REAL-TIME FUZZY COMPUTATIONS

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REAL-TIME FUZZY COMPUTATIONS

• Dr. Brian T. Hemmelman
• Chaitanya Chandrana

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Background

• Traditional digital systems are based on binary
  numbers and Boolean algebra
• Systems can be equally well modeled with fuzzy
  set theory
• Nonlinear control systems are an especially good
  place for the application of fuzzy controllers

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Boolean Logic vs. Fuzzy Logic

• Boolean logic allows statements to be only 100
  TRUE or FALSE
• Fuzzy logic allows statements to be partially
  TRUE and partially FALSE at the same time

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Boolean Logic vs. Fuzzy Logic

• Boolean degree of membership ?A(x) 1 if x ? A
  and ?A(x) 0 if x ?A
• Fuzzy degree of membership ?A(x) 0,1

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Boolean Logic vs. Fuzzy Logic
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Fuzzy Set Operators

• Logic OR (Union) ?A ? ?B max ?A,?B

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Fuzzy Set Operators

• Logic AND (Intersection) ?A ? ?B min?A?B

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Fuzzy Set Operators

• Logic NOT (Complement) ?A 1 - ?A(x)

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Fuzzy Control Algorithm

• Read crisp inputs
• Fuzzify inputs
• Apply fuzzy associative matrix (rules)
• Compute fuzzy outputs
• Defuzzify outputs

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Fuzzification
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Fuzzification

• Humidity Degree of Error in Degree
  of Membership Humidity MembershipVery
  Dry 0.0 Neg. High 0.0Dry 0.0 Neg.
  Low 0.4Normal 0.7 None 0.6Humid 0.5 Pos.
  Low 0.0Very Humid 0.0 Pos. High 0.0

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Fuzzy Associative Matrix
Neg. High Neg. Low None Pos. Low Pos. High
Very Dry PH PH PH PL ZE
Dry PH PH PL ZE NL
Normal PH PL ZE NL NH
Humid PL ZE NL NL NH
Very Humid ZE NL NH NH NH
PH High Positive PL Low Positive ZE Zero NL
Low Negative NH High Negative
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Fuzzy Inference

• Apply fuzzy associative matrix to all
  combinations of inputs
• If humidity is Very Dry and error in humidity
  is Negative Low then water output is High
  Positive
• If humidity is Humid and error in humidity is
  None then water output is Low Negative
• Etc.

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Fuzzy Inference

• Assign minimum value to output membership
  function
• If humidity is 0.7 Normal and error in humidity
  is 0.6 None then water output is 0.6 Zero
• If humidity is 0.7 Normal and error in humidity
  is 0.4 Negative Low then water output is 0.4
  Low Positive
• Etc.

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Center Of Area Defuzzification
(ActiveArea_NegLow)(Center_NegLow)
(ActiveArea_Zero)(Center_Zero) (ActiveArea_Zero)
(Center_Zero) (ActiveArea_PosLow)(Center_PosLo
w)
ActiveArea_NegLow ActiveArea_Zero
ActiveArea_Zero ActiveArea_PosLow
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Center Of Area Defuzzification
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Real-Time Control For Temperature
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Fuzzy Associative Matrix
HN N SN ZE SP P HP
Real Cold VC VC VC NO LH H VH
Cold VC VC C NO LH H VH
Little Cold VC VC C NO LH H VH
Moderate VC C C NO H H VH
Little Hot VC C LC NO H VH VH
Hot VC C LC NO H VH VH
Real Hot VC C LC NO VH VH VH
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Defuzzification

• Actual defuzzified output control signal is value
  is a set point for portable heater/fan unit
• This signal was translated through a stepper
  motor control circuit to turn the control on
  heater/fan unit

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Experimental Setup
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Experimental Setup
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Conclusions

• Digital fuzzification of real-world signals
• Hardwired rule inference using fuzzy associative
  matrix
• Hardwired center of area defuzzification
• All fuzzy set computations performed completely
  in parallel
• Real-time system response