Fuzzy PID Control

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
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
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
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 PDI Controller
11
Fuzzy Incremental Controller
12
Fuzzy - PID Gain Relation
Controller Kp 1/Ti Td
FP GEGU
FInc GCEGCU GE/GCE
FPD GEGU GCE/GE
FPDI GEGU GIE/GE GCE/GE
13
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)
Controller Kp Ti Td
P 0.5Ku
PI 0.45Ku Tu/1.2
PID 0.6Ku Tu/2 Tu/8
16
Z-N oscillation of 1/(1s)3
17
PID control of 1/(1s)3
18
Hand-Tuning

1. Set Td 1/Ti 0
2. Tune Kp to satisfactory response, ignore any
   final value offset
3. Increase Kp, adjust Td to dampen overshoot
4. Adjust 1/Ti to remove final value offset
5. Repeat from step 3 until Kp large as possible

19
Quick reference to controllers
Controller Advantage Disadvantage
FP Simple Maybe too simple
FPD Less overshoot Noise sensitive, derivative kick
FInc Removes steady state error, smooths control signal Slow
FPDI All in one Windup, derivative kick
20
Scaling
21
Nyquist 1/(s1)3 with PID
22
Tuning Map 1/(s1)3
23
1/(s1)3 with FPDI
24
Summary

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