PID controllers in nineties

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PID Controllers in Nineties Muhidin Lelic Corning Incorporated Science and Technology Division Corning, NY

M. Lelic 12/7/99

CORNING Inc. L 5033PRE

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Overview





Purpose: extract the essence of the most recent development of PID control Based on the survey of papers (333) in nineties in the following journals:












IEEE Transactions on Automatic Control (23) IEEE Transactions of Control Systems Technology (26) IEEE Transactions on Robotic and Automation (11) IEEE Transactions on Industrial Electronics ( 2) IEEE Control Systems Magazine ( 4) IFAC Automatica (59) IFAC Control Engineering Practice (29) International Journal of Control (20) International Journal of Systems Science ( 2) International Journal of Adaptive Control and Signal Processing ( 2) IEE Proceedings - Control Theory and Applications (30)

M. Lelic 12/7/99

CORNING Inc. L 5033PRE

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Overview


Based on the survey of papers (333) in nineties:















Journal of the Franklin Institute Control and Computers Computing & Control Engineering Journal Computers and Chemical Engineering AIChE Journal Chemical Engineering Progress Chemical Engineering Communications Industrial and Engineering Chemistry Research ISA Transactions Journal of Process Control Transactions of ASME ASME Journal of Dynamic Systems, Measurements and Control Electronics Letters Systems & Control Letters

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( 5) ( 1) ( 3) ( 1) (16) ( 2) ( 1) (55) (21) (13) ( 1) ( 3) ( 2) ( 1)

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Paper Classification














Ziegler-Nichols based PIDs Frequency domain based PIDs Relay based PIDs Optimization methods based PIDs Internal Model Control PIDs Robust PID controllers Nonlinear PIDs Adaptive PIDs Anti-windup techniques Neural Network/Fuzzy Logic based PIDs PID control of Distributed Systems

(10) (22) (29) (20) (15) (30) (12) (28) (13) (34) ( 3)

Multivariable PIDs Applications of PID controllers

(29) (56)

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Forms of PID controller  de  1 u = K p  e + ∫ edt + Td  dt   Ti

e = yr − y

Standard form

 1  Gc ( s ) = K ′1 + (1 + Td′ s )  Ti′s  Gc ( s ) = k +

  1 Gs ( s ) = K p 1 + + Td s   Ti s 

 dy f  1  uc = k c  e + edt − Td dt   Ti

ki + kd s s

Cascade form Parallel form

∫

Filtered derivative term

e = yr − y yf =

1 y 1 + sTd / N

 dy f  1 uc = kc  (βyr − y ) + edt − Td  Ti dt  

∫

M. Lelic 12/7/99

Weighted setpoint form

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Modeling (step response)

Kp

Kp

A0 τ

A1

τ

T

T

a

a G ( s ) = e −τs sτ

M. Lelic 12/7/99

G (s) =

K p e − sτ 1 + sT

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T +τ = T=

A0 Kp

A1 1 e Kp

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Modeling (frequency domain) N (a) =

4d πa

j Im{G( jω)}

Process

y

(1/ K, j0)

φm

ω= 0

1 Re{G( jω)} K

PID −1/ N (a)

ω = ωc

(a) Relay Excitation

(b) Correlation Method: • use PRBS test signal u(t), • measure y(t), • find cross-correlation function between u(t) and y(t) • compute the impulse response g(t) • transform g(t) to G(s) and find the parameters of the model

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Tuning Techniques







Ziegler-Nichols Frequency domain tuning Relay based tuning Tuning using optimization Internal model control tuning Other tuning techniques

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(10) (22) (29) (20) (15) (30)

