-top direction

3

set IN pattern as bottom-top-bottom direction

4

set IN pattern as bottom-top-bottom direction

Note: The basic IN (top value) uses the crude values: IN = diag{0.0675 0.0675 2.4 2.4}kgm2.

The inference mechanism given in Table 2 can be illustrated visually by studying the graphics shown in Figs. (15) to (18). This is assumed to be effectively designed after the knowledge has been taken into account and the output variable has been constructed based on the input function. The figures illustrate the link between the velocity and inertia matrix that is in turn related to the joints and wheels. Figs. (15) and (16) show the graphical results in the form of angular velocity-IN relationship of the knowledge at the joints of the manipulator with reference to Table 2. Figs. (17) and (18) are the corresponding results for the wheels.

Figure 15: Angular velocity signal as input of KBF for the manipulator.

Figure 16: Expected IN signal as output of KBF for the manipulator.

In Figs. (16) and (18), the red dotted lines indicate the fixed IN without adaptation (for the RACAFC scheme). By implementing the appropriate relationship between the input and the output variables, the design of the fuzzy system is made clear. Hence, in this study, a simple fuzzy structure is selected to demonstrate the feasibility of the proposed method that can lead to simple adjustment of the fuzzy specification.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 149

Figure 17: Angular velocity signal as input of KBF for the platform.

Figure 18: Expected IN signal as output of KBF for the platform.

3.3.3. KBF Design From the knowledge-based procedure described in the previous section and with reference to Tables 1 and 2, a set of KBF functions can be derived as follows: )…

IN KBF1

f KB1 (

IN KBF2

f KBF2 (

act2

IN KBFL

f KBFL (

actL

IN KBFR

f KBFR (

actR

act1

(22)

)…

(23)

)…

(24)

)…

(25)

where f KBF1 ( act1 ) , f KBF2 ( act2 ) , f KBFL ( actL ) , and f KBFR ( actR ) in equations (22) to (25) are specific functions for the respective joints or wheels. In this study, the KBF is designed for each of the subsystem partially in a simple form with single-input and single-output (SISO) configuration rather than designing a universal KBF with four inputs ( act1 , act2 , actL , and actR ) and corresponding four outputs (INKBF1, INKBF2, INKBFL, and INKBFR). The main advantage of considering the designed partial fuzzy system is that it is relatively simple and easy to maintain. In this way, the proposed RACKBFAFC scheme has been designed in the simplest possible form. A Mamdani-type fuzzy system with three triangular shaped membership functions (MF) representing the input and three Gaussian shaped MF of the output are selected for each input-output relationship. The fuzzy variables for the input are namely, smaller, normal and larger. The term smaller was used instead of ‘small’ to imply that it is a derived knowledge (more meaningful) compared to the word ‘small’ which is just an ordinary information. The fuzzy variable normal is to represent the middle (or average) of the input value. Similarly, the term larger can be more meaningful than using the word ‘large’ alone for the knowledge-based system. It is to distinguish the meaning of information and knowledge more precisely [44]. For the manipulator, normal is set to zero velocity by considering that the joints move in two directions (clock wise and counter-clock wise) with limited angle (not more than 180˚ to the left or right). During the operation, zero is the condition in which the link or joint is not actually moved. For the platform, normal is selected to be 1.815 rad/s to meet the desired linear velocity of the MM. However, the setting of normal is adjusted manually using a relatively small value by considering the respective desired angular velocity of joints or wheels. Figs. (19) to (22) show the implementation of the inference mechanism in the KBF design. Considering Figs. (19) to (22) and also with regard to Figs. (15) to (18), all the respective KBF system designs can be accomplished simply by using basic Mamdani types of fuzzy logic with some considerations as follows:

150 Artificial Intelligence Resources in Control and Automation Engineering

Mailah et al.

Figure 19: MF of input of joint-1 and joint-2.

Figure 20: MF of output of joint-1 and joint-2.

Figure 21: MF of input wheel-L and wheel-R.

Figure 22: MF of output wheel-L and wheel-R.

AND method: minimum, OR method: maximum, Implication method: minimum, Aggregation method: maximum, and Defuzzification method: centroid. The rules that satisfy the inference mechanism shown in Figs. (19) to (22) were then designed as follows: 1.

IF actual velocity is smaller THEN inertia matrix is LOW

2.

IF actual velocity is normal THEN output is HIGH

3.

IF actual velocity is larger THEN output is LOW

From the off-line test, this fuzzy system can easily perform an input-output mapping. The trained fuzzy system is then embedded into the overall control scheme for on-line implementation.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 151

4. SIMULATION Fig. (23) shows a Simulink model of the RACKBFAFC scheme.

Figure 23: Simulink diagram of the proposed RACKBFAFC.

Fig. (24) depicts the detailed Simulink diagram that is contained in the KBFAFC block while Fig. (25) shows the detailed diagram of the KBF System block.

Figure 24: Simulink diagram of the KBFAFC block.

The given task of the MM is to move its platform in a circular motion with a curvature radius of 10 m, at a velocity of 0.2 ms-1 (at point F) and the initial heading angle orientation of /2.4 rad to the zero angle of the world Cartesian coordinate. The manipulator is programmed to follow a specified curve track at the righthand side of the platform starting from (10.41, 0.35) m of the world Cartesian coordinate. The initial tip position is set to point (10.55, 0.35) m. The values of Kp and Kd of the RAC schemes were derived from a number of trial runs. Note that the first two elements are related to the two-link planar manipulator while the last three refer to those of the mobile platform. The best combination is given as follows [27]: K pRACAFC

diag 350 350 450 450 0.004

K dRACAFC

diag 320 320 320 320 0.0017

and

152 Artificial Intelligence Resources in Control and Automation Engineering

Mailah et al.

Figure 25: Simulink diagram of the KBF System block.

5. RESULTS AND DISCUSSION For convenience, all the results of the RACKBFAFC scheme pertaining to trajectory tracking control are presented in comparison to the results of the established RACAFC for benchmarking purpose. The Trajectory Track Error (TTE) shall be the main criterion for the performance evaluation of the MM system as it also reflects the robustness of the system in countering the disturbances. The discussion shall be based on the following headings: Effect of constant disturbance torque, Qc Effect of impact disturbance force, Qimp Effect of vibration, Qvib

5.1. Effect of Constant Disturbance Torque, Qc As an initial evaluation on the robustness, constant disturbance torques, Qc, were introduced to the RACKBFAFC where Qc = [Qclink-1;Qclink-2;Qcwheel-L;Qcwheel-R] is set as follows: a.

Qcb

2 2 5

b.

Qcd

30 30 30

5

T

Nm (small Qc),

30

T

Nm (very high Qc).

Figs. (26) to (29) show the TTE of the arm and platform of the RACKBFAFC versus RACAFC scheme. From the figures, it is obvious that RACKBFAFC is superior to RACAFC. The results also show that the variation of the constant disturbance torques can be significantly compensated by the KBFAFC element.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 153

Figure 26: TTE of arm, Qcb = [2;2;5;-5] Nm.

Figure 27: TTE of arm, Qcd = [30;30;30;-0] Nm.

Figure 28: TTE of platform, Qcb = [2;2;5;-5] Nm.

Figure 29: TTE of platform, Qcd=[30;30;30;-30] Nm.

5.2. Effect of Impact Disturbance Force, Qimp Figs. (30) to (33) show the response at the tip end position for RACAFC and RACKBFAFC schemes when the impacts were introduced at t = 8.5 s for the joints, and t = 10 s for the wheels. As can be seen, the error in RACAFC tends to be larger with the increase in the magnitudes of the impacts. In contrast, the RACKBFAFC consistently rejects the effect of impacts even when subjected to the highest impact force at Qgain = 3.

Figure 30: TTE of arm, Qimp, Qgain = 0.1.

Figure 31: TTE of arm, Qimp, Qgain = 0.5.

154 Artificial Intelligence Resources in Control and Automation Engineering

Figure 32: TTE of arm, Qimp, Qgain = 1.

Mailah et al.

Figure 33: TTE of arm, Qimp, Qgain = 3.

Next, an investigation of the moving platform subject to the impacts is discussed. Figs. (34) to (37) show the error at point F of the platform due to the impacts with Qgain = 0.1, 0.5, 1.0, and 3.0. The results obtained as shown in the Figs. are very clear. As predicted, the RACKBFAFC applied to the platform can significantly reject the impacts even at Qgain = 3. The method to adapt the inertia matrix estimation based on evidences (disturbance existences that are measured from the actual velocity) is thus proven to be very effective.

Figure 34: TTE of platform, Qimp, Qgain = 0.1.

Figure 35: TTE of platform, Qimp, Qgain = 0.5.

Figure 36: TTE of platform, Qimp, Qgain = 1.

Figure 37: TTE of platform, Qimp, Qgain = 3.

Mobile Manipulator with Resolved Acceleration

Artificial Intelligence Resources in Control and Automation Engineering 155

5.3. Effect of Vibration, Qvib The robustness of the proposed scheme was also tested by introducing vibratory excitation in the form of a high frequency harmonic force during the trajectory tracking task. Figs. (38) to (41) show the effect of the vibration on the RACKBFAFC at the tip end position. The RACKBFAFC clearly demonstrates the superiority in rejecting the vibration at the tip end position. Even at Qgain = 3, the error produced is less than 0.15 mm margin.

Figure 38: TTE of arm, Qvib, Qgain = 0.1.

Figure 39: TTE of arm, Qvib, Qgain = 0.5.

Figure 40: TTE of arm, Qvib, Qgain = 1.

Figure 41: TTE of arm, Qvib, Qgain = 3.

The effect of vibration on the platform is also well compensated by the RACKBFAFC as shown in Figs. (42) to (45). The average steady-state error of the platform for all introduced vibrations is less than 0.03 mm. In this case, the RACKBFAFC performs much better than RACAFC in which the error is seen to improve by more than 50 %. 6. CONCLUSIONS A novel intelligent-based mobile manipulator system has been realized through the implementation of RACKBFAFC scheme. It is shown to perform excellently for the given trajectory tracking task under the influence of various disturbances. The knowledge-based procedure from knowledge investigation to knowledge processing is proven to be very effective towards designing the proposed fuzzy system to compute the necessary estimated inertia matrix of the MM system. The ‘captured’ knowledge related to the velocity-inertia matrix relationship is successfully applied as a basis to design the KBF for the intelligent AFC of the MM. The design of the partial KBF for each of subsystem related to the joints and wheels is also found to be very efficient in reducing the mathematical burden and complexity of the fuzzy system structure. Thus, RACKBFAFC can be considered as one of the effective practical approaches to robust motion control for mobile manipulator system.

