FUZZY LOGIC CONTROL. Helsinki University of Technology Control Engineering Laboratory

Transcription

1 FUZZY LOGIC CONTROL

2 FUZZY LOGIC CONTROL (FLC) Control applications most common FL applications Control actions based on rules Rules in linguistic form Reasoning with fuzzy logic FLC is (on the surface) nonanalytic General design methods still in infancy The effect of control parameter changes on control result difficult to estimate Tuned case by case

3 FUZZY LOGIC CONTROL (FLC) Classical FLC r + - e FLC Process y Taking a shower (our process) in the bathroom. (y=water temperature, r=desired water temperature.) What is the rule base for FLC?

4 FUZZY LOGIC CONTROL (FLC) FLC and conventional PID as a backup r + - e FLC + - Process y PID

5 FUZZY LOGIC CONTROL (FLC) FL tuning conventional PID r + - e PID u Process y FL

6 FUZZY LOGIC CONTROL (FLC) FL in gain scheduling PID r + - e PID 1 u Switch Process y PID 2 FL

7 FUZZY LOGIC CONTROL FLC is a fuzzy system consisting of Fuzzification interface Fuzzy inference Knowledge base Defuzzification interface

8 FUZZY LOGIC CONTROL FUZZY SYSTEM Knowledge base Input Inference Fuzzification Defuzzification Output

9 FUZZY LOGIC CONTROL - Structure Control inputs Fuzzy sets (membership functions) of inputs Rules Control outputs Fuzzy sets (membership functions) of outputs Fuzzy reasoning Defuzzification

10 FUZZY LOGIC CONTROL - Structure Control inputs error, change in error, process input and output, setpoint Fuzzy sets (membership functions) of inputs number of sets, type of membership functions, location of membership functions Rules Control outputs control, change in control, control parameters, setpoint

11 FUZZY LOGIC CONTROL - Structure Fuzzy sets (membership functions) of outputs number of sets, location of membership functions Fuzzy reasoning max-min, sum-product, etc. Defuzzification center of gravity, max, etc.

12 FUZZY LOGIC CONTROL Structure

13 FLC Closed-loop step responses to guide in construction of rules

14 FUZZY LOGIC CONTROL - PD type PD type fuzzy u = K e+ K e p D If e is and e is then u is REMARK: PD especially for servo problems

15 FUZZY LOGIC CONTROL - PID type PID type fuzzy (position algorithm) u = Kpe+ KDe + K I e( α) dα t 0 If e is and then u is e k i= 0 is and ek ( ) is

16 FUZZY LOGIC CONTROL - PID type PID type fuzzy (velocity algorithm) u = K e+ K e + K e( α) dα p D I t 0 If e is and then u is e is and 2 ek ( ) is

17 FUZZY LOGIC CONTROL - PI type PI type fuzzy u = K e+ K e dt, p I t 0 Take derivative on both sides u = K e + K e p I If e is and e is then u is

18 FUZZY LOGIC CONTROL PD type, rule base PD type FLC (position algorithm) If e(k) is positive and e(k) is positive, then u(k) is large If e(k) is positive and e(k) is negative, then u(k) is medium If e(k) is negative and e(k) is positive, then u(k) is medium If e(k) is negative and e(k) is negative, then u(k) is small

19 FUZZY LOGIC CONTROL PI type, rule base PI type FLC (velocity algorithm) If e(k) is positive and e(k) is positive, then u(k) is positive If e(k) is positive and e(k) is negative, then u(k) is zero If e(k) is negative and e(k) is positive, then u(k) is zero If e(k) is negative and e(k) is negative, then u(k) is negative

20 FUZZY LOGIC CONTROL - Example Example: Consider a dynamic system of first order dynamics and delay with a transfer function Gs () s 1.2e = 10s + 1 The reference signal is a unit step. Develop a fuzzy PI(D) feedback controller for the feedback system and study its performance.

21 FUZZY LOGIC CONTROL - Simulation SOLUTION: Simulink diagram of the system is constructed next Open Simulink with the command» simulink and then proceed to use blocks in the appropriate block libraries.

22 FUZZY LOGIC CONTROL- Simulation

23 FUZZY LOGIC CONTROL- Simulation In MATLAB command side open fuzzy toolbox» fuzzy Develop the fuzzy system (Fuzzy Logic Controller) In order to use in the command side, save to workspace. If you want to use the system later, save to disk. The easiest thing to get started is to pick a fuzzy controller from fuzzy demos. Open tank, and use the controller tank.

24 FUZZY LOGIC CONTROL- demo sltank

25 FUZZY LOGIC CONTROL- Simulation Open Fuzzy Logic Controller to see the name of the fuzzy system (FIS matrix)

26 FUZZY LOGIC CONTROL- Simulation Open Fuzzy Logic Toolbox and from fuzzy demos tank.fis and study its rule base

27 FUZZY LOGIC CONTROL- Simulation You can use tank or start changing it according to your own design. You can graphically adjust membership functions. One modification is given on the next slide REMARK : We have position type of controller output is u.

28 FUZZY LOGIC CONTROL- Simulation

29 FUZZY LOGIC CONTROL - Simulation

30 FUZZY LOGIC CONTROL PI type (velocity) To reduce steady-state error to zero integrator is needed Try to set up PI type of fuzzy controller Study typical step responses to set up the rule base

31 FUZZY LOGIC CONTROL PI type (velocity) If e(k) is positive and e(k) is positive, then u(k) is positive If e(k) is positive and e(k) is negative, then u(k) is zero If e(k) is negative and e(k) is positive, then u(k) is zero If e(k) is negative and e(k) is negative, then u(k) is negative

32 FUZZY LOGIC CONTROL velocity type uk ( ) uk ( ) uk ( ) = uk ( ) uk ( 1)

33 FUZZY LOGIC CONTROL velocity type

34 FUZZY LOGIC CONTROL Easy to set up a working fuzzy controller even for difficult-to-control processes (but previously controlled by operator) Easy to understand the rule base in simple cases No sense to use FLC in straightforward linear cases, if implementation reasons would not require it Complications will arise when rule base increases Speed could be a bottleneck in some cases, if many rules