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Introduction to Fuzzy Control

Introduction to Fuzzy Control. Lecture 10.1 Appendix E. Fuzzy Control. Fuzzy Sets Design of a Fuzzy Controller Fuzzification of inputs: get_inputs() Fuzzy Inference Centroid Defuzzification. Fuzzy Logic. Normal “Crisp” logic where everything must be either True or False leads to

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Introduction to Fuzzy Control

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  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” logicwhere everything must be eitherTrue 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 Not Young Age

  9. Membership Functions Not Old Old Age

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

  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 therefrigerator.

  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 Inputs Map to Fuzzy Sets get_inputs(); Fuzzy RulesIF A AND B THEN L** fire_rules(); Defuzzification find_output(); 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 weightvalues associated with each input membership function. NM NS Z PS PM 0.7 0.2 X1 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

  23. 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

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