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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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Presentation Transcript
outline
Outline
  • FLC design procedure
    • Defuzzification
    • Fine-tuning fuzzy rules.
  • Dog chases cat example implementation details

(C) 2001 by Yu Hen Hu

flc design procedures
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

implementation details

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

representing fuzzy sets
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

representing rules
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

inference
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

inference8
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

simulation result

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