Modeling Mechanical Electrical And Hydraulic Systems

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© 2006 The MathWorks, Inc.

Modeling Mechanical, Electric, and Hydraulic Systems in Simulink®

Terry Denery, Ph.D. Physics-Based Modeling Tools

Physics-Based Modeling Methods Improve Control System Design

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Plant

Sensors

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Controller

Actuators

u

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Electrical Mechanical Device

y

Multidomain systems (mechanical, electrical, hydraulic, chemical, . . .) Successful controller development requires thorough and accurate understanding of plant 2

Electrical Mechanical Device

Plant

Sensors

Actuators

Important Physical Domains Mechanical -3D Multi-Body Dynamics SimMechanics -Driveline Mechanics SimDriveline

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Electrical Mechanical Device

Plant

Sensors

Actuators

Important Physical Domains Electrical -Circuits SimPowerSystems -Motors and Actuators -Power Systems

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Electrical Mechanical Device

Plant

Sensors

Actuators

Important Physical Domains Hydraulics

-Circuits SimHydraulics -Motors and Actuators -Power Systems

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Sensors

Controller

Actuators

u

+

Electrical Mechanical Device

Control System Plant

y

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Control System

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Power Delivery

Electrical Power Network Hydraulic Power Network Mechanical Driveline Power Network 8

Electrical Mechanical Electrical Power Network Hydraulic Power Network Mechanical Driveline Power Network

Device

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Control Systems within Control Systems

Mechanical Device

Plant

Sensors

Controller

Actuators

u

+

Electrical

y

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Biggest Benefit – Delivered Through Simulink® ƒ

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Rich Modeling Environment – Physical – Behavioral – Data-Driven Control System Development Tool – One environment for controller and plant – Code generation that enables HIL testing – Easy access to control tools

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Why did we build SimHydraulics? ƒ ƒ

Hydraulics is widely used in motion actuation systems Customer Feedback – – –

“Extend benefits of Model-Based Design to hydraulic system design” “Develop better plant models for better controller development” “Co simulation with other products is difficult and impractical”

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Pros and Cons for Hydraulics Pros: ƒ High power density ƒ Straight-line actuators are simple, efficient and reliable ƒ Variable speed is easily obtained ƒ Simple, efficient, and centralized control ƒ Overload protection

Cons: ƒ High cost ƒ Complex and costly maintenance ƒ Extremely vulnerable to dirt and contamination ƒ Possible leaks ƒ Noise and vibrations ƒ Fire hazards

Design Trend is Electro-Hydraulics: Transmit power electrically, but deliver through local hydraulic networks 13

Hydraulic System Schematic Diagram

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Block Diagrams p p = p p ( t ),

q O1 = K 1

qA = K A ⋅

pP − pA ,

qO 2 = K 1

p A − pT ,

dp A , dt q A = qO1 − qO 2 , = qO1 ,

p P − p T = ( p P − p A ) + ( p A − p T ).

qP

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Physical System Diagrams

Hydraulic Schematic

SimHydraulics Model

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Demonstrations

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Building Blocks

Mechanical

Mechanical

Signal

Hydraulic

Hydraulic

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Actuation

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Multidomain with SimMechanics

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Two Approaches to Modeling Dynamic Systems First-Principles Modeling

Use an understanding of the system’s physics to derive a mathematical representation

− L2 sin(α ) + nw2 (− sin(α − γ )) sin(γ ) − ne ( − sin(α − γ )) cos(α − γ )α& 2 − n cos(α − γ )γ& 2 α& = ∫ 1 − ne sin 2 (α − γ )

dγ

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Two Approaches to Modeling Dynamic Systems First-Principles Modeling

Use an understanding of the system’s physics to derive a mathematical representation

Data-Driven Modeling

Use system test data to derive a mathematical representation

⎡ s +1 ⎤ 2 α )⎥+ nw (− sin(α − γ )) sin(γ ) − ne ( − sin(α − γ )) cos(α − γ )α& ⎢ 3 − L sin( α& =s∫ +3s +2 ⎥ 1 − ne sin (α − γ ) H(s) = ⎢ 2 ⎢ s +3 ⎥ ⎥ ⎢ 2 ⎣ s +s +1 ⎦ 2

2

2

2

− n cos(α − γ )γ& 2

dγ

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Each Approach Has Its Merits First-Principles Modeling

Data-Driven Modeling

Advantages: ƒ Provides insight into the

Advantages: ƒ Can be a fast method for

system’s underlying behavior ƒ Enables performance prediction for unbuilt systems

developing an accurate model ƒ Instills confidence because it uses data from an actual system

Disadvantages:

Disadvantages:

ƒ Effects like friction and turbulence are difficult to characterize ƒ May be time consuming to develop

ƒ Requires a physical system to acquire test data ƒ Lacks description of physics of the system ƒ May need multiple data sets to cover range of system operation 23

Tools that Span Both Modeling Approaches Complete Modeling Environment

Data-Driven

First-Principles Simulink SimHydraulics SimMechanics SimDriveline SimPowerSystems

Simulink® Parameter Estimation

System Identification Toolbox Neural Network Toolbox Fuzzy Logic Toolbox 24

Inform Model with Test Data Simulink Parameter Estimation ƒ ƒ

Data fitting and optimization techniques Sets parameters defined by physics-based modeling tools

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Code Generation with Real-Time Workshop® ƒ

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Generate ANSI C code Hardware-in-the-loop (HIL) simulations S-functions In-house code

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General Engineering Simulation

MATH

MATLAB & Simulink

Domain Programming Effort Knowledge

Engineering Simulation

Flexibility of mathematical modeling enables you to simulate almost anything. 27

Hydraulic Engineering Simulation MATLAB & Simulink

MATH

Domain Programming Effort Knowledge

SimHydraulics

Dom. Know.

Prog. Effort

Hydraulic Simulation

SimHydraulics brings you further by reducing your requirements for hydraulic domain knowledge and programming effort. 28

Multidomain Simulation MATLAB &Simulink

MATH

DK

PE

SimMechanics

DK.

PE

SimPowerSystems

DK.

PE

SimDriveline

DK.

PE

SimHydraulics

DK.

PE

Controls Tools

DK

PE

Real Time Workshop

DK.

PE

Parameter Estimation

DK.

PE

Multidomain Simulation

The MathWorks provides the best combination of tools for multidomain simulations. 29