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Fuzzy Logic Control: Design, Defuzzification, and Fine-Tuning Procedures

This lecture focuses on the design procedure of Fuzzy Logic Controllers (FLC), covering essential steps such as defuzzification and fine-tuning fuzzy rules. It addresses the implementation details through practical examples, including a dog chases cat scenario. Emphasizing the importance of evaluating control rule quality with testing data, this presentation highlights refinement processes and the comparison of FLC with existing algorithms. The complexity of effectively fine-tuning control rules and balancing benefits against competing solutions is discussed to provide a comprehensive understanding of FLC effectiveness.

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Fuzzy Logic Control: Design, Defuzzification, and Fine-Tuning Procedures

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  1. Lecture 35Fuzzy Logic Control (III)

  2. Outline • FLC design procedure • Defuzzification • Fine-tuning fuzzy rules. • Dog chases cat example implementation details (C) 2001-2003 by Yu Hen Hu

  3. FLC Design Procedures Step 4. Defuzzification Step 5. Fine-tuning the control rules and performance evaluation • Evaluate the quality of the control rules using testing data set, and iteratively refine the definition of the fuzzy sets, and the fuzzy control rules. • Most time consuming, tedious, and difficult part. • Evaluate the effectiveness of a fuzzy controller by comparing to (if available) existing base line algorithms, analyzing cost benefit trade-off, implementation issues, etc. • FLC is only one of many alternatives! The value of FLC must be weighted against competing solutions. (C) 2001-2003 by Yu Hen Hu

  4. 1 0.5 mu(ang) 0 -150 -100 -50 0 50 100 150 1 0.5 mu(dz) 0 -30 -20 -10 0 10 20 30 Implementation Details • Fuzzification: • Use discrete support. The universe-of-discourse of support are sampled at uniform (or non-uniform) intervals. • Each fuzzy set (linguistic variable) is represented as a vector. Each element of the vector represents the values of the membership function at a particular point in the universe of discourse. • DCC example • Support vectors (both in degrees) sang: [–180 –150 –120 –90 –60 –30 0 30 60 90 120 150 180] sdz: [ –30 –25 –20 –15 –10 –5 0 5 10 15 20 25 30] (C) 2001-2003 by Yu Hen Hu

  5. Representing Fuzzy Sets M=[1 .67 .33 0 0 0 0 0 0 0 0 0 0; % LN 0 .33 .67 1 .67 .33 0 0 0 0 0 0 0; % SN 0 0 0 0 .33 .67 1 .67 .33 0 0 0 0; % ZO 0 0 0 0 0 0 0 .33 .67 1 .67 .33 0; % SP 0 0 0 0 0 0 0 0 0 0 .33 .67 1]; % LP Each row is represent a different fuzzy variable Each column of M is a sampling point over the universe of discourse of the support. To fuzzify ang(t) = 20o, first represent it on the support sang using interpolation: a = [0 0 0 0 0 0 1/3 2/3 0 0 0 0 0] Next, determine the fuzzy representation (input fuzzy variable activation)of ang(t): a = a M’ = [ 0 0 7/9 2/9 0 ] LN SN ZO SP LP (C) 2001-2003 by Yu Hen Hu

  6. Representing Rules ang &? dz weight LN SN ZO SP LP LN SN ZO SP LP rule=[ 1 0 0 0 0 1 1 0 0 0 0 1; % if ang is LN then dz is LN 0 1 0 0 0 1 0 1 0 0 0 1; % if ang is SN then dz is SN 0 0 1 0 0 1 0 0 1 0 0 1; % if ang is ZO then dz is ZO 0 0 0 1 0 1 0 0 0 1 0 1; % if ang is SP then dz is SP 0 0 0 0 1 1 0 0 0 0 1 1]; % if ang is LP then dz is LP &? = 1 if there is only one input fuzzy variable (this case) or the second fuzzy variable is to be ignored for that rule. Each row is a rule. (C) 2001-2003 by Yu Hen Hu

  7. Calculate rule activation from input fuzzy variable activation Activation = max(antecedent part of each rule * fuzzy set activation) LN SN ZO SP LP 0 0 7/9 2/9 0 w 0 0 7/9 2/9 0 Rule# 1 2 3 4 5 Inference (C) 2001-2003 by Yu Hen Hu

  8. Inference • Calculate output fuzzy set activation • Multiply each w (rule activation value) to the output variable portion of each corresponding rule. (assuming only one output variable) • Since multiple rules may be activated, find the maximum activation (fuzzy-OR) of each output fuzzy set. This gives the activation of individual output fuzzy set. • B’ is found using either the max-product method, or the max-min method (C) 2001-2003 by Yu Hen Hu

  9. 15 100 Cat Dog 50 10 angle y-axis 0 5 -50 0 -100 0 10 20 30 40 0 10 20 30 40 x-axis time 60 10 40 0 azi 20 dzi -10 0 -20 -20 0 10 20 30 40 0 10 20 30 40 time time Simulation Result (C) 2001-2003 by Yu Hen Hu

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