156 Artificial Intelligence Resources in Control and Automation Engineering

Figure 42: TTE of platform, Qvib, Qgain = 0.1.

Figure 43: TTE of platform, Qvib, Qgain = 0.5.

Figure 44: TTE of platform, Qvib, Qgain = 1.

Figure 45: TTE of platform, Qvib, Qgain = 3.

Mailah et al.

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

Y. Umeda and T. Yakoh, “Configuration and readhesion control for a mobile robot with external sensors”, IEEE Ind Electron., vol. 49, pp. 241-247, February 2002. H. G. Tanner, “Nonholonomic navigation and control of cooperating mobile manipulators”, IEEE T Robotic Autom., vol. 19, pp. 53-61, February 2003. E. Papadopoulos, I. Papadimitriou, and I. Poulakakis, “Polynomial-based obstacle avoidance techniques for nonholonomic mobile manipulator systems”, Robot Auton Syst., vol. 51, pp. 229-247, June 2005. H. Najjaran and A. Goldenberg, “Real-time motion planning of an autonomous mobile manipulator using a fuzzy adaptive Kalman filter”, Robot Auton Syst., vol. 55, pp. 96-106, February 2007. L. Cetin and E. Uyar, “Design and control of a mobile manipulator with stereo vision guidance”, Int. J. of Mechatronics and Manufacturing Systems, vol. 2, pp. 369-382, 2009. K. Nait-Chabane, S. Delarue, P. Hoppenot, and E. Colle, “Strategy of approach for seizure of an assistive mobile manipulator”, Robot Auton Syst., vol. 57, pp. 222-235, February 2009. C.C. Wang and V. Kumar, “Velocity control of mobile manipulators”, in IEEE International Conference on Robotics and Automation, 1993, pp. 713-718. C. Perrier, P. Dauchez, and F. Pierrot, “A global approach for motion generation of non-holonomic mobile manipulator”, in IEEE International Conference on Robotics and Automation, 1998, pp. 2971-2976. B. Bayle, J.Y. Fourqet, and M. Renaud, “Manipulability analysis for mobile manipulators”, in IEEE International Conference on Robotics and Automation, 2001, pp. 1251-1256.

Mobile Manipulator with Resolved Acceleration

[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

[33] [34] [35] [36]

Artificial Intelligence Resources in Control and Automation Engineering 157

E. Papadopoulos and I. Poulakakis, “Planning and obstacle avoidance for mobile robots”, in IEEE International Conference on Robotics and Automation, 2001, pp. 3967-3972. T.G. Sugar and V. Kumar, “Control of cooperating mobile manipulators”, IEEE T Robotic Autom., vol. 18, pp. 94-103, February 2002. K. Tchon, “Repeatability of inverse kinematics algorithms for mobile manipulator”, IEEE T Automat Contr., vol. 47, pp. 1376-1380, August 2002. Y. Kanayama, Y. Kimura, F. Miyazaki, and T. Noguchi, “A stable tracking control method for an autonomous mobile robot”, in IEEE International Conference on Robotics and Automation, 1990, pp. 384-389. G. Yasuda and H. Takai, “Sensor-based path planning and intelligent steering control of nonholonomic mobile robot” in 27th Annual Conference IEEE Industrial Electronics Society, 2001, pp. 317-322. F. Pourboghrat, “Exponential stabilization of nonholonomic mobile robot”, Comput Electr Eng., vol. 28, pp. 349-359, September 2002. R. Fierro and F.L. Lewis, “Control of a nonholonomic mobile robot: backstepping kinematics into dynamics”, in 34th IEEE Conference on Decision and Control”, 1995, pp. 3805-3810. R. Fierro and F.L. Lewis, “Control of nonholonomic mobile robot using neural networks”, IEEE T Neural Networ., vol. 6, pp. 589-600, July 1998. T. Fukao, H. Nakagawa, and N. Adachi, “Adaptive tracking control of a nonholonomic mobile robot”, IEEE T Robotic Autom., vol. 16, pp. 609-615, October 2000. Y. Yamamoto and X. Yun, “Effect of the dynamics interaction on coordinated control of mobile manipulators”, IEEE T Robotic Autom., vol. 12, pp. 816-824, October 1996. R. Colbaugh, “Adaptive stabilization of mobile manipulator”, in American Control Conference, 1998, pp. 1-5. A. Mohri, S. Furuno, M. Iwamura, and M. Yamamoto, “Sub-optimal trajectory planning of mobile manipulator” in IEEE International Conference on Robotics and Automation, 2001, pp. 1271-1276. S. Lin and A.A. Goldenberg, “Neural-network control of mobile manipulator”, IEEE T Neural Networ., vol. 12, pp. 1121-1133, September 2001. E. Papadopoulos and J. Poulokakis, “Planning and model-based control for mobile manipulators”, in IEEE/RSJ International Conference on Robots and Systems, 2000, pp. 1810-1815. J.R. Hewit and J.S. Burdess, “Fast dynamic decoupled control for robotics using active force control”, Mech Mach Theory., vol. 16, pp. 535-542, 1981. J.Y.S. Luh, M.W. Walker, and R.P.C. Paul, “Resolved-acceleration control of mechanical manipulator”, IEEE T Automat Contr., vol. 25, pp. 486-474, June 1980. R. Campa, R. Kelly, and E. Garcia, “On stability of the resolved acceleration control”, in IEEE International Conference on Robotics and Automation, 2001, pp. 3523-3528. M. Mailah, E. Pitowarno, and H. Jamaluddin, “Robust motion control for mobile manipulator using resolved acceleration and proportional-integral active force control”, Int J Adv Robot Syst., vol. 2, pp. 125-134, June 2005. E. Pitowarno, M. Mailah, and H. Jamaluddin, “Knowledge-based trajectory error pattern method applied to an active force control scheme”, IIUM Engineering Journal, vol. 3, pp. 1-15, 2002. M. Mailah, J.R.Hewit, and S. Meeran, “Active force control applied to a rigid robot arm”, Jurnal Mekanikal, vol. 2, pp. 52-68, June 1996. M. Mailah, “Intelligent active force control of a rigid robot arm using neural networks and iterative learning algorithms”, PhD thesis, University of Dundee, UK, 1998. M. Mailah and O.M. Yong, “Intelligent adaptive active force control of a robot arm with embedded iterative learning algorithms”, Jurnal Teknologi, vol. 35, pp. 85-98, December 2001. E. Pitowarno and M. Mailah, “Control of mobile manipulator using resolved acceleration iterative learning proportional-integral active force control”, International Review of Mechanical Engineering, pp. 549-558, September 2007. G. Priyandoko, M. Mailah, and H. Jamaluddin, “Vehicle active suspension system using skyhook adaptive neuro active force control”, Mech Syst Signal Pr., vol. 23, pp. 855-868, April 2009. M. Mailah, H.J. Abadi, M.Z.M. Zain, and G. Priyandoko, “Modeling and control of a human-like arm incorporating muscle models”, P I Mech Eng C-J Mec., vol. 223, pp. 1569-1577, July 2009. J.R. Hewit and J.S. Burdess, “An active method for the control of mechanical systems in the presence of unmeasurable forcing”, Mech Mach Theory., vol. 21, pp. 393-400, 1986. M. Mailah and G. Priyandoko, “Simulation of a suspension system with adaptive fuzzy active force control”, Int J Simul Model., vol. 6, pp. 25-36, March 2007.

158 Artificial Intelligence Resources in Control and Automation Engineering

[37] [38] [39]

[40] [41] [42] [43] [44]

Mailah et al.

F.V.D. Rhee, H.R.V.N. Lemke, and J.G. Duckman, “Knowledge based fuzzy control of system”, IEEE T Automat Contr., vol. 35, pp. 148-155, February 1990. Y. Ouci and E. Tazaki, “Heuristic approach to topology generation for knowledge based fuzzy petri nets”, in 2nd Intenational Conference on Knowledge-Based Intelligent Electronics System, 1998, pp. 331-334. N.D. Nanayakkara and J. Samarabandu, “Unsupervised model based image segmentation using domain knowledge-based fuzzy logic and edge enhancement”, in International Conference on Multimedia and Expo, 2003, pp. 577-580. C.H. Tsai, C.H. Wang, and W.S. Lin, “Robust fuzzy model-following control of robot manipulator”, IEEE T Fuzzy Syst., vol. 8, pp. 462-469, August 2000. L. Hildebrand and M. Fathi, “Knowledge-based fuzzy color processing”, IEEE T Syst Man Cy C., vol. 34, pp. 499-505, November 2004. M.K. Ciliz, “Rule base reduction for knowledge-based fuzzy controllers with application to a vacuum cleaner”, Expert Syst Appl., vol. 20, pp. 175-184, January 2005. Y. Kuwata abd M. Yatsu, “Managing knowledge using a semantic network”, in AAAI Spring Symposium: Artificial Intelligence in Knowledge Management, 1997, pp. 94-98. G.M. Marakas, Decision Support Systems in The Twenty-First Century. New Jersey: Prentice Hall, 1999.

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 159-179

159

CHAPTER 7 Intelligent Systems Used in Continuous Casting Process Gelu Ovidiu Tirian* “Politehnica” University of Timisoara, Faculty of Engineering Hunedoara, Hunedoara, Romania Abstract: This first chapter of this paper work refers to Simulink implementation of a neural and fuzzy system of crack prediction, detection, and rejection during the continuous casting processes. The neural and fuzzy system is made up by a neural network used for fissure detection and a fuzzy controller for predicting and rejecting them. This system uses a signal received from the neural network and some data to correct the casting speed and the primary cooling water. The second part of chapter describes the industrial Fuzzy System Decision (FSD) deployment of crack prediction and elimination as well as the adaptive system meant for eliminating any sliding between the semi-finished and the roll drawings (SFA), when the FSD casting speed performs any corrections. The last part of chapter describes an adaptive fuzzy system to eliminate any sliding that may occur between the billets and roll drawings in steel continuous casting plants. Any sliding may compromise the tuning speed of hardware caused by prediction system and crack elimination – therefore, speed corrections are common and applied as a necessary step. Design and production systems are based on an original research of the author.

