1. Introduction to Fuzzy Control Lecture 10.1 Appendix E

2. Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

3. Fuzzy Logic

4. Normal “Crisp” logic where everything must be either True or False leads to PARADOXES

5. The sentence on the other side of the line is false The sentence on the other side of the line is false

6. A barber has a sign that reads: “I shave everyone who does not shave himself” Who shaves the barber?

7. Fuzzy Logic Lotfi Zadeh - Fuzzy Sets - 1965 Membership functions –Degree of membership between 0 and 1 Fuzzy logic operations on fuzzy sets A and B –NOT A => 1 - A –A AND B => MIN(A,B) –A OR B => MAX (A,B)

8. Membership Functions Young Age Not Young

9. Membership Functions Old Age Not Old

10. Membership Functions Age Not Old Not Young Middle Age = Not Old AND Not Young

11. Probabiltiy vs. Fuzziness Probability describes the uncertainty of an event occurrence. Fuzziness describes event ambiguity. Whether an event occurs is RANDOM. To what degree it occurs is FUZZY.

12. Probability: There is a 50% chance of an apple being in the refrigerator. Fuzzy: There is a half an apple in the refrigerator.

13. Fuzzy logic acknowledges and exploits the tolerance for uncertainty and imprecision.

14. Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

15. Fuzzy Membership Functions

16. Fuzzy Control Map to Fuzzy Sets Fuzzy Rules IF A AND B THEN L * * Defuzzification Inputs Output get_inputs(); fire_rules(); find_output();

17. Algorithm for a fuzzy controller do_forever { get_inputs(); fire_rules(); find_output(); }

18. Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

19. Fuzzification of inputs

20. get_inputs(); Given inputs x1 and x2, find the weight values associated with each input membership function. ZNMNSPSPM X1 0.2 0.7 W = [0, 0, 0.2, 0.7, 0]

21. Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification

22. Fuzzy Inference

24. Comparing the MAX rule and the SUM rule

25. Fuzzy Control Fuzzy Sets Design of a Fuzzy Controller –Fuzzification of inputs: get_inputs() –Fuzzy Inference –Centroid Defuzzification