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FUZZY LOGIC CONTROLLER application; Solved Example

fuzzy logic controller diagram

 Fuzzy Logic Controller

FUZZY LOGIC CONTROLLER to determine the wash time of Domestic washing machines

Design a fuzzy logic controller to determine the wash time of the domestic washing machine. Assume the input is dirt & grease on clothes. Use three descriptors for input variables and five descriptors for output variables. Derive the set of rules for controller action and defuzzification. Show that if the cloths are solid to a larger degree the wash time will be more and vice versa.

Step 1:

Define Input and Output Variables:

Input Variable:

  • Dirt

(SD) Small dirt

(MD) Medium dirt

(LD) Large dirt

  • Grease

(NG) No grease

(MG) Medium grease

(LG) Large grease

Output Variable:

  • Wash Time

       Very Short (VS)

       Short (S)

       Medium (M)

       Long (L)

        Very Long (VL)

Step 2:

Define Membership Functions:

Define membership functions and output variables (We use triangular Membership function)

 

* Membership Function for Dirt:

Fuzzy logic controller 
Fuzzy Logic
Solved Example of Fuzzy Logic
Practical apllication of fuzzy logic
Fuzzy logic controller

 

* Membership Function for Grease:

Fuzzy logic controller 
Fuzzy Logic
Solved Example of Fuzzy Logic
Practical appllication of fuzzy logic
Fuzzy logic controller

 

* Membership Function for Wash time:

Fuzzy logic controller 
Fuzzy Logic
Solved Example of Fuzzy Logic
Practical appllication of fuzzy logic
Fuzzy logic controller
Fuzzy logic controller

Step 3:

From a rule base:

Fuzzy logic controller 
Fuzzy Logic
Solved Example of Fuzzy Logic
practical apllication of fuzzy logic

Step 4:

Rule Evaluation:

Assume Dirt = 60%, Grease = 70%

 

Fuzzy logic controller 
Fuzzy Logic
Solved Example of Fuzzy Logic
Practical appllication of fuzzy logic

 

The above four equation leads to 4 rules that need to evaluate:

  • Dirt is Medium and Grease is Medium
  • Dirt is Medium and Grease is Large
  • Dirt is Large and Grease is Medium
  • Dirt is Large and Grease is Large

Since the antecedent part of each of the above rule is connected by and operator we use min operator to evaluate strength of each rule.

Fuzzy logic controller
Fuzzy logic controller
Fuzzy logic controller 
Practical application of fuzzy logic
Solved example of fuzz logic

 

MAX Membership function

Step 5:

Defuzzification:

Since we use “Mean of Maxdefuzzification technique

 Maximum strength = Max (S1, S2, S3, S4)

                                 = Max (3/5, 2/5, 1/5, 1/5)

  = 3/5

 

This corresponds to rule 1

. Rule 1: Dirt is medium and Grease is medium has maximum strength (3/5)

To find out the final defuzzified value, we now take average (mean) of μM (z)

Fuzzy logic controller
Fuzzy logic controller

 

This is the output of wash time of washing machine. This is the practical application of Fuzzy logic controller

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