MM6 PID Controllers. Readings: Section 4.2 (the classical three-term controllers, p except subsection 4.2.5); Extra reading materials

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1 MM6 PID Controller Reading: Section 4.2 the claical three-term controller, p except ubection 4.2.5; Extra reading material 9/9/2011 Claical Control 1

2 What have we talked in MM5? Stability analyi Steady-tate error Effect of zero & additional pole 9/9/2011 Claical Control 2

3 MM5 : BIBO Stability A ytem i aid to have bounded input-bounded output BIBO tability if every bounded input reult in a bounded output regardle of what goe on inide the ytem he continuou LI ytem with impue repone ht i BIBO table if and only if ht i abolutely integrallable All ytem pole locate in the left half -plane - aymptotic internal tability Routh Criterion: For a table ytem, there i no change in ign and no zero in the firt column of the Routh array 9/9/2011 Claical Control 3

4 MM5 : Steady-State Error Objective: to know whether or not the repone of a ytem can approach to the reference ignal a time increae Aumption: he conidered ytem i table Analyi method: ranfer function + final-value heorem Poition-error contant Velocity contant Acceleration contant 9/9/2011 Claical Control lim 1 1, 1 lim lim lim R R R R Y R e DC-ain lim lim lim o a o v o p

5 MM5 : Effect of Additional Zero & Pole Chapter 6 An additional zero in the left half-plane will increae the overhoot If the zero i within a factor of 4 of the real part of the complex pole An additional zero in the right half-plane will depre the overhoot and may caue the tep repone to tart out in the wrong direction An additional pole in the left half-plane will increae the rie time ignificantly if the extra pole i within a factor of 4 of the real part of the complex pole 9/9/2011 Claical Control 5

6 oal for thi lecture MM6 Definition characteriitc of PID control P- controller PI- controller PID controller Ziegler-Nichol tuning method Quarter decay ratio method Ultimate enitivity method 9/9/2011 Claical Control 6

Adequate diturbance rejection Inenitive to model & meaurement error Avoid exceive control

7 Control objective Reference/ Set-point Control i a proce of cauing a ytem output variable to conform to ome deired tatu/value MM1 Control Objective Stable MM5 Quick reponding MM3, 4 Adequate diturbance rejection Inenitive to model & meaurement error Avoid exceive control action Suitable for a wide range of operating condition 9/9/2011 extra Claical reading: Control oodwin lecture 7

8 Feedback Control CharacteriticMM4 Control Objective Stable Quick reponding Adequate diturbance rejection Inenitive to model & meaur. error Avoid exceive control action A wide operating range Sytem error can be made le enitive to diturbance with feedback than they are in open-loop ytem In feedback control, the error in the controlled quantity i le enitive to variation in the ytem gain/parameter Deign tradeoff between gain and diturbance 9/9/2011 Claical Control 8

9 Recall example in MM5: 10/9 9/0.95 Speed up the original ytem by uing feedback P- control Eliminate the teady-tate error by uing feedforward gain 9/9/2011 Claical Control 9

10 Definition of PID Controller PID Mean: P: Proportional control I : Integral control D: Derivative control u t u t u t e t I t t 0 D e d e t PID Control Sytem Structure: cacade control rt + - et PID Controller Plant yt 9/9/2011 Claical Control 10

11 PID Control: Proportional Control I Control Structure Cloed-loop Control Sytem ime Domain : u t e t U Frequency Domain : D E rt + - et P-Controller: Plant yt cl D 1 D 1 9/9/2011 Claical Control 11

12 PID Control: Proportional Control II Cloed loop Control Sytem rt + - et P-Controller: Plant yt Advantage: a imple controller amplifier Diadvantage: Steady tate offet/error problem type-0, -1, -2 ytem MM5 Diturbance rejection problem 2 1 a lim o e 0 a 9/9/2011 Claical Control 12 unity p v feedback lim 0 lim 0 o o y e e v p

9/9/2011 Claical Control 13 Example: Speed Control of a DC Motor Working mechanim of a DC motor t torque contant i a armature current e electromotive force

13 9/9/2011 Claical Control 13 Example: Speed Control of a DC Motor Working mechanim of a DC motor t torque contant i a armature current e electromotive force emf contant Differential equation decription. m e a t e i a a t m a e t m m m e a a a a a a t m m m v R R b J implified v i R i L i b J : See FC p.47-49

14 P-Control for the DC Motor I Download motorp.mdl Pole of the original ytem? Image the tep repone undamped, underdamped, critially damped or over damped ype of thi original ytem? 9/9/2011 Claical Control 14

P-Control for the DC Motor II une gain value, what we can oberve: Larger gain lead to quicker repone, but with larger ocillation here i alway teady-tate error.

