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Lecture 35 Fuzzy Logic Control (III)

Lecture 35 Fuzzy Logic Control (III). Outline. FLC design procedure Defuzzification Fine-tuning fuzzy rules. Dog chases cat example implementation details. FLC Design Procedures. Step 4 . Defuzzification Step 5 . Fine-tuning the control rules and performance evaluation

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Lecture 35 Fuzzy Logic Control (III)

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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 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 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 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 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 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 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 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 by Yu Hen Hu

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