Keywords: Fuzzy system, neural network, control, crack, continuous casting. 1. INTRODUCTION During the process of continuous casting the melted steel from the melting pot is passed - through the distributor - into the water-cooled crystallizer tank. Thus, there is a crust whose outside layers turn solid later on. One of the main problems of this process is that crack may occur or the material breaks, due to several reasons [4]. When the portion that had suffered the crack gets out of the crystallizer, the cast iron pours out and the casting process must be stopped. Such an accident is avoided by detecting any crack and reducing the casting speed, or even increasing the primary cooling water flow which allows the iron to become solid [9, 10]. Fig. (1) describes the steel continuous casting equipment.

Casting mould Distribution device

Cast steel Immersion tube

Crystallizing Meniscus Liquid area Supporting rolls

Cutting point

Solidification crust Length of the solidification chord Semi-product Cast wire Figure 1: Steel continuous casting equipment. *Address correspondence to Gelu Ovidiu Tirian: “Politehnica” University of Timisoara, Faculty of Engineering Hunedoara, No.5 Revolutiei Street, 331128, Hunedoara, Romania; Tel:+40-254-207540; Fax:+40-254-207501; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

160 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

The elements which make the continuous casting equipment are described according to the moment they occur throughout the elaboration process of steel continuous casting. They are the following: the cast device, the distributor, the crystallizing apparatus, and the oscillometer, the secondary cooling off area; the exaggeration and straightening area, the start beam, the aggregate for semi-products yielding. In Fig. (9), we describe the structure of the crack detection systems. Such cracks may occur during the continuous casting process, especially in case of those who are based on a neuronal network [13]. This network produces a “1”-logical output signal when it detects a primary crack inside the crystallizing apparatus, otherwise it produces a “0”- output signal. This information should be used properly in order to avoid any possible crack before the material exits the crystallizing apparatus [11]. Since the current installations cannot do that, this paper proposes a fuzzy solution which could be added to the current structure of the control system of the continuous casting. Besides that, it uses all the features of the fuzzy logic [1, 2, and 4] and it is able to predict any possible crack [5], providing the best solutions and actions in order to prevent any cracks inside the crystallizing apparatus. We can use this structure with any type of continuous casting installation, but only along with the neuronal network used for primary crack detection [9, 10]. Thus, considering the prediction principle we have chosen, we believe it is able to eliminate any fault during the casting process - if the cast material shows any cracks when coming out of the crystallizing apparatus [6]. 2. SIMULINK IMPLEMENTATION SYSTEM A. System Description To review the functioning of both neural and fuzzy systems, we carry out the simulation in a MatlabSimulink environment. The implementation scheme is described in Fig. (2). [17].

Figure 2: Implementation in Matlab-Simulink system.

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 161

Block Temperature Data Generation In the beginning, we have used recordings of the unfolding process. The best solution was to use two separate sets, one normal and one in case there was a crack. To switch between the two sets of data, we used a switch - control implemented with Simulink-State flow. Depending on a given parameter at the input of the block, it switched between the two sets of data (1 - with cracks, 0 – no cracks). Block "CT Temperature" operated successively (every 120 seconds) the "0" or "1" data, which basically caused the crack. All data was memorized in “look-up data” tables. Neural Data Processing Block We are able to identify any fissure if using data received from all 48 thermocouples mounted in 12 rows and 4 columns (on one side of the crystallizing apparatus) [12]. For each thermocouple, a dynamic neural network processed 10 consecutive temperature values. Any data received from a dynamic network is processed by a space network which analyzes the values received from the two adjacent thermocouples. The input size value of such space networks (0 or 1) is introduced into a logical SAU (OR) block [9]. Fig. (3) describes the connection between two dynamic networks and a space network for data processing from two adjacent thermocouples.

Figure 3: Connecting two dynamic networks to a space network for data processing from two thermocouples.

According to the results of the logical SAU operation (we have analyzed the output values of the space networks), when leaving the neural block we get a 0-value (there is no primary crack), and a 1-value (there is a primary crack) [8, 12]. Fuzzy Controller (RG-F) According to the value of the output value of the neural network, RG-F starts two different base sets: a corresponding base in case there are no cracks for “0” (225 rules), and a corresponding base in case there are some primary cracks (75 rules) [7]. The first set has four entries (casting speed, primary cooling water flow, distributor temperature, and technological risk). We can illustrate them during the process (in real situations). We have used the “Process data block” to simulate it. The “technological risk” parameter is not necessary for the second set of rules, because its value is the highest since we have already detected some cracks. The two outputs of the RG-F (pv - speed correction, and pq - flow correction), are used for the limitation block [10]. Fig. (4) describes the implementation of RG-F “0”, and Fig. (5) describes the implementation of RG-F “1” in the environment Matlab-Simulink.

162 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

Figure 4: Implementation in Matlab - Simulink to RG-F with basic rules “0”.

Figure 5: Simulink implementation of the RG-F with basic rules "1".

Block Prescribing Block prescribing replaces any value required for both speed and flow (v *, q *) inside the installation their new corrected values vc, qc), and the result is the RG-F outputs. For simulation, the values v * and q * are considered equal to all measured sizes of the process (from "Block data processing"). B. Validation of Simulated System Operation We have applied two different sets of data measured during the current process and stored into tables in case of validation of the simulated system operation, and for the input crack detection neural network. One of the sets refers to the situation when there are no cracks and the other one in case cracks occur. Neural network outputs reach both “0” and “1” values, and they show the network works correctly and it detects all cracks (in case they occur). For each of the two cases generated at the RG-F input, there are several input values (flow, speed, temperature, and risk). If the neural network has produced a number “0” output, there are no cracks or flow, speed, and temperature. If the neural network has produced a number “1” output value, there are primary cracks. These values are described in Figs. (6) and (7):

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 163

a)

Time variation (120 seconds) of RG-F input values,

b)

Speed correction and new speed values,

c)

Flow correction and new flow values.

Fig. (6) describes the situation during the first simulation of 30 seconds, when both the cooling water flow and casting speed are low, the temperature inside the crystallizing apparatus is high, and the technological risk is low. Speed correction is very low, hence required casting speed is almost unchanged. During the next simulation of 30 seconds, the technological risk increases, the fuzzy controller causes speed correction, and it also avoids any crack (while casting speed decreases). During the whole time, cooling water flow increases significantly. We can see that the other two simulation rounds are similar. When analyzing all cases described in Fig. (6) and Fig. (7), we draw the following conclusions: -

RG-F analyzes the input values and elaborates speed corrections and water flow correctly, according to the two base sets connected to each output of the neural network,

-

Fore-writing block corrects all required values for speed and flow, according to RG-F outputs.

By simulating in a Matlab-Simulink system, we have proved that all solutions are correct – predicting, detecting and rejecting any crack during continuous casting. Such simulation is made for performing a check out of the fuzzy system. During operation, all size values do not change so fast, hence some input value combinations are not that predictable. Once the system is implemented, the rules referring to such situations could be eliminated.

a) RG-F Input Data

164 Artificial Intelligence Resources in Control and Automation Engineering

b) Output data – speed

c) Output data - flow Figure 6: RG-F Validation (RN=0).

Gelu Ovidiu Tirian

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 165

a) RG-F input data

b) Output data – speed

c) Output data - flow Figure 7: RG-F validation (RN = 1).

166 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

3. ADAPTIVE CONTROL SYSTEM OF CONTINUOUS CASTING PROCESS BASED ON A FUZZY LOGIC MECHANISM Amongst others, the fuzzy system refers to the casting speed corrections which apply during the current control [8, 15]. These loop corrections are designed like some steps and may cause a sliding between the bar and roll drawing (sliding occurs when the casting process starts, but it is not very important). To remove any sliding which may compromise the speed tuning, we have designed a new fuzzy system. We refer to it later on. This system was used in practice and confirmed the elimination of slides. 3.1. Proposed System Structure As it can be seen in Fig. 1, the drive system consists of 4 molded bar induction motors, supplied by frequency converters, and it has been designed and built by Siemens Company (SIMOVERT system). Frequency converters contain, in addition to other standard parts, elements associated to speed control loop (the controller is PI) [16]. However, for a uniform distribution of the effort amongst the 4 subunits, a converter works as a master and the other 3 as slaves. From the outside, this configuration allows us to use the required speed only for the master converter, and it should send it forward to the other elements (slaves), while ensuring an equal torque to all 4 wheels that entail the drawing rolls. All tunable parameters can be modified (those externally included) through the data line that is connected to the converters. The analysis of fuzzy prediction system used for cracks rejection and simulation – with the Simulink system - has proved that, depending on specific cases, it had applied some speed loop tuning [14]. Sudden application of such corrections will result in rolling-sliding reel drives, practically extending the time elapsed between the occurrence and correction when the bar (and not the engine) reaches a new value prescribed speed. The emergence of sleeping leads to decreasing the slipping friction coefficient bar-roll, and to time increasing. Because effective methods of prediction and rejection of cracks depend on how quickly the tuning speed increases, we designed elimination and slipping control system as much as possible. The principle method is presented in Fig. (8). M

M

M

M Continuously cost semi-finished

roll drawing

nr

free roll

n

Speed Speed digital digital transducer transducer

n slide (digital signal)

Figure 8: Drive system of the bar cast.

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 167

As noted, we mounted a free additional roll which works when moved by the cast bar. If the bar does not slide along the shooting rolls (driven by each engine respectively), two roller speeds turn equal and therefore there will be no sliding. The bigger the sliding is, the more the two speeds will vary. Speed is measured with numerical transducers like those of the facility meanwhile the installation of an additional roller does not cause any problems. An item of loss will produce a "gliding" signal. To eliminate slipping we designed a fuzzy system [16], examining two input quantities: speed correction ( v) imposed by the fuzzy system for crack elimination, the sliding itself (s) which changes the dynamic behavior of the engine speed tuning loop [17], and coefficient Ti editing (full time) of the PI controller of the frequency converter. Fig. (9) highlights the adaptive system for speed controller. slide, (s) speed corection, ( v)

Fuzzy system

Reference value for speed, compensated vc

+ -

Ti

Controller PI

Process

v

Figure 9: Tuning system for speed control.

