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Fuzzy PID Control

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

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Fuzzy PID Control

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  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. n l Ref e u x y Plant Controller - Single Loop Control

  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. e E u U GE GU f Rule base Fuzzy P controller

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

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

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

  12. Fuzzy - PID Gain Relation

  13. n l Ref e u x y Plant Controller - Tuning

  14. Ziegler-Nichols Tuning • Increase Kp until oscillation, Kp = Ku • Read period Tu at this setting • Use Z-N table for approximate controller gains

  15. Ziegler-Nichols (freq. method)

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

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

  18. Hand-Tuning • Set Td = 1/Ti = 0 • Tune Kp to satisfactory response, ignore any final value offset • Increase Kp, adjust Td to dampen overshoot • Adjust 1/Ti to remove final value offset • Repeat from step 3 until Kp large as possible

  19. Quick reference to controllers

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

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

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

  23. 2 200 1.5 0 u Controlled output y 1 -200 0.5 100 100 0 0 0 -100 -100 0 10 20 30 40 CE E 6 1 0.8 4 0.6 Control signal u Membership 2 0.4 0 0.2 -2 0 0 10 20 30 40 -100 -50 0 50 100 Time [s] Input family: Neg and Pos 1/(s+1)3 with FPD+I

  24. Summary • Design crisp PID • Replace it with linear fuzzy • Make it nonlinear • Fine-tune it

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