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MM7 Practical Issues Using PID Controllers

Readings: • FC textbook: Section 4.2.7 Integrator Antiwindup (p.196-200) • Extra reading: Hou Ming’s lecture notes (p.60-69)• Extra reading: M.J. Willis notes on PID controler

What have we talked in MM6?

• PID controllers • Ziegler-Nichols tuning methods

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K(1+1/Tis+ TDs)PlantG(s)

+

-R(s) E(s) Y(s)

MM6:Characteristics of PID Controllers Proportional gain, Kp larger values typically mean faster

response. An excessively large proportional gain will lead to process instability and oscillation.

Integral gain, Ki larger values imply steady state errors are eliminated more quickly. The trade-off is larger overshoot

Derivative gain, Kd larger values decrease overshoot, but slows down transient response and may lead to instability due to signal noise amplification in the differentiation of the error.

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MM6: PID Tuning Methods- Trial-Error

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See Hou Ming’s lexture notes

MM6: PID Tuning – Zieglor Niechols (I)

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Pre-condition: system has no overshoot of step response

See Hou Ming’s lexture notes

MM6: PID Tuning – Zieglor Niechols (II)

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Pre-condition: system order > 2

See Hou Ming’s lexture notes

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Goals for this lecture (MM7)Some practical issues when developing a PID controler:

Integral windup & Anti-windup methods Derivertive kick When to use which controller? Operational Amplifier Implementation Other tuning methods

PI control: Reset time Control Structure TI – integral/reset time

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)11()()( :DomainFrequency

))(1)(()( :Domain Time0

sTK

sEsUD(s)

deT

teKtu

I

t

tI

Integral windupIntegration (I) actuator saturation phenomena

Anti-windup Turn off the integral action as soon as the actuator saturates

Anti-windup methods Implement with a dead zone Implement with a nonlinearity Others...

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Integral Windup

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Anti-windup Techniques

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Example: DC Motor Control with Saturation

Download motorPIsaturation.mdlmotorPIantiwind.mdl

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Control effort

Output responses

Download motorPIsaturation.mdlmotorPIantiwind.mdl

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Download motorPIsaturation.mdlmotorPIantiwind.mdl

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Goals for this lecture (MM7)Some practical issues when developing a PID controler:

Integral windup & Anti-windup methods Derivertive kick When to use which controller? Operational Amplifier Implementation Other tuning methods

Derivative Kick (I) Reducing oscillations in feedback systems is the

key advantage of derivative controlHowever,

Does not eliminate offset Slows the response

Derivative kick: if we have a setpoint change, a spike will be caused by D controller, which is called derivative kick.

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sTsEsUD(s)

(t)eTtu

D

D

)()(

)(

Derivative Kick (II)

Derivative kick can be removed by replacing the derivative term with just output (y), instead of (rset-y).

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)11()()(

)(1)(()( 0

sTsT

KsEsUD(s)

(t)eTdeT

teKtu

DI

D

t

tI

)()()11(

))(1)(()( 0

ssYTsEsT

KU(s)

(t)yTdeT

teKtu

DI

D

t

tI

Derivative Kick (III)

Derivative kick can be reduced by introducing a lowpass filter before the set-point enters the system

The bandwidth of the filter should be much larger than the closed-loop system’s bandwidth

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)11()()(

)(1)(()( 0

sTsT

KsEsUD(s)

(t)eTdeT

teKtu

DI

D

t

tI

K(1+1/Tis+ TDs)PlantG(s)

+

-R(s) E(s) Y(s)filter

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Goals for this lecture (MM7)Some practical issues when developing a PID controler:

Integral windup & Anti-windup methods Derivertive kick When to use which controller? Operational Amplifier Implementation Other tuning methods

When to use which controller?P I D PI PID present back forward Present & back All time Systems with slow responses, tolerant to offset

Not often used alone, as is too slow

Not used alone because is too sensitive to noise and does not have setpoint

Often used Often used, most robust, but can be noise sensitive

Example use: float valves, thermostats, humidistat.

Example use: used for very noisy systems

Example use: none

Example use: thermostats, flow control, pressure control

Examples: Cases where the system has inertia that could get out of hand: temperature and concentration measurements on a reactor for example. Avoid runaway.

Estimate

When to use

Examples

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Example from http://www.controlguru.com

• Change set point from 39 to 42% CO•Observe delay (0.8)• Observe max slopeof response at T=27

Slope=

Kmax= output change/Input change=k1/k2

(140 139)(26.2 27.5)

0.77

0.773

0.26

Max slope

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¼ decay ratio is not conservative standard (too oscillatory).

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Goals for this lecture (MM7)Some practical issues when developing a PID controler:

Integral windup & Anti-windup methods Derivertive kick When to use which controller? Op-Amp Implementation Other tuning methods

Op-Amp Implementation (I)

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?

Op-Amp Implementation (II)

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?

Op-Amp Implementation (III)

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?

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Goals for this lecture (MM7)Some practical issues when developing a PID controler:

Integral windup & Anti-windup methods Derivertive kick When to use which controller? Op-Amp Implementation Other PID tuning methods

Controller Synthesis - Time Domain

Time-domain techniques can be classified into two groups: Criteria based on a few points in the response

settling time, overshoot, rise time, decay ratio, settling time

Criteria based on the entire response, or integral criteria

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Cohen-Coon Tuning Method Pre-condition: first-order system with some time delay Objective: ¼ decay ratio & minimum offset

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( ) (1st order)1

sKeG ss

Controller Ziegler-Nichols Cohen-Coon

Proportional CKK 3

1

CKK

Proportional +

Integral

33.3

9.0

I

CKK

2.20.1

33.033.3

083.09.0

I

CKK

Proportional +

Integral +

Derivative

5.0

0.2

2.1

D

I

CKK

2.00.1

37.0

813

632

270.035.1

D

I

CKK

Comparison of Ziegler-Nichols and Cohen-Coon Equations for Controller Tuning (1940’s, 50’s)

( ) (1st order)1

sKeG ss

These methods are not suitable for systems where there is zero(s) or virtually no time delay!9/9/2011 28Classical Control

FORTD Model Approximation Motivation:

many empirical PID tuning methods are based on first-order system with time delay

FORTD model approximation System identifcation method Matlab: ident

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1. Integral of square error (ISE)

2. Integral of absolute value of error (IAE)

3. Time-weighted IAE

Design: Pick controller parameters to minimize integral.

IAE allows larger deviation than ISE (smaller overshoots)ISE longer settling timeITAE weights errors occurring later more heavilyApproximate optimum tuning parameters are correlatedwith K, , ...

0

2 dt)t(eISE

0

dt)t(eIAE

0

dt)t(etITAE

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Other Criteria for Performance

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( ) (1st order)1

sKeG ss

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MM7 Exercisecontinue MM6 execise: Design a P, PI, PID controller for the following DC motor speed control, According to quarter decay method.

Implement the above system with an actuator saturation in simulink model with umax=2, umin=-2. Design an integrator antiwindup strategy for your designed PI controller.

Download ZN_tuning_motor.mdl