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Ziegler-Nichols Tuning • Originated by work of Ziegler and Nichols, 1942 • Still in broad industrial use • Several improvements reported • Controllers tuned by this method tend to have large overshoot • Two methods - time and frequency domain based • Improvements reported (DePoor & I’Malley, 1989; Manz & Taconi, 1989; Chen, 1989; Hang & Sin, 1991, Astrom et al, 1992; Cox et al, 1997)

dy f   1 uc = kc  (βyr − y ) + edt − Td  Ti dt  

∫

Kp

τ

T a

Controller P PI PID

K 1/a 0.9/a 1.2/a

Ti

Td

3L 2L

L/2

0 < β > ( τ 3 + τ 4 + ... + τ n ) = τ e In the neighborhood of the gain crossover frequency, ωcg = 1 / 2τ e , G(s) is approximated by G(s) =

K , with τ1 ≥ 4τ e (1 + τ1 s)(1 + τ e s ) Tuning of PID controller by Kessler’s method (Voda and Landau, 1995) Controller Type PI

Assumed Model K G1 ( s ) = , τ1 ≥ τ e ( 1 + τ1 s )( 1 + τ e s )

PID G2 ( s ) =

K , ( 1 + τ1 s )( 1 + τ 2 s )( 1 + τ e s )

τ1 , τ 2 ≥ τ e

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Controller Parameters Kp =

Td =

0 . 5 τ1 Kτ e

, Ti = 4τ e

4τ 2 τ e , τ 2 + 4τ e

Ti = τ 2 + 4τ e , Kp =

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τ1 ( τ 2 + 4 τ e ) 8 Kτ e2

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Kessler’s method salient features











Produces good phase and gain margins by imposing the slope 20 dB/dec around the gain crossover frequency Handles well nonlinearities and time varying parameters, and takes into account unmodeled dynamics (represented by the equivalent time constant τe (Voda and Landau, 1995) The frequency 1/ τe can be found from the Nyquist diagram where the phase margin is around 45°. This frequency also represents the closed loop bandwidth This frequency can be determined from a relay with hysteresis feedback experiment, as follows: PID Tuning by Kessler-Landau-Voda method (KLV) Controller Type PI

Assumption α ω135 = τe

PID

τ 2 ≈ 1 / ω135 ⇒ ω135 = 1 / βτ e , 1 < β < 2

Controller Parameters Kp =

Kp = Ti =

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1 4α 4 .6 , Ti = = 3 .5 τ e ω135 ω135

β( 4 + β) 8 2G (ω135 )

,

4+β 4 , Td = βω135 ( 4 + β)ω135

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Industrial Controllers














ABB Commander 355:
Gain scheduling, feedforward, cascade, ratio control, autotune for 1/2 wave od minimal overshoot Foxboro 762C:
Exact Self-tuning control, dynamic compensation: lead/lag, impulse, dead time. Fuji Electric PYX:
Autotuning, fuzzy logic feedback control Honeywell (few different models):
Self-tuning, autotuning, gain scheduling, fuzzy logic overshoot suppression Yokogawa:
Autotuning, overshoot suppression (at sudden change of setpoint), gain scheduling M. Lelic 12/7/99

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Implementation Issues


Commercial controllers Of the shelf units Mostly digital versions with sophisticated auto-tuning features Used in SISO (or multi-loop control architectures) Give satisfactory results (according to the Corning engineers) Digital controllers have 0.1s sampling period - good for process control
Contain many of additional features based on many years of application experience (integral windup prevention, integral preload, derivative limiting, bumpless transfer
The above features make PID safe to use.






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Embedded Controllers












Customized to the specific needs (when there are special requirements for speed, size, ...) Needed when the custom version of PID control (combined with monitoring, alarm processing, communication software … if needed) Can accommodate virtually any tuning method Very fast control loops require fixed-point arithmetic and special electronics for implementation (DSP, FPGA,…) Example: optical amplifier gain and output optical power control - needs very fast sampling rates.

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Conclusions

















PID (PD, PI) controllers received lot of attention during ‘90 Centennial work of Ziegler and Nichols (1942) still widely used in industrial applications and as a enchmark for new techniques Despite of a huge number of theoretical and application papers on tuning techniques of PID controllers, this area still remains open for further research There is lack of comparative analysis between different tuning techniques No common benchmark examples There is a number of industrial controllers based on modern tuning techniques Embedded controllers are good candidates for new PID techniques The area is still open for research

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