3.2. Designing a Sliding Fuzzy-Control System In order to achieve a sliding fuzzy-control system we have chosen two sizes – one input and one output. We have also established some linguistic terms (for inputs and outputs), the connection functions, and rule basis [16]. Fig. (10) describes a block diagram of fuzzy systems realized with the Matlab software. Figs. (11-13) refer to membership function of the two sizes - input and output. The rule basis is reproduced in Fig. (14), a simulation for a real case - in Fig. (15), and control surface in Fig. (16).

Figure 10: Block diagram of fuzzy sliding system.

Figure 11: Membership function "slide".

168 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

Figure 12: Membership function "speed correction".

Figure 13: Membership function “Ti”.

Considering all process features we have adopted some trapezoidal-type connection functions for both input and output sizes. The type of connection functions for input quantities is described in both Figs. (11) and (12). For the "slipping" input size we have chosen three linguistic terms, meanwhile for "speed correction" we have chosen five linguistic terms. For output size “Ti” we have chosen three linguistic terms [16]. Tables 1, 2, and 3 describe the real values and normal values for selected linguistic terms of input and output sizes. 1) slide (s). Table 1: Number of states: 3 States

Real domain [%]

Standardized values domain

small

0 30

0 0,3

medium

15 85

0,15 0,85

big

70 100

0,7 1

2) casting speed correction (casting speed correction, [m/min]). Table 2: Number of states: 5 States

Real domain [%]

Standardized values domain

Vmall

0 -4

0 0,25

small

-4 -8

0,15 0,45

medium

-8 -12

0,35 0,65

big

-12 -16

0,55 0,85

Vbig

-16 -20

0,75 1

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 169

3) Ti (real time) Table 3: Number of states: 3 States

Real domain [Ti(s)]

Standardized values domain

small

35 40

0 0,375

medium

38 50

0,25 0,75

big

48 62

0,625 1

The max-min inference is a Mamdani-type [3], the inference table for some of the rules is shown in Fig. (14).

Figure 14: Inference table for RG-F slide.

Command areas are obtained by simulation, according to the graphics represented in Fig. (10) – they are shown in Figs. (15) and (16).

Figure 15: Control surface Ti = f (speed correction, sliding).

170 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

Figure 16: Control surface Ti = f (sliding, speed correction).

3.3. Implementation and Simulation of the Rate Tuning System It was performed by using both the Matlab-Simulink simulation environment implementation and the simulation of casting speed control system, so the current system for speed control and the block system equipped with the sliding fuzzy control - was proposed. Simulation of the Current System for Speed Control Regarding the output size (constant Ti of PI controller), Fig. (17) presents the Simulink implementation of the existing loop speed control inside the facility, the gantry system has the following data: KL=10, T1=1s, T2=2s, transfer function: T2 T1 K L

GL s s

1 T1

s

1 T2

(3)

Granting parameters of PI controller initially mounted are: Kp=0.0125 and Ki=1/Ti=0.027(Ti=37s). Given these parameters, the speed loop response is shown in Fig. (18).

Figure 17: Speed tuning loop.

In this case it is noted that time growth is about 7s. Due to this rather quick response, it is safe emergence of slipping material-imposing drawing roller gears. By changing the parameters of the PI regulator to the following values - Kp = 0.0125 and Ki=1/Ti=0.027(Ti=62,5s) - we get the response represented in Fig. (19). In this case (highly regarded), the increasing time reached almost 14s, and it provided the complete disappearance of sliding – it was verified through experiments. We can also observe that both slope overtuning and lower overall growth rate disappeared, which avoided any further slide [16].

Artificial Intelligence Resources in Control and Automation Engineering 171

Amplitude

Intelligent Systems used in Continuous Casting

Time (s)

Amplitude

Figure 18: Speed response system for Ti=37s.

Time (s) Figure 19: Speed response system for Ti = 62.5 s.

Implementation and Simulation Speed Tuning System Equipped with Fuzzy Sliding Control The adaptive system used to eliminate sliding was implemented in Simulink and it is described in Fig. (20). The two entries (slide and speed correction) were applied to random signals; at the exit, we have obtained the system response for each combination of inputs – Fig. (21). We should point out that input quantities are, in fact, generated by the system designed for prediction and crack elimination ( v speed correction and speed corrected value), as well as for sliding detection system. Fig. (21) describes the control system responses: a)

Speed response,

172 Artificial Intelligence Resources in Control and Automation Engineering

b)

Speed correction,

c)

Slip,

d)

Tir (integral time of controller),

e)

vc (corrected value speed).

Gelu Ovidiu Tirian

Figure 20: Simulink implementation of speed tuning system. a) Speed response

b) Speed correction

c)Slip

d)Tir

e) vc

Figure 21: Control system responses.

Analyzing the curves represented in Fig. (21) and implemented by the adaptive Simulink system for casting speed tuning – Fig. (20) - we note that:

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 173

-

“v ” = speed correction (produced by the system of cracks prediction and elimination) is turned into real values (inside the "adaptation correction” block) along with the amount required for the “v” speed (constant value; equal to 1.8 [m/min]) – they both make up the right value speed – “vc “, - required by the tuning loop.

-

Ti = the output size for sliding fuzzy system is transformed into real values (values 0 1) and turned into real values – “Tir adaptation block”), forming a Tir variable (integral time of controller, with values between 37 [s] and 62 [s]).

-

The sliding entry fuzzy control system has been used for random values - between 0 and 1 and close to 30 [s]. This enabled us to change the Tir, and finally the speed response curve – Fig. (8). The analysis of this last curve reveals that the speed required corrections were made with an appropriate dynamic behavior: during the first 30 [s] the slipping regulator was small; the casting speed increased rapidly and stopped at about 1.8 m/min; later on, the correction had very low speed – almost approaching 0; when Tir 30 [s], both speed correction and slipping increased; required speed dropped to 1.75 m/min; shooting increased to 58 [s]; and the response fell slowly to 1.75 m/min without any sliding.

Evolution curves mentioned in the following periods of 30 [s] confirm that the proposed system leads to our scope: the actual implementation of speed corrections without any sliding. This was confirmed during the industrial working. 4. EXPERIMENTAL DETERMINATION To validate industrial principles and methods of cracks prediction and elimination, specialists have tried to implement it in a real continuous casting plant, while in operation – Fig. (22).

Figure 22: Real continuous casting plant.

Since it is an operating plant, implementation was accomplished without significant disruption of the production process; otherwise, it would have immediately lead to unacceptable economic loss for the company.

174 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

Major subassemblies of the installation and key operating parameters during tests are described in Fig. (23) - a print-screen of the process control system.

Figure 23: Continuous casting facility – print-screen of the industrial process control system.

This was implemented with the help of the SDF industrial cracks prediction and elimination adaptive system meant to eliminate semi finished draw rollers sliding (SFA). Working conditions were very strict, enabling minimum disruption process and assistance of specialized hardware. Implementing solutions within the industrial plant consisted mainly of the following [18]: A.

Two plates full development were purchased, software included.

B.

On one plate, we implemented ADF cracks prediction and elimination system, and on the other plate the adaptive system to eliminate sliding (SFA). Since the software implementation is performed in C-language, related programs were designed.

C.

Specialists have introduced these systems within the driving continuous casting process.

D.

Technological parameters were performed during the casting: up to 1042 a.m., cooling water flow was very high, the casting speed reached its average values, temperature distributor and technological risk were high, and SDF pointed out high risk of cracks. Then, when we did a very small correction of cooling water flow rate and a large correction of casting speed - 1.6 m/min. At 1043 a.m., the distributor temperature was lower and got smaller. SDF noticed a decrease of rupture risk, enabling a low speed correction – Fig. (24). Accordingly, the casting speed increased to 2 m/min. Following the rules, the first situation corresponds to rule 207, and the second to rule 205. From Fig. (24) - recorded directly from the process - we conclude that SDF interpreted all situations correctly and applied related remedies.

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 175

E.

We have also made a series of tests to check the operation of the SFA. Its implementation was carried out by specialists of the beneficiary, in accordance to their internal rules.

F.

All the records presented happened while using the production control system. Implementation agreement with the SDF and SFA systems has been very difficult, since the continuous casting line was still working. The above mentioned agreement was achieved and supported by business professionals within the company. They led all the research they considered very interesting and useful. They also wanted confirmation of their practice.

Figure 24: Casting speed evolution meant to decrease crack risk.

Initially SFA was no longer used. At 1030 a.m., we had to increase the casting speed - from 1-2 m/min. In Fig. (25) we can see that there is an increase in active roll. Because of the fast growth, sliding occurred between the roll and the cast material. Passive wheel speed changes like in Fig. (26), and lasts for 48 seconds. The duration is rather big. At 1036 a.m., the phenomena repeated in reverse order (we ordered a decrease in the speed drawing). It was confirmed that in case sliding occurs more often, the effective time of casting speed could change. Next, we have used API system. At 1041 a.m., we ordered to increase the speed of 1-2 m/min again – Fig. (27). Note that in this case the active drawing roller speed varies a little (approximately 18 seconds), bar cast speed increased and no sliding occurred – Fig. (28) - within 18 seconds. To conclude, we see that SFA acted under rule base.

176 Artificial Intelligence Resources in Control and Automation Engineering

Figure 25: Variation of active wheel speed without SFA.

Figure 26: Variation of passive wheel speed without SFA .

Gelu Ovidiu Tirian

Intelligent Systems used in Continuous Casting

Artificial Intelligence Resources in Control and Automation Engineering 177

Figure 27: Active wheel speed variation while API is working.

Figure 28: Variation passive roller speed while SFA is working.

