Post on 04-Apr-2018
9/9/2011 Classical Control 1
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
9/9/2011 Classical Control 2
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.
9/9/2011 Classical Control 3
MM6: PID Tuning Methods- Trial-Error
9/9/2011 Classical Control 4
See Hou Ming’s lexture notes
MM6: PID Tuning – Zieglor Niechols (I)
9/9/2011 Classical Control 5
Pre-condition: system has no overshoot of step response
See Hou Ming’s lexture notes
MM6: PID Tuning – Zieglor Niechols (II)
9/9/2011 Classical Control 6
Pre-condition: system order > 2
See Hou Ming’s lexture notes
9/9/2011 Classical Control 7
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
9/9/2011 Classical Control 8
)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...
9/9/2011 Classical Control 9
Integral Windup
9/9/2011 Classical Control 10
Anti-windup Techniques
9/9/2011 Classical Control 11
Example: DC Motor Control with Saturation
Download motorPIsaturation.mdlmotorPIantiwind.mdl
9/9/2011 Classical Control 12
Control effort
Output responses
Download motorPIsaturation.mdlmotorPIantiwind.mdl
9/9/2011 Classical Control 13
Download motorPIsaturation.mdlmotorPIantiwind.mdl
9/9/2011 Classical Control 14
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.
9/9/2011 Classical Control 15
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).
9/9/2011 Classical Control 16
)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
9/9/2011 Classical Control 17
)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
9/9/2011 Classical Control 18
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
9/9/2011 19Classical Control
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
9/9/2011 20Classical Control
¼ decay ratio is not conservative standard (too oscillatory).
9/9/2011 Classical Control 21
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)
9/9/2011 Classical Control 22
?
Op-Amp Implementation (II)
9/9/2011 Classical Control 23
?
Op-Amp Implementation (III)
9/9/2011 Classical Control 24
?
9/9/2011 Classical Control 25
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
9/9/2011 26Classical Control
Cohen-Coon Tuning Method Pre-condition: first-order system with some time delay Objective: ¼ decay ratio & minimum offset
9/9/2011 Classical Control 27
( ) (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
9/9/2011 Classical Control 29
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
9/9/2011 30Classical Control
Other Criteria for Performance
9/9/2011 31Classical Control
( ) (1st order)1
sKeG ss
9/9/2011 32Classical Control
9/9/2011 Classical Control 33
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