1. Fuzzy PID Control - Reduce design choices - Tuning, stability - Standard nonlinearities

2. Design Procedure * Build and tune a conventional PID controller first. Replace it with an equivalent linear fuzzy controller. Make the fuzzy controller nonlinear. Fine-tune the fuzzy controller. *) Relevant whenever PID control is possible, or already implemented

3. Single Loop Control ux l n yeRef - Controller Plant

4. Rule Base With 4 Rules 1. If error is Neg and change in error is Neg then control is NB 3. If error is Neg and change in error is Pos then control is Zero 7. If error is Pos and change in error is Neg then control is Zero 9. If error is Pos and change in error is Pos then control is PB

5. PID Control

6. Fuzzy P controller f Rule base u GU U GE Ee

7. FP Rule Base 1. If E(n) is Pos then u(n) is 100 2. If E(n) is Zero then u(n) is 0 3. If E(n) is Neg then u(n) is -100

8. Fuzzy PD Controller e GE GCE f Rule base E CE u GU U de/dt

9. FPD Rule Base 1. If E(n) is Neg and CE(n) is Neg then u(n) is -200 3. If E(n) is Neg and CE(n) is Pos then u(n) is 0 7. If E(n) is Pos and CE(n) is Neg then u(n) is 0 9. If E(n) is Pos and CE(n) is Pos then u(n) is 200

10. Fuzzy PD+I Controller CE e GE f PD rules GCE + + GU E GIE IE uU de/dt

11. Fuzzy Incremental Controller e GE GCE f Rule base E CE GCU 1/s U CU cu de/dt

12. Fuzzy - PID Gain Relation ControllerKpKp 1/T i TdTd FPGE*GU FIncGCE*GCUGE/GCE FPDGE*GUGCE/GE FPD+IGE*GUGIE/GEGCE/GE

13. Tuning ux l n yeRef - Controller Plant

14. Ziegler-Nichols Tuning Increase K p until oscillation, K p = K u Read period T u at this setting Use Z-N table for approximate controller gains

15. Ziegler-Nichols (freq. method) ControllerKpKp TiTi TdTd P0.5K u PI0.45K u T u /1.2 PID0.6K u T u /2T u /8

16. Z-N oscillation of 1/(1+s) 3

17. PID control of 1/(1+s) 3

18. Hand-Tuning 1.Set T d = 1/T i = 0 2.Tune K p to satisfactory response, ignore any final value offset 3.Increase K p, adjust T d to dampen overshoot 4.Adjust 1/T i to remove final value offset 5.Repeat from step 3 until K p large as possible

19. Quick reference to controllers ControllerAdvantageDisadvantage FPSimpleMaybe too simple FPDLess overshoot Noise sensitive, derivative kick FInc Removes steady state error, smooths control signal Slow FPD+IAll in one Windup, derivative kick

20. Scaling e GE GCE f Rule base E CE u GU U α α 1/α de/dt

21. Nyquist 1/(s+1) 3 with PID -202 0 1 2 Kp = 4.8, Ti = 15/8, Td = 15/32

22. Tuning Map 1/(s+1) 3 -202 0 2 000 a) -202 0 2 001 b) -202 0 2 010 c) -202 0 2 011 d) -202 0 2 100 e) -202 0 2 101 f) -202 0 2 110 g) -202 0 2 111 h)

23. 1/(s+1) 3 with FPD+I

24. Summary 1.Design crisp PID 2.Replace it with linear fuzzy 3.Make it nonlinear 4.Fine-tune it