178 Artificial Intelligence Resources in Control and Automation Engineering

Gelu Ovidiu Tirian

5. CONCLUSIONS In the first part, this chapter describes a Matlab-Simulink simulation of the entire system. Considering this aspect, we have designed the simulation design, designed input sign generators, a neural network, a fuzzy regulator, and the fore-writing block for speed and flow values. When using this method, we have been able to use several input data sets, and the design has correctly generated all output values, acknowledging the whole system. In the second part of this chapter, the system we propose allows sliding elimination of billets and draw rolls used during steel continuous casting. Functioning along with cast material crack prediction and elimination, sliding could jeopardize its actions. We designed and developed a fuzzy regulator by analyzing two input sizes: slip and speed correction change during the whole regulator time, and hence the speed loop has a dynamic behavior. We have come up with an adaptive system for casting speed control, which has confirmed our goals when simulated with Matlab-Simulink. Finally, we implemented an industrial SDF crack prediction and elimination adaptive system to eliminate sliding of semi-finished draw rollers (SFA). Following implementation of the SDF and SFA, industry achieved very good results, which enabled eliminating both crack and sliding of semi-finished draw rolls. REFERENCES [1]

[2] [3]

[4] [5] [6] [7] [8] [9]

[10]

[11]

[12] [13]

[14]

S. Bouhouche, M. Lahreche, A. Moussaoui and J. Bast, Quality Monitoring “Using Main Component Analysis and Fuzzy Logic. Application in Continuous Casting Process”, American Journal of Applied Science (AJAS), 4(9), ISSN: 1546-9239, 637-644, 2007. D. Drainkov, H. Hellendoom and M. Reinfrank, Introduction to Fuzzy Control, Springer-Verlag, Berlin, 1993. I. Lagrat, A. El Ougli and I. Boumhidi, “Optimal Adaptive Fuzzy Control for a Class of Unknown Nonlinear Systems”, WSEAS TRANSACTIONS on SYSTEMS and CONTROL, Issue 2, Volume 3, February, ISSN: 1991-8763, 89-98, 2008. C.C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller”, IEEE Trans. Systems, Man & Cybernetics 20(2), 404-435, 1990. C. Li, “Thermo-Mechanical Finite Element Model of Shell Behaviour in Steel Continuous Casting”, In: Sixth Asia-Pacific Symposium on Engineering Plasticity and its Applications, 2-6 December, Sydney, Australia, 2002. T. Nakamura and K. Kazuho, “Breakout Prediction System in Continuous Casting Process”, United States Patent, No.5, 548,520, Date of Patent 20 aug.1996. R.E. Precup, “Fuzzy Controllers”, Academic Horizons Publishing House, ISBN: 973-9400-61-2, Timi oara, Romania, 1999. J. Singh and A. Ganesh, “Design and Analysis of GA Based Neural/Fuzzy Optimum Adaptive Control”, WSEAS TRANSACTIONS on SYSTEMS and CONTROL, Issue 5, Volume 3, ISSN: 1991-8763, 2008. G.O. Tirian, “Neural System for CraCk Detection in Continuous Casting”, In: 12th International Research/Expert Conference - Trends in the Development of Machinery and Associated Technology TMT 2008, Istanbul, Turkey, August 26th-30th, pp. 649-652, 2008. G.O. Tirian and C. Pinca-Bretotean, “Software Implementation of Neuronal Systems Enabling Wire Breaking Prediction with Continuous Casting”, Proceedings of the 7th WSEAS International Conference on Circuits, Electronics, Control and Signal Processing, Tenerife, Spain, December 15-17, 151-156, 2008. G.O. Tirian, S. Rusu-Anghel, M. P noiu and C. Pinca-Bretotean, “Control of Continuous Casting Process Using Neural Networks”, Proceedings of the 13th WSEAS International, Rhodes Island, Greece, July 23rd-25th, ISSN: 1790-5109, ISBN:978-960-474-099-4, 199-204, 2009. G.O. Tirian and C. Pinca-Bretotean, “Applications of Neural Networks in Continuous Casting”, WSEAS TRANSACTIONS on SYSTEMS, Issue 6, Volume 8, June, ISSN: 1109-2777, 693-702, 2009. G.O. Tirian, O. Prostean and I. Filip, “Control System of Continuous Casting Process for Crack Removal”, In: 5th International Symposium on Applied Computational Intelligence and Informatics (SACI), ISBN: 978-14244-4478-6, pp. 265-269, Timi oara, Romania, 2010. G.O. Tirian, O. Prostean, S. Rusu-Anghel, C. Pinca-Bretotean and D. Cristea - “Fuzzy System for Implementing Crack Control with Continuous Casting“, In: Annals of DAAAM &Proceedings of the 20th International

Intelligent Systems used in Continuous Casting

[15]

[16]

[17]

[18]

Artificial Intelligence Resources in Control and Automation Engineering 179

DAAAM Symposium, Volume 20,No.1, ISSN 1726-9679, ISBN 978-3-901509-70-4, pp.1661-1662, 25th-28th November, Vienna, Austria, 2009. G.O. Tirian, G. Prostean, S. Rusu-Anghel and D. Cristea “Adaptive Control System of Continuous Casting Based on a Fuzzy Logic Mechanism“, IEEE International Conferences on Computational Cybernetics and Technical Informatics, ISBN 978-1-4244-7431-8, pp. 379-382, 27th-29th May, Timisoara, Romania, 2010. G.O. Tirian, C. Pinca and M. Topor, “Simulation of Neural and Fuzzy System to Predict, Detect and Eliminate Crack with Continuous Casting”, International Symposium on Advanced Engineering &Applied Management 40th Anniversary in Higher Education, 4th-5th November, Hunedoara, section II, pp 145-150, ISBN 978-973-009340-7, 2010. G.O. Tirian, C. Pinca, C. Chioncel and S. Mezinescu “Industrial Implementation of Prediction, Detection, and Crack Removal System with Continuous Casting”, International Symposium on Advanced Engineering &Applied Management 40th Anniversary in Higher Education, 4th-5th November, Hunedoara, section II, pp. 13-18, ISBN 978-973-0-09340-7, 2010. M.F. Zulfatman and Rahman, “Application of Self-Tuning Fuzzy PID Controller on Industrial Hydraulic Actuator Using System Identification Approach” International Journal on Smart Sensing and Intelligent Systems, vol.2, no.2, pp. 246-261, June 2009.

180

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 180-192

CHAPTER 8 A Novel Electric Load Demand Forecaster Using Taguchi’s Method and Artificial Neural Network Albert W.L. Yao1*, J.H. Sun1, H.T. Liao2, C.Y. Liu3 and C.T. Yin4 1

National Kaohsiung First University of Science and Technology, Taiwan; 2Ming Hsing University of Science and Technology, Taiwan; 3Southern Taiwan University, Taiwan and 4Tongtai Machine & Tool Co. Ltd., Taiwan Abstract: The use of Artificial Neural Network (ANN) for electric load forecasting has been proposed in many studies. Among these studies, the daily peak load or total load with weather consideration was mostly predicted in order to dispatch high-quality electricity or assess electric load efficiently for power utilities. However, load demand forecasting from the standpoint of consumers is seldom discussed. With the global market competition, enterprises invest in instruments to cut down on large electricity bills of operating costs. A formal study shows that the regular ANN training model was inadequate to deal with volatile load patterns, especially in Very Short-Term Electric Demand Forecasting (VSTEDF). In this paper, we present Taguchi’s and rolling training methods of ANN for VSTEDF. By using this proposed rolling training model, the electric load demand is predicted precisely every 2 minutes. The forecasting error is smaller than 3%. Compared with the conventional ANN model and Grey model, the proposed Taguchi-ANN-based predictor has better accuracy in the application of VSTEDF. The improved Taguchi-ANN-based electricity demand forecaster in conjunction with the PC-based electricity demand-control system is a cost-effective and efficient means to manage the usage of electricity.

Keywords: Artificial neural networks (ANN), electric load forecasting. 1. INTRODUCTION Due to the lack of domestic natural energy resources, over 95% of the energy consumed in Taiwan is imported from overseas, and owing to the growth of the economy and global market competition, the supply and demand for high-quality and inexpensive electric power has become an important issue to electric power plants, business owners, and government. In order to assess electricity requirements efficiently and supply high-quality electricity to consumers economically, electric power companies face financial and technical challenges. Tracking electric load generation at all times and knowledge of the future load is a basic requisite in the efficient operation of a power-generating facility. In the past few decades, numerous researchers have presented different methods for electric load forecasting. Among the studies carried out, many models for load forecasting have been proposed, such as time-series models, regression-based models, ANN models and Grey prediction. These models are reported and documented showing success in long-term, medium-term, short-term, and very-short-term forecasting [1-8]. Many factors (such as weather, day, hour, human, social and other activities, random effects, etc.) affect power load nonlinearly. These factors complicate accurate forecasting of load. Operating costs of the power system depend on the forecasting accuracy. Numerous researchers have adopted ANN for load forecasting. Fung and Tummala [1] combined economic factors such as electricity price, gross domestic product, and weather conditions to predict the long-term load consumption for each electricity market in Hong Kong. Charytoniuk and Chen [2] focused on predicting relative changes in load-based. Instead of modeling relationships between load, time, weather conditions, they extrapolated recently observed load patterns to the nearest future. Srinivasan et al. [3] used a three-layer-architecture Back-Propagation Network Model (BPN) to predict the daily peak load in *Address correspondence to Albert W.L. Yao: National Kaohsiung First University of Science and Technology, Taiwan; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

A Novel Electric Load Demand Forecaster

Artificial Intelligence Resources in Control and Automation Engineering 181

Singapore. Lu et al. [4], Kiartzis [5], Khotanzad [6], Chow and Leung [7], and Bakirtzis [8] used different BPN models to predict hourly load, daily total load, and daily peak load. However, the load demand forecasting from the standpoint of consumers is seldom discussed. With increased competition in the global market, enterprises have recently invested more in instruments to reduce large electricity and operation costs in order to increase business competitiveness. Additionally, power companies generally have many different rate schedules and penalty policies of poor-power-factor loads to customers. Therefore, the practice of demand control of electric system has drawn a lot of attention from governments, manufacturers, and researchers. Likewise, the electric bill is always one of the largest monthly expenses at educational institutions. In 2003, a cost-effectively PC-based Automated Monitoring and Controlling Electric System (AMCES) was developed and installed at National Kaohsiung First University of Science and Technology (NKFUST) to monitor and control the electric load on campus [9]. The AMCES system is a closed-loop control system with an artificial intelligence based predictor of ANN model. However, the conventional ANN model was inadequate to deal with a volatile electric load system on campus. The aim of this study is to design an ANN-based dynamic forecaster for VSTEDF. The testing region is at NKFUST, Taiwan. We present a novel method for establishing the training data of ANN to overcome the deficiencies of Back-Propagation Network (BPN) on VSTEDF. This chapter is organized as follows. Section 2 begins with the system configuration of the AMCES at NKFUST. Section 3 shows our preliminary forecasting results using conventional BPN. Section 4 presents the development of rolling model of BPN for VSTEDF. Section 5 illustrates the results and discussions. Section 6 ends with the conclusion of this chapter. 2. SYSTEM FRAMEWORK A network AMCES was developed at NKFUST to monitor and control the electric load on campus [9]. The configuration and the components of the AMCES, which is based on PC-based Open-Modular-Controllers (OMC), a PC-based visual Human-Machine Interface and Data Acquisition System (HMI/DAS), are shown in Fig. (1). The present AMCES provides an on-line economical and effective service to supervise and control the electric facilities fulltime.

