Class 1 April 2012.pdf

7/27/2019 Class 1 April 2012.pdf

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EE04 804(B) Soft Computing Ver 1.2

Module

3

Fuzzy Logic Controller

(Case Studies)

5/1/2012 1

Dr. Sasidharan Sreedharanwww.sasidharan.webs.com


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Fuzzy Logic- Crisp & Fuzzy sets-fuzzy relations fuzzy conditional

statements- fuzzy rules- fuzzy

algorithm. Fuzzy Logic Controller

Fuzzy Interface knowledge base

decision making logic

defuzzification interface- design of

fuzzy logic controllercase studies.

Module III


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Fuzzy Cruise Controller

3

The controller is used to maintain a vehicle at a desiredspeed.

The system consists of two fuzzy inputs namely speed

difference and acceleration

The fuzzy output is throttle control.

Fuzzy cruise controller

Speed

Difference

Acceleration

Throttle

control


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The Fuzzy rule base

4

1. If (speed difference is NL) and (acceleration is ZE) then (throttle control is PL)

2. If (speed difference is ZE) and (acceleration is NL) then (throttle control is PL)

3. If (speed difference is NM) and (acceleration is ZE) then (throttle control is PM)

4. If (speed difference is NS) and (acceleration is PS) then (throttle control is PS)

5. If (speed difference is PS) and (acceleration is NS) then (throttle control is NS)

6. If (speed difference is PL) and (acceleration is ZE) then (throttle control is NL)

7. If (speed difference is ZE) and (acceleration is NS) then (throttle control is PS)

8. If (speed difference is ZE) and (acceleration is NM) then (throttle control is PM)

NL: Negative Large; PM : Positive Medium; ZE: Zero

NS: Negative Small; PL: Positive Large; PS: Positive Small

NM: Negative Medium


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Fuzzy rule base

5

Speed Difference Acceleration Throttle Control

NL ZE PL

ZE NL PL

NM ZE PM

NS PS PS

PS NS NS

PL ZE NL

ZE NS PS

ZE NM PM

NL: Negative Large; PM : Positive Medium; ZE: Zero

NS: Negative Small; PL: Positive Large; PS: Positive Small

NM: Negative Medium


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Fuzzy Sets

6


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Fuzzification of inputs

7


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Fuzzification Example

8


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Membership function

9

NSDelta 1= 100-63 = 37

Delta 2=127-100 = 27

Slope1 = 1/32 = 0.03125

Slope2= 1/32 = 0.03125

ZE

Delta 1= 100-95 = 5

Delta 2=159-100 = 59Slope1 = 1/32 = 0.0315

Slope2= 1/32 = 0.0315

37 * 0.031 25

( ) m in 2 7 * 0 .0 31 25

1

0. 8438

N S x

5 * 0 .0 3 1 2 5

( ) m in 5 9 * 0 .0 31 25

1

0. 1563

Z E x

NL,NM,PS,PM,PL is zero

Speed difference = 100


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Membership function

10

NM

( ) 0.7813N M

x

Acceleration= 70

NS

Acceleration= 70

( ) 0.2188NS

x


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Rule strength

11

1.Min (0,0) =0

2.Min (0.1563,0) = 0

3.Min (0,0) = 0

4.Min (0.8438,0) = 0

5.Min (0,0.2188) = 06.Min (0,0) = 0

7.Min (0.1563,0.2188) = 0.1563

8.Min (0.1563,0.7813) = 0.1563

Rule strength is obtained by

computing the minimum of

the membership functions


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Fuzzy output

12

Fuzzy output of the system is the fuzzy ORof all the

fuzzy outputs of the rules with non zero rule strengths.

In the event of more than one rule qualifying for thesame fuzzy output, the stronger among them is chosen.


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Defuzzification

13

The centre of gravity method is applied to defuzzify the

output.

Initially the centroids are computed for each of the

computing output membership functions


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Rule Base

14


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Defuzzification

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For the fuzzy set PS

X-axis centroid point =159

Rule strength applied to determine output area = 0.1563

Shaded area =1 1

1.( )

2

1 ( 0 .1 5 6 3) (6 4 6 3 .8 2 )2

9.99

h a b

For the fuzzy set PM

X-axis centroid point =191

Rule strength applied to determine output area = 0.1563

Shaded area =

1 1

1.( )

2

1( 0 .1 5 6 3) (6 4 6 3 .8 2 )

29.99

h a b

Weighted average:

CG = (9.99*159+9.99*191)/19.98

= 175Throttle control (normalized)

setting


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Short Answer Questions

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1. Explain about fuzzy relations

2. What are fuzzy associative memories? What is its use

3. Describe fuzzy conditional statements and fuzzy rules

4. Explain knowledge base and decision making logic

5. Describe about fuzzy algorithms

6. What are the various defuzzification methods

7. What is fuzzification? Give an example8. What are fuzzy associative memories? What is its use?

9. Describe briefly fuzzy logic crisp and fuzzy sets and fuzzy

relations.

10. Explain briefly knowledge base and decision-making logic.11. Describe about fuzzy algorithm

12. Describe about defuzzification interface.


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Essay type questions

17

1. Explain fuzzy logic, crisp and fuzzy sets, fuzzy rules and

fuzzy algorithm.

2. Explain fuzzification interface, knowledge base anddefuzzification interface.

3. Describe fuzzy algorithm

4. Compare various defuzzification methods

5. Describe fuzzy rules, fuzzy algorithm, design of fuzzy logiccontroller.

6. Describe fuzzy inference. Discuss fuzzy inferring

procedures.

7. Describe briefly fuzzification interface, knowledge base and

decision-making logic?

8. Explain about defuzzification interface and design of fuzzy

logic controller.

9. Describe about design of fuzzy logic controller and case

studies.


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Fuzzy associative memory (FAM)

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Fuzzy associative memories (FAMs) belong to the class of fuzzy

neural networks (FNNs).

A FNN is an artificial neural network (ANN) whose input

patterns, output patterns, and/or connection weights are fuzzy-

valued

Kosko's FAM suffers from an extremely low storage capacity andhence his overall fuzzy system comprises several FAM matrices.

Given a fuzzy input, the FAM matrices generate fuzzy outputs

which are then combined to yield the final result.

To overcome the original FAMs storage capacity limitations,

several researchers have developed improved FAM versions that

are capable of storing multiple pairs of fuzzy patterns.


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Regards

www.sasisreedhar.webs.com

Class 1 April 2012.pdf

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