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 9/9/2011 Classical Control 1
Rs + - Es K1+1/T i s+ T D s Plant Gs Ys What have we talked in MM6? PID controllers Ziegler-Nichols tuning methods 9/9/2011 Classical Control 2
MM6:Characteristics of PID Controllers Proportional gain, K p larger values typically mean faster response. An excessively large proportional gain will lead to process instability and oscillation. Integral gain, K i larger values imply steady state errors are eliminated more quickly. The trade-off is larger overshoot Derivative gain, K d 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 See Hou Ming s lexture notes 9/9/2011 Classical Control 4
MM6: PID Tuning Zieglor Niechols I Pre-condition: system has no overshoot of step response See Hou Ming s lexture notes 9/9/2011 Classical Control 5
MM6: PID Tuning Zieglor Niechols II Pre-condition: system order > 2 See Hou Ming s lexture notes 9/9/2011 Classical Control 6
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 9/9/2011 Classical Control 7
PI control: Reset time Control Structure T I integral/reset time 9/9/2011 Classical Control 8 1 1 Frequency Domain : 1 Time Domain : 0 s T K s E s U Ds d e T t e K t u I t t I
Integral Windup Integral windup Integration 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
Anti-windup Techniques 9/9/2011 Classical Control 10
Example: DC Motor Control with Saturation Download motorpisaturation.mdl motorpiantiwind.mdl 9/9/2011 Classical Control 11
Download motorpisaturation.mdl motorpiantiwind.mdl Output responses Control effort 9/9/2011 Classical Control 12
Download motorpisaturation.mdl motorpiantiwind.mdl 9/9/2011 Classical Control 13
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 9/9/2011 Classical Control 14
Derivative Kick I Reducing oscillations in feedback systems is the key advantage of derivative control However, Does not eliminate offset Slows the response u t T et D U s Ds E s T D s 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
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 1 1 1 0 s T T s K s E s U Ds et T d e T t e K t u D I D t t I 1 1 1 0 s sy T s E T s K Us yt T d e T t e K t u D I D t t I
Derivative Kick III 1 t u t K e t e d TDet T t0 U s 1 Ds K1 T E s T s I 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 I D s Rs filter + - Es K1+1/T i s+ T D s Plant Gs Ys 9/9/2011 Classical Control 17
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 9/9/2011 Classical Control 18
When to use which controller? Estimate When to use Examples 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 Often used Often used, most robust, but can be noise sensitive Example use: float valves, thermostats, humidistat. Example use: used for very noisy systems setpoint 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. 9/9/2011 Classical Control 19
¼ decay ratio is not conservative standard too oscillatory. Max slope Change set point from 39 to 42% CO Observe delay 0.8 Observe max slope of response at T=27 Slope= 140 139 26.2 27.5 0.77 Kmax= output change/ Input change=k1/k2 0.77 0.26 3 Example from http://www.controlguru.com 9/9/2011 Classical Control 20
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 9/9/2011 Classical Control 21
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
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 9/9/2011 Classical Control 25
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 Classical Control 26
Cohen-Coon Tuning Method s Ke Gs 1st order s 1 Pre-condition: first-order system with some time delay Objective: ¼ decay ratio & minimum offset 9/9/2011 Classical Control 27
s Ke Gs 1st order s 1 Comparison of Ziegler-Nichols and Cohen-Coon Equations for Controller Tuning 1940 s, 50 s Controller Ziegler-Nichols Cohen-Coon Proportional KK C KK 1 C 3 Proportional + KK 0.9 KK C C 0.9 Integral I 3.33 0.33 I 3.33 1.0 2.2 Proportional + KK 1.2 KK C C 1.35 Integral + 2.0 I 32 6 I Derivative 13 8 D 0.5 0.37 D 1.0 0.2 0.083 0.270 These methods are not suitable for systems where there is zeros or virtually no time delay! 9/9/2011 Classical Control 28
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
Other Criteria for Performance 1. Integral of square error ISE 2. Integral of absolute value of error IAE 3. Time-weighted IAE ITAE et Design: Pick controller parameters to minimize integral. IAE allows larger deviation than ISE smaller overshoots ISE longer settling time ITAE weights errors occurring later more heavily Approximate optimum tuning parameters are correlated with K,,... 0 ISE t et dt 0 2 dt IAE 0 et dt 9/9/2011 Classical Control 30
s Ke Gs 1st order s 1 9/9/2011 Classical Control 31
9/9/2011 Classical Control 32
MM7 Exercise continue 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 u max =2, u min =-2. Design an integrator antiwindup strategy for your designed PI controller. Download ZN_tuning_motor.mdl 9/9/2011 Classical Control 33