High Level Language Module

HMI Station

Campus Network / Ethernet

Open Modular Controller

… … … … … …

RS485

…

Digital Power Analyzer

Figure 1: Configuration of AMCES and its components. It is based on PC-based OMC, a PC-based visual HMI/DAS and digital power analyzers.

182 Artificial Intelligence Resources in Control and Automation Engineering

Yao et al.

One important feature of this hybrid AMCES platform is that its information can be transferred through network. OMC provides a reliable instrument for demand control of electricity, using PC-based HMI/DAS, whereby OMCs are optimized for executing data collection and on-demand control of electricity. The PC, which is running HMI/DAS at the front-end which is full of graphics and report tools, makes intuitive operation interfaces. Information from this platform can be distributed through a company’s local area network or the World Wide Web (WWW). 3. PRELIMINARY FORECASTING BY CONVENTIONAL BPN The past research of ANN-based load forecasting often involved the daily peak load or total load with the factors of temperature, seasons, or days. Fig. (2) shows the typical ANN architecture for electric load forecasting. It includes temperature, electric load and days as inputs for ANN training. The selection of input variables for ANN training always plays an important role. ANN establishes the relationships between the inputs and outputs through the training operation. If inputs do not represent relevant information to the predict output, ANN cannot be expected to accurately predict the dependent outputs [10]. However, there are no general rules for selecting input variables. It depends heavily on the experience or preliminary tests [11].

Figure 2: Conventional ANN architecture for load forecasting. It often includes the temperature, load, and the daytypes as input variable for the neural network.

In our preliminary study, we adopted a conventional BPN model and considered the electric loads and the temperatures of the last 2 and 4 minutes, and the temperature of the next 2 minutes as the training inputs for the BPN. Then, using this established model to forecast and examine the electric load for the next 2 minutes (see Table 1). The forecasting values of the conventional BPN were shown in Fig. (3). As can be seen, the total average absolute error is about 14.1%. Hence, the conventional BPN model is clearly inadequate to deal with a volatile system like VSTEDF. The volatility of the usage of electricity on NKFUST’s campus is possibly due to the load characteristics of lamps, motors, and air-conditioning varying according to class schedules and the operation of equipment. Weather-related effects are also a significant factor. Heat waves and humidity in southern Taiwan are major factors influencing electric loads in summer. Specifically, the electric load for lighting and air-conditioning is greatly affected by the temperature and the presence of clouds. However, other uncontrolled factors affecting the electric load of the indoor activity are class schedules, the attendance of students, laboratory hours, and so on. The pattern of electric load consumption is not always regular in the daily use of electricity on campus. Table 1: The description of input variables of VSTEDF by using the conventional BPN model. Input nodes 1 & 2 are loads of the last 2 and 4 minutes respectively. Input nodes 3 & 4 are the temperatures of the last 2 and 4 minutes. Input node 5 is the temperature of the next 2 minutes. The output variable is the load prediction. Input node

Variables

1&2

Load (M – i ), i = 2, 4,

3&4

Temperature (M – i ), i = 2, 4,

5

Temperature for the next 2 minutes (M + 2)

Output node

Forecasting load

*M = Minute

A Novel Electric Load Demand Forecaster

Artificial Intelligence Resources in Control and Automation Engineering 183

Figure 3: Preliminary forecasting result by conventional BPN model, which considers the electric load and temperature as the input variables of the network, shows that the conventional BPN model shows poor results on VSTEDF.

From our preliminary study, the distribution plot of the load versus the temperature is shown in Fig. (4). It clearly indicates that the factor of temperature is less relevant to the electric load for short-term prediction. Therefore we considered the relationship of load-temperature as a relatively long time constant and ignored the temperature input in this study. KW

Figure 4: Distribution plot of load versus temperature. It shows that the electric load is less relevant to the temperature.

4. ROLLING MODEL OF BPN FOR VSTEDF A. Rolling Model of BPN Input Patterns Conventional BPN-based load forecasting is a kind of nonlinear regression model, which is derived based on the functional relationship between the lagged values of the time series inputs and several reasonable explanatory variables [12]. In the application of VSTEDF, it is very difficult to determine the influencing factors owing to the volatile change of electric load. However, the electricity load is a form of time series data. The models of traditional methods for time series prediction involve the methods of Moving Average (MA), Auto-Regression (AR), or the combination of the two, the ARMA model [13]. In the AR model, it sums up the weighted n immediate past values of yi and the weighted value of the present input to predict the current value of the time-series (see equation 1). That is,

184 Artificial Intelligence Resources in Control and Automation Engineering n

yi

a j yi

j

a1 yi

1

a2 yi

an yi

2

Yao et al.

(1)

n

j 1

However, it takes a lot of effort to solve the coefficient aj by the least square method in the AR model. Unlike AR modeling, the ANN model only needs several historical input variables to train the ANN to predict the output. Furthermore, the Grey prediction adopts the rolling model technique, which utilizes the forward data points in the same series to construct a Grey model for predicting the next data [14]. That is, the Grey predictor refers a new data, and drops the oldest data to keep the fixed number in the model. This led us to an idea to construct a novel rolling model technique of the BPN input patterns for VSTEDF see Fig. (5).

Figure 5: The diagram of rolling model of input pattern of BPN. It refreshes new input data by dropping the oldest data.

y hk

2

f(

k 1 n

whk )

f(

i 1

wxi )

Lˆn

1

Figure 6: BPN forecasting model that consists of one hidden layer with two hidden neurons (H1 and H2), and n input neurons (x1, …, xn). The non-linear relationship between forecasting load and lagged values of load can be calculated by the BPN algorithm.

Fig. (6) shows a BPN forecasting model that consists of one hidden layer with two hidden neurons (H1 and H2), and n input neurons (x1, …, xn). Equations (2) to (5) show the formulae of the model. That is, the forecasting model can be described by (5) Lˆn 1 f ( L1 , L2 ,..., Lt ) , where Lt denotes the set of historical load inputs.

h1

f1 ( x1 , x2 ,

1 exp h2

w11 L1

f 2 ( x1 , x2 ,

1 exp

, xn )

f1 ( L1 , L2 ,

1 w12 L2

, xn )

w21 L1

, Ln )

w1n Ln

f 2 ( L1 , L2 ,

1 w22 L2

(2) 1

, Ln )

w2 n Ln

(3) 2

A Novel Electric Load Demand Forecaster

Lˆn

y

1

1 exp Lˆn

1

Artificial Intelligence Resources in Control and Automation Engineering 185

f 3 (h1 , h2 ) 1 w46 h1 w56 h2

(4) 3

f ( L1 , L2 ,..., Lt )

(5)

where x = input variable of BPN y = output variable of BPN

Lˆt = forecasted load L = historical values of load w = weights of ANN = bias of ANN h = the signal flow of hidden neurons B. Planning and Implementation of Training Process for VSTEDF

The process of model training is the most important task of the application of ANN. The applicability of training data will seriously affect the prediction of the ANN-based forecaster. The selection of some other parameters of the ANN is also important to the predictor’s performance, such as the learning rate, the numbers of hidden layers and neurons, and the momentum, which also need to decided smartly and scientifically. Fig. (7) is the proposed flowchart of the training process for the application of VSTEDF. In the very beginning, the rules for selecting training data have to be chosen. Then, the training data has to be normalized due to the limitation of the BPN’s transfer function. We also employed Taguchi’s experimental method as a means to obtain the optimal parameter settings of the BPN. The details will give in the following sub-sections. (1) Training Samples Selection

The performance of the BPN-based predictor strongly depends on the selection of training samples. The training data should cover the entire expected input space and then during the training process training vector pairs must be randomly selected from the sample set. If the training data set has closer similarity, the trained network may perform excellent result. Hence, it is necessary to provide different proper types of training samples and proper noise for decreasing the sameness [15]. Hence, in the application of VSTEDF, the training data should be classified and the ANN model should be well trained by different school day types in order to increase the accuracy of prediction. In this study, we specified our training inputs into two types of load trend, the class hours, and the daily peak temperature, owing to the electricity consumption habit of school. By Class Hour: The load consumption profile at NKFUST is highly related to the class hour (see Fig. (8)). Generally speaking, the load in the first class hour of the day is much lower than others because these classes start at 8 o’clock in the morning. In order to eliminate confounding the training process of ANN, we classified the training data into eight class hours per day in this study.

186 Artificial Intelligence Resources in Control and Automation Engineering

Yao et al.

Gathering the historical data from AMCES Selecting the training samples by temperature The load of 1st class hour

The load of ... The load of 2nd class hour 7th class hour

The load of 8th class hour

Data normalization Rolling modeling Parameter setting Training

No

Convergent? Yes Load forecasting Figure 7: Proposed flowchart for VSTEDF training by rolling model of BPN.

Figure 8: Load trend is varied by the school class hours at NKFUST.

