PID Controllers. Control Engineering by Dr. L. K. Wong. Dr. WONG, Lik-Kin

Transcription

1 PID Controller Control Engineering by Dr. L.. Wong Dr. WONG, Lik-in Page

2 Outut Feedback Control Sytem Reference Controller Plant Outut Feed back only the outut ignal Eay acce Obtainable in ractice Dr. WONG, Lik-in Page 2

3 PID Controller Proortional controller ure gain or attenuation Integral controller integrate error Derivative controller differentiate error Dr. WONG, Lik-in Page 3

4 Proortional Controller u e Controller inut i error reference outut Controller outut i control ignal P controller involve only a roortional gain or attenuation Dr. WONG, Lik-in Page 4

5 Integral Controller u i edt Integral of error with a contant gain Increae ytem tye by Infinity teady-tate gain Eliminate teady-tate error for a unit te inut Dr. WONG, Lik-in Page 5

6 Page 6 Dr. WONG, Lik-in Integral Controller G R E G E Y G G R Y 0 lim lim lim lim G G R E t e e t

7 Derivative Control u d de dt Differentiation of error with a contant gain Reduce overhoot and ocillation Do not affect teady-tate reone Senitive to noie Dr. WONG, Lik-in Page 7

8 Controller Structure Single controller P controller, I controller, D controller Combination of controller PI controller, PD controller PID controller Dr. WONG, Lik-in Page 8

9 PID Controller PI controller u e i edt PD controller u e d de dt PID controller u e i edt d de dt Dr. WONG, Lik-in Page 9

10 PID Controller PI controller U i E PD controller U E d PID controller i U d E Dr. WONG, Lik-in Page 0

11 Controller Performance P controller PI controller PD controller PID controller Dr. WONG, Lik-in Page

12 Block Diagram Reference PID Controller Plant Outut Dr. WONG, Lik-in Page 2

13 Page 3 Dr. WONG, Lik-in P Controller 2 G E U 2 OLTF CLTF 2

14 P Controller Increae in gain ugrade both teady-tate and tranient reone reduce teady-tate error reduce tability Dr. WONG, Lik-in Page 4

15 P Controller.5 Ste Reone From: U Amlitude To: Y Time ec. Dr. WONG, Lik-in Page 5

16 P Controller 2 Ste Reone From: U Amlitude To: Y Time ec. Dr. WONG, Lik-in Page 6

17 Proortional Controller 50 Bode Diagram From: U L Phae deg; Magnitude db To: Y L Frequency rad/ec Dr. WONG, Lik-in Page 7

18 Page 8 Dr. WONG, Lik-in PI Controller G G E Y E U i i i i i CLTF 2 3

19 PI Controller 2.6 Ste Reone From: U.4 i 2.2 i Amlitude To: Y 0.8 i i Time ec. Dr. WONG, Lik-in Page 9

20 Page 20 Dr. WONG, Lik-in PD Controller E U d 2 OLTF d 2 d d CLTF

21 PD Controller 2 d 0 Ste Reone From: U d 0.7 Amlitude To: Y d 2 d Time ec. Dr. WONG, Lik-in Page 2

22 Page 22 Dr. WONG, Lik-in PID Controller 2 E E U i d d i OLTF i d i d i d CLTF 2 3 2

23 PID Controller 5, i 5, d Ste Reone From: U 5, i 5, d 2 Amlitude To: Y , i 2, d 2, 2, i, d 2, Time ec. Dr. WONG, Lik-in Page 23

24 Deign of PID Controller Baed on the knowledge of P, I and D trial and error manual tuning imulation Dr. WONG, Lik-in Page 24

25 Deign of PID Controller Ziegler-Nichol method baed on a oen-loo roce baed on a critical gain Dr. WONG, Lik-in Page 25

26 Ziegler-Nichol Method G τ d e τ Sloe R /τ Time delay L τ d τ Dr. WONG, Lik-in Page 26

27 Ziegler-Nichol Method P controller /RL PI controller 0.9/RL, i 0.27/RL 2 PID controller.2/rl, i 0.6/RL 2, d 0.6/R Dr. WONG, Lik-in Page 27

28 Ziegler-Nichol Method 2 Increae a ure gain u of a cloed-loo ytem until the ytem i marginally table Meaure the eriod of ocillation P u unit i econd Dr. WONG, Lik-in Page 28

29 Ziegler-Nichol Method 2 P controller 0.5 u PI controller 0.45 u, i 0.54 u /P u PID controller 0.6 u, i.2 u /P u, d u P u Dr. WONG, Lik-in Page 29

30 Digital P and D Controller U z E z u t u k de t dt e k e k T Dr. WONG, Lik-in Page 30

31 Page 3 Dr. WONG, Lik-in Digital I Controller [ ] [ ] z E z z T z U z E z ze T z U z zu k e k e T k u d e k u k u d e t u t u T k kt t t τ τ τ τ

32 Digital PID Controller Ez i T z 2 z Uz z d Tz Dr. WONG, Lik-in Page 32

33 Concluion Proertie of P, I, D, PI, PD, and PID controller Deign of PID controller Digital PID controller Dr. WONG, Lik-in Page 33

34 Reference M. Goal, Digital Control Engineering. John Wiley & Son. B. C. uo, Automatic Control Sytem. Englewood Cliff, N.J.: Prentice Hall, 995. G. F. Franklin, J. D. Powell, and A. Emami- Naeini, Feedback Control of Dynamic Sytem. Singaore: Addion-Weley, 988. Dr. WONG, Lik-in Page 34