15 P-Control for the DC Motor II une gain value, what we can oberve: Larger gain lead to quicker repone, but with larger ocillation here i alway teady-tate error. hi error decreae a value increae Effect of diturbance i alway exiting in the repone, which caue extra teady-tate error he effect of diturbance can be reduced by increaing value introduce one more degree-of-freedom... 9/9/2011 Claical Control 15

16 9/9/2011 Claical Control 16 PID Control: PI Control I Control Structure I integral/reet time Cloed loop-control Sytem 1+1/ i Plant 1 1 Frequency Domain : 1 ime Domain : 0 E U D d e t e t u I t t I + - R E Y D D I I I I I cl

17 PID Control: PI Control II R + - E 1+1/ i Plant Y Control-loop tranfer function Advantage: Eliminate teady tate offet/error why? ood teady-tate diturbance rejection why? How about the tranient repone? 9/9/2011 Claical Control 17

18 Example: PI-Control for the DC Motor Download motorpi.mdl 9/9/2011 Claical Control 18

19 9/9/2011 Claical Control 19 PID Control: PID Feedback Control I Control Structure D Derivative/rate time Cloed loop Control Sytem 1+1/ i + D Plant E U D et d e t e t u D I D t t I + - R E Y D D I I D I I I D cl

20 PID Control: PID Feedback Control II R + - E 1+1/ i + D Plant Y Advantage: Increae the damping Improve the tability ood tranient and teady diturbance rejection he mot popular control technique ued in indutry! 9/9/2011 Claical Control 20

21 PID-Control for the DC Motor Download motorpid.mdl 9/9/2011 Claical Control 21

22 Effect of contant Diturbance 9/9/2011 Claical Control 22

23 9/9/2011 Claical Control 23

24 PID Control: Characteritic Summary A proportional controller p will have the effect of reducing the rie time and will reduce,but never eliminate, the teady-tate error An integral control i will have the effect of eliminating the teady-tate error, but it may make the tranient repone wore. A derivative control d will have the effect of increaing the tability of the ytem, reducing the overhoot, and improving the tranient repone. CL RESPONSE RISE IME OVERSHOO SELIN IME S-S ERROR p Decreae Increae Small Change Decreae i Decreae Increae Increae Eliminate d Small Change Decreae Decreae Small Change 9/9/2011 Claical Control 24

25 PID Control: eneral Deign Procedure When you are deigning a PID controller for a given ytem, follow the tep hown below to obtain a deired repone. Obtain an open-loop repone and determine what need to be improved Add a proportional control to improve the rie time Add a derivative control to improve the overhoot Add an integral control to eliminate the teady-tate error Adjut each of p, i, and d until you obtain a deired overall repone. 9/9/2011 Claical Control 25

26 oal for thi lecture MM6 Definition & characteriitc of PID control P- controller PI- controller PID controller Ziegler-Nichol tuning method Quarter decay ratio method Ultimate enitivity method 9/9/2011 Claical Control 26

27 PID rial uning 9/9/2011 Claical Control 27

28 Ziegler-Nichol Mthod hee well-known tuning rule were publihed by Z-N in Z-N controller etting are widely conidered to be an "indutry tandard". Other reading/reource: Control utorial for Matlab, Proce Control Article, Software Review, 9/9/2011 Claical Control 28

29 uning PID: Quarter decay ratio method I u t 1 t e t e d Det t0 I D U E 1 1 I D Ziegler-Nichol Quarter decay ratio method: Precondition: ytem i table Open loop tuning method Step repone: Proce reaction curve Slope rate R=/ Lag time L 9/9/2011 Claical Control 29

30 uning PID: Quarter decay ratio method II Exercie 1: Deign a P, PI, PID controller for the DC motor example, According to quarter decay m. 9/9/2011 Claical Control 30

31 uning PID: Quarter decay ratio methodiii Pratical iue in Quarter decay ratio method: Proce reaction curve X % Change of control output R %/min. Rate of change at the point of inflection POI D min. ime until the intercept of tangent line and original proce value om/pid/tutorial/pid6. html 9/9/2011 Claical Control 31

32 Chapter 12 ypical proce reaction curve: a non-elf-regulating proce, b elf-regulating proce. 9/9/2011 Claical Control 32

33 X % Change of control output pid6.html uning PID: Quarter decay ratio methodiv R %/min. Rate of change at the point of inflection POI D min. ime until the intercept of tangent line and original proce value 9/9/2011 Claical Control 33

34 pid6.html uning PID: Quarter decay ratio methodv Another mean of determining parameter baed on the ZN open loop i: After "bumping" the output, watch for the point of inflection and note: i min ime from output change to POI P % Proce value change at POI R %/min Rate of change at POI X % Change in output D i calculated: D=i - P/R D & X are then ued /9/2011 Claical Control 34

35 uning PID: Ultimate Senitivity MethodI R + - E Ultimate: u Plant Y Place controller into automatic with low gain, no reet or derivative. radually increae gain, making mall change in the etpoint, until ocillation tart. Adjut gain to make the ocillation continue with a contant amplitude. Note the gain Ultimate ain, u, and Period Ultimate Period, Pu. 9/9/2011 Claical Control 35

36 uning PID: Ultimate Senitivity MethodII Cloed loop tuning method 9/9/2011 Claical Control 36

37 MM6 Exercie Deign a P, PI, PID controller for the following DC motor peed control, According to quarter decay method. Download ZN_tuning_motor.mdl 9/9/2011 Claical Control 37

Position Control of a Large Antenna System

Position Control of a Large Antenna System Poition Control of a Large Antenna Sytem uldip S. Rattan Department of Electrical Engineering Wright State Univerity Dayton, OH 45435 krattan@c.wright.edu ABSTRACT Thi report decribe the deign of a poition