By Daily Peak Temperature: In our preliminary study, we did not consider the temperature as the input pattern of the network. As a result, the model made a poor prediction (see Fig. (9)). In the Forecast-1, we found the peak temperature of the day was 21.4 , which was much lower than the actual average peak temperature 28.9 of the training days. But if we chose the input patterns with closer temperature range, the predicted results improved dramatically. In the Forecast-2 the average temperature of the training days is 23.5 . As shown in Fig. (9), the Forecast-1’s training data were the previous week with the average temperature of 28.9 . Yet, the Forecast-2 considered similar temperature day pattern with an average temperature of 23.5 . Therefore, in this study we also classified the input patterns by the daily peak temperature.

A Novel Electric Load Demand Forecaster

Artificial Intelligence Resources in Control and Automation Engineering 187

Figure 9: The daily peak temperature of input patterns will affect the performance of prediction. Forecast-1 is the prediction ignoring the temperature effects. Forecast-2 takes the temperature effects into account.

(2) Data Normalization

In this project we chose the sigmoidal activation function as the transfer function for the BPN. Therefore, the load values should be normalized to the range of 0 to 1. The calculation formula of normalization is as following: H

y

L

Max Min

x

Max L Min H

(6)

Max Min

where x: original data y: normalized data H: top limit of normalization L: bottom limit of normalization Max: maximum value of original data Min: minimum value of original data (3) BPN Parameter Settings

There are several learning factors that may influence BPN training that should be well examined. In this study, we employed Taguchi’s experimental design method [16] to optimize factors such as the network’s learning rate, momentum, the number of hidden neurons, and the number of previous load points. Table 2 shows the control factors and their levels. We chose an L9 orthogonal array to set up the experimental matrix (see Table 3). Table 2: The Control factors and their levels in Taguchi’s experimental design Control factors

Level 1

Level 2

Level 3

A（Previous load point）

3

4

5

B（Momentum）

0.1

0.3

0.5

C（The number of hidden neurons）

5

10

15

D（Learning rate）

0.1

0.3

0.5

188 Artificial Intelligence Resources in Control and Automation Engineering

Yao et al.

Table 3: Experimental matrix and calculated SN ratio ( ) using the L9 orthogonal array Exp. No.

Factors

η

A

B

C

D

1

1

1

1

1

-7.01

2

1

2

2

2

-8.63

3

1

3

3

3

-9.94

4

2

1

2

3

-10.24

5

2

2

3

1

-7.01

6

2

3

1

2

-8.94

7

3

1

3

2

-8.27

8

3

2

1

3

-11.10

9

3

3

2

1

-7.92

Table 4: Average values of SN ( ) for each factor level. The absolute values of the underlined values are the smallest levels for each factor. This combination is the candidate of the optimal combination set of the parameters of BPN Factor

A

B

C

D

1

-8.53

-8.51

-9.02

-7.31

2

-8.73

-8.91

-8.93

-8.61

3

-9.10

-8.93

-8.41

-10.43

Max.－Min.

0.57

0.42

0.61

3.12

Level

Note: (dB).

The reacting table of SN, the Signal-to-Noise Ratio ( ) for each factor and level are listed in Table 4. We chose the smallest-is-the-best. Therefore, we obtained the optimal parameter setting as A1B1C3D1. However, from the ANOVA in Table 5, we can see that the contribution of factors A to C is very little. Therefore, we should adjust the level of factor C from 3 to 1 in order to improve the performance. The final optimal parameter setting is A1B1C1D1. That is, the number of lagged load points is 3; the momentum is 0.1; the number of hidden neurons is 5; the learning rate is 0.1. Table 5: ANOVA Table. The contributions of factors A, B and C are very little. Therefore, the level of factor C has to be adjusted from 3 to 1, in order to improve the performance. The final optimal parameters combination becomes A1B1C1D1 Factor

Degree of freedom

Sum of square

Mean square

Contribution

A

fA = 2

SA = 0.5007

VA =0.2504

ρA = 3.10%

B

fB = 2

SB = 0.3478

VB = 0.1739

ρB = 2.15%

C

fC = 2

SC = 0.6535

VC = 0.3267

ρC = 4.04%

D

fD = 2

SD = 14.671

VD = 7.3355

ρD = 90.71%

Total

fT = 8

ST = 16.173

5. RESULTS AND DISCUSSION A. Testing Results

After the training process, we used the trained BPN model to examine our electric load demand off-line. Figs. (10) to (12) show the forecasted results for regular school days, weekends, and school recess days (the winter break) respectively. The average absolute error of general school days is 2.14%, weekend days’

A Novel Electric Load Demand Forecaster

Artificial Intelligence Resources in Control and Automation Engineering 189

error is 3.14%, and winter break days’ error is 1.98%. It shows a good performance of this forecast. Figure (13) shows the forecasting error frequency distribution in this test. Among these predicting points, about 55% of errors are less than 2%, and only about 7.28% errors are higher than 5%.

Figure 10: Actual load vs. forecasted load of general school days (Monday to Friday). It shows accurate predictions.

  Figure 11: Actual load vs. forecasted load of weekend. The predictions are accurate and satisfactory.

Figure 12: Actual and forecasted loads of school winter recess. It also shows accurate prediction.

B. Discussion

From the analysis of the forecast error frequency distribution (Fig. (13)) and distribution diagram of actual loads versus forecasted loads (Fig. (14)), it shows that the proposed Taguchi-ANN-based forecaster is adequate for VSTEDF for general school days. But in the condition of sudden change of load, the proposed model was not able to deal with this unexpected fluctuation. As shown in Fig. (15), the 94th point of load rose sharply; the error rose to 12.76%. But the prediction for the next point (the 95th point) adjusted and matched the actual load quickly. It lessened the error to 1.64%. This unexpected result would not decrease the value of this presented Taguchi-ANN-based load demand predictor because the forecasting interval is in every 2 minutes. But the Taiwan Power Company records the over-demand-value load only for intervals of every 15 minutes. Therefore, this type of error will compensate quickly in the next 2 minutes. A brief

190 Artificial Intelligence Resources in Control and Automation Engineering

Yao et al.

comparison of the forecasting results with the Grey prediction [14] and BPN is shown in Fig. (16). The forecasting results of the BPN are more accurate than the Grey prediction.

Figure 13: Forecasting error frequency distribution chart. The errors of more than 55% forecasted values are smaller than ±2%, and only about 7.28% are greater than ±5% error.

Figure 14: Distribution diagram of actual load versus forecasted load. It shows the forecasted values are accurate and satisfactory.

Figure 15: Diagram of load profile with sudden change at the 94th point. The accuracy of prediction at the sudden change point dropped dramatically. But it recovers quickly at the next point.

A Novel Electric Load Demand Forecaster

Artificial Intelligence Resources in Control and Automation Engineering 191

Figure 16: Comparison between Grey prediction and BPN. The prediction of the rolling model of BPN is better than the one of Grey theory.

6. CONCLUSIONS

Instantaneous-load forecasting plays an important role for both power plants and consumers today. Power plants need a faster forecasting technique to operate the power systems more reliably and flexibly for optimization strategies. Consumers are able to cut down on electricity bills and avoid overuse penalties with the proposed AMCES and VSTEDF. In this chapter, we proposed a rolling modeling technique, which is similar to the AR model, to construct the BPN input patterns for very short-term electric demand forecasting. The rolling modeling technique only needs several previous input variables to construct the BPN model to accurately predict the electric demands at two-minute interval. At the stage of training samples selection, we specified our training inputs by two types of load trend, the class hour and the daily peak temperature. This is consistent with the electricity consumption pattern of school. We also optimized the factors of BPN to obtain a more robust forecasting model by adopting Taguchi’s experimental design method. The experimental results show that the forecast error is smaller than 3%. Although this model is unable to forecast the sharp load profile changes, the error is quickly compensated for in the next forecasting interval. The results also show that it is feasible to design a simple and satisfactory dynamic forecaster for predicting the very short-term electric demand by the rolling input pattern model of BPN. REFERENCES [1]

[2] [3] [4] [5] [6] [7] [8]

Y. H. Fung, and V.M.R. Tummala, "Forecasting of electricity consumption: A comparative analysis of regression and artificial neural network models," in Proc. 1993 The 2nd International Conf. on Advances in Power System Control, Operation and Management, vol. 2, pp. 782-787, 1993. W. Charytoniuk, and M.S. Chen, "Very short-term load forecasting using artificial neural networks," IEEE Trans. Power Systems, vol. 15, no. 1, pp. 263-268, 2000. D. Srinivasan, A.C. Liew, and J.S.P. Chen, "Short term forecasting using artificial neural network approach," in Proc. 1991 The 1st International Forum on Applications of Neural Networks to Power Systems, pp. 12-16, 1991. C.N. Lu, H.T. Wu, and S. Vemuri, "Neural network based short term load forecasting," IEEE Trans. Power Systems, vol. 8, no. 1, pp. 336-342, 1993. S.J. Kiartzis, A.G. Bakirtzis, and V. Petridis, "Short-term load forecasting using neural networks," Electric Power Systems Research 33, pp. 1-6, 1995. A. Khotanzad, R. Afkhami-Rohani, and D. Maratukulam, "ANNSTLF – artificial neural network based short term load forecaster–generation three," IEEE Trans. Power Systems, vol. 13, no. 4, pp. 1413-1422, 1998. T.W.S. Chow, and C.T. Leung, "Neural network based short-term load forecasting using weather compensation," IEEE Trans. Power Systems, vol. 11, no. 4, pp. 1736-1742, 1996. A.G. Bakirtzis, "A neural network short-term load forecasting model for the Greek power system," IEEE Trans. Power Systems, vol. 11, no. 2, pp. 858-863, 1996.

192 Artificial Intelligence Resources in Control and Automation Engineering

[9] [10] [11] [12] [13] [14]

[15] [16]

Yao et al.

A.W.L. Yao, and C.H. Ku, "Developing a PC-based automated monitoring and control platform for electric power systems," Electric Power Systems Research, vol. 64, pp. 129-136, 2003. I. Drezga, and S. Rahman, "Input variable selection for ANN-based short-term load forecasting," IEEE Trans. Power Systems, vol. 13, no. 4, pp. 1238-1244, 1998. K. S. Swarup, and B. Satish, "Integrated ANN approach to forecast load," IEEE Computer Applications in Power, vol. 15, pp. 45-51, 2002. S. Makridakis, S.C. Wheelwright, and R.J. Hyndman, Forecasting Methods and Applications, 3rd ed., New York: John Wiley & Sons, 1998. N.K. Bose, and P. Liang, Neural Network Fundamentals with Graphs, Algorithms, and Applications, Singapore: McGraw-Hill, 1996. J.H. Chen, "Development of online demand-control system for electricity by using Grey theory and fuzzy control," Master’s thesis, Dept. Mechanical and Automation Eng., National Kaohsiung First Univ. of Science and Technology, Kaohsiung, Taiwan, 2001. P.K. Liaw, "The application of neural network for electric load demand forecasting," Master’s thesis, Dept. of Industrial Eng. and Management, Yuan Ze Univ., Chungli, Taiwan, 1994. R.E. Walpole, R.H. Myers, and S.L. Myers, Probability and Statistics for Engineers and Scientists, New Jersey: Prentice Hall, 1998.

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 193-197

193

CHAPTER 9 An Application of a Dynamic Matrix Control Algorithm: Path Tracking Using Predictive Control J. Espelosín*, A. Hamilton, L. Acosta, J. Toledo and E.J. González Departamento de Ingeniería de Sistemas y Automática, Arquitectura y Tecnología de Computadores, Universidad de La Laguna, Spain Abstract: An automatic steering system for a self-guided vehicle must be able to track its course smoothly and accurately. In order to meet this requirement, a predictive controller has been implemented in the Verdino prototype. In this chapter the principles behind this kind of controller, as well as the details of the actual implementation, are presented.

Keywords: Dynamic matrix control algorithm, path tracking, predictive control. 1. INTRODUCTION Verdino is an autonomous electric vehicle that has been electronically and mechanically adapted to be computer controlled, and it is designed to transport people within a bioclimatic housing development. To carry out the steering task, a predictive control algorithm for Verdino was developed and the correct functioning of the implementation tested via different experiments. This chapter presents the most relevant tests and is organized as follows: Section 2 describes the main concepts of the predictive controller algorithm; Section 3 describes the details of implementing the predictive controller for an autonomous vehicle; the results and conclusions are presented in Sections 4 and 5, respectively. 2. CONCEPTS OF PREDICTIVE CONTROL The algorithm chosen to perform the steering control tasks of the Verdino prototype is a predictive controller. When the reference trajectory is known beforehand, a predictive algorithm offers important advantages in comparison to other algorithms that are simpler to implement. The precepts contained in the control strategies included under the term predictive control, according to [1, 2], are: This kind of algorithm uses an explicit plant model that is able to predict the system output up to a given time (prediction horizon). The future control signals obtained by the controller are calculated by minimizing an objective function to a certain number of steps (control horizon). Sliding horizon concept. The prediction is carried out and the objective function is minimized in order to obtain input commands for the plant. The first control command obtained in the minimization is applied, discarding the rest, after which the horizon shifts into the future, these steps being repeated for every sampling period. The different predictive control algorithms differ in the models used to describe the system and in the cost function to be minimized. In our case we have chosen the Dynamic Matrix Control (DMC) algorithm. In [3, 4], other successful *Address correspondence to J. Espelosin: Departamento de Ingeniería de Sistemas y Automática, Arquitectura y Tecnología de Computadores, Universidad de La Laguna, Spain; E-mail: [email protected] Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

194 Artificial Intelligence Resources in Control and Automation Engineering

Espelosín et al.

implementations of predictive controllers are shown. The mathematical model used in this method to represent the system is the step response. The cost function used is intended to minimize future errors and control efforts. The name of the algorithm comes from the fact that the dynamic of the system is represented in a single matrix formed by the step response elements. Mathematical expressions for the prediction and the cost function are:

yˆ = Gu + f

(1)

p

yˆ t + j | t

J=

w t+ j

j=1

(2)

m

+

2

u t+ j 1

2

j=1

where ŷ is a vector with dimension equal to the prediction horizon containing the predicted outputs up to the prediction horizon, w is the future output desired value, u is a vector with dimension equal to the control horizon containing the future control actions, G is the dynamic matrix control of the system and f is the free response vector, with dimension equal to the prediction horizon. The free response is a prediction of how the system will behave if the command stays constant and equal to the last command calculated. The λ parameter allows the path tracking errors and the control efforts to be weighted separately, such that we could design a controller that attempts to adjust to the desired trajectory regardless of usage command. Or the controller could be more permissive with the path tracking errors by reducing the number of commands, saving energy in the control. The main methodology of a predictive controller could be summarized as: the model of the process is used to predict the future outputs using the information from past input signals, past control commands as well as from future control actions calculated by an optimizer. To calculate the future control signals, the optimizer uses the cost function mentioned earlier. Keeping this explanation in mind, the model process is fundamental to the correct operation of the system. The model must be accurate, but at the same time simple. 3. IMPLEMENTATION

The bicycle model was selected to represent the vehicle. Furthermore, this model includes the dynamic of the steering system. Fig. (1) shows the bicycle model representation. Fig. (2) shows the different parts of a model based predictive controller and the signals between the modules.

Figure 1: Bicycle model.

An Application of a Dynamic Matrix Control

Artificial Intelligence Resources in Control and Automation Engineering 195

Where is the steering angle and is the vehicle orientation with reference to geographic north. The velocity of the vehicle is represented by q. The perpendicular velocity vector is represented by r. Symbols d1 and d2 represent the distance between the wheels and the prototype’s center of gravity. The sum of d1 and d2 is d.

Figure 2: MPC structure.

The desired trajectory consists of an array of points. The information contained at each point includes its Cartesian coordinates, an orientation referred to geographic north and a linear velocity. This trajectory is generated by driving the vehicle manually while an application collects the information generated by the sensors.

Figure 3: Main loop of the algorithm.

196 Artificial Intelligence Resources in Control and Automation Engineering

Espelosín et al.

If the optimization process does not include the restrictions of the physical model, it is possible to obtain the minimization of the next cost function analytically: J = eeT + uu T

(3)

Where e is the vector of predicted errors up to the prediction horizon and u is the vector of future signal control increments up to the control horizon. The mathematical expression for calculating future commands is obtained by taking the derivative of J and equating it to zero:

u = GT G + I

1

GT w

f

(4)

The optimizer will be able to calculate the steering angle so as to minimize the differences between the free response and the desired trajectory. In other words, the optimizer will calculate the steering angle that yields the best path tracking. The software reads the sensors and sets the values of the internal states of the system in each iteration. These states are the position, orientation and velocity of the vehicle. With these values, the step response of the system is calculated. The parameters of the step response form the dynamic matrix G. The vehicle’s behavior is predicted by calculating the values from the sensors at the beginning of the iteration. The vehicle’s predicted movement is compared to the desired trajectory from the point closest to the prototype. The future errors vector is the result of this comparison. The future commands are obtained using equation (4). Only the first term of the future commands vector is applied, keeping in mind the concept of sliding horizon. Finally, the variables of the algorithm are updated. The steps in the algorithm are shown in Fig. (3). 4. RESULTS Many experiments in path tracking were carried out at the facilities of the University of La Laguna (ULL) and of the Instituto Tecnológico y de Energías Renovables (ITER) [Technical and Renewable Energies Institute]. The prototype exhibited adequate behavior, keeping the orientation errors and the distance to the trajectory below the admissible thresholds. As the accuracy of the GPS system decreased, path tracking errors appeared.

Figure 4: Error orientation and distance.

An Application of a Dynamic Matrix Control

Artificial Intelligence Resources in Control and Automation Engineering 197

To check the algorithm for proper behavior, an experiment was conducted consisting of an approach maneuver. The vehicle begins the approach two meters away from the trajectory at a 25º orientation with respect the closest point on the trajectory. Fig. (4) shows the trend in the orientation error as well as in the distance between the prototype and the trajectory. Fig. (5) shows the desired trajectory and the path followed by the vehicle.

Figure 5: Approach maneuver.

5. CONCLUSIONS When a person drives a car, he unconsciously predicts the vehicle’s behavior based on previous experience and on knowledge of vehicle operation. It is thanks to these predictions that people are able to drive properly. By implementing a DMC algorithm in the Verdino prototype, we have tried to demonstrate that a mobile robot is able to carry out this kind of prediction in order to drive a car in the same way that a person does. As we can see in Figs. (4) and (5), the prototype reduces the distance to the desired trajectory smoothly and quickly. The application of a predictive control algorithm for a path tracking problem thus exhibits proper behavior. REFERENCES [1] [2] [3] [4]

E.F. Camacho and C. Bordóns, "Model Predictive Control", London; Springer Verlag, ISBN 3-540-76241-8. 1999 P. 280. E. F. Camacho and C. Bordons, Control predictivo: Pasado, presente y futuro. RIAI, Revista Iberoamericana de Automatica e Informatica Industrial, 5-28, 2004. J. Gómez Ortega and E.F. Camacho, “Mobile robot navigation in a partially structured environment using Neural predictive control”, Contr Eng Prac, 4, pp.1669-1679, 1996.  Ollero. A, Amidi O., (1991) Predictive path tracking of mobile robots. Application to the CMU NAVLAB.

Artificial Intelligence Resources in Control and Automation Engineering, 2012, 198-198

Index C Complex dynamic systems 15-72 Complex hierarchical systems 15-72 Congestion control 92-107 Continuous casting 159-179 Control 15-72 Crack 159-179 D DC Motor 3-14, 69, 75-79, 108-133, 138, 142, 166 Decision 15-72 Dynamic Matrix Control Algorithm 193-197 E Electric load forecasting 180-192 F Fuzzy 6, 12-13, 27, 35-36, 73-91, 92-107, 109-111, 112, 117-119, 135-158, 161-162, 171-173 I Inertia Wheel Inverted Pendulum 73-91 Intelligent controller 3-14 K Knowledge-based fuzzy active force control 135-158 M Mobile manipulator 135-158 Modeling 15-72 N Neural networks: 120-134, 159-179, 180-192 P Particle Swarm Optimization 3-14 Path tracking 193-197 PID 3-14, 75-90,141 Predictive Control 193-197 V Video Streaming 92-107

Evelio J. González, Leopoldo Acosta Sánchez and Alberto F. Hamilton Castro (Eds) All rights reserved - © 2012 Bentham Science Publishers

198