ECTE441/841/941Intelligent ControlAutumn 2020Lecture 03 2Subject Outline Introduction to intelligent control and fuzzy sets Fuzzy operations and rules Fuzzy inference and PID control Fuzzy controller design and tuning Fuzzy extension TSK fuzzy control3Objectives of the Lecture Be able to use a fuzzy inference system. Develop a better understanding of the fuzzy approachby applying it to a specific example. Be able to apply PID for fuzzy logic controlMamdani Fuzzy Inference Systems4Structure of the lecture Fuzzy inference system Introduction Graphic approach Defuzzification Example PID control Structure and function Operation mechanism Tuning5Tipping Problem Problem: Given two numbers between 0 and 10 thatrepresents the quality of service and food at a restaurant(when 10 is excellent for service and delicious for food)what should the tip be for a specific visit? This problem is based on a tipping custom in UnitedStates which is on average 15% of the bill. This,however, can change depending on the quality of theservice and food provided.Rule 1: If service is poor or food is rancid then tip is cheapRule 2: If service is good then tip is averageRule 3: If service is excellent or food is delicious then tip is generous6Repeat (1)~(3) for All RulesMark: Service =3, food=8If service is poor or food is rancid then tip is cheap71 Fuzzy Inference SystemFuzzy Inference SystemCrispInputCrispOutput8Fuzzy Inference System AggregationMethod Defuzzify4. 5.FuzzifyInputsFuzzyOperationImplicationOperationFuzzifyInputsFuzzyOperationImplicationOperation…1.1.2.2.3.3.For each fuzzy rule: Rule 1: If service is poor or food is rancid then tip is cheapRule 2: If service is good then tip is averageRule 3: If service is excellent or food is delicious then tip is generous9Fuzzy MFsMF: Service MF: Food MF: Tip Rule 1: If service is poor or foodis rancid then tip is cheap Rule 2: If service is good thentip is average Rule 3: If service is excellent orfood is delicious then tip isgenerousFuzzy Matrix Each line for a rule Each column for a fuzzy inputor output Align each origin of fuzzy inputand output both vertically andhorizontally10(4) Aggregate All Outputs11(5) COA Defuzzify iA iiA i iCOAYAYACOAyy yyy dyy ydyy( )( ).( )( )12MOM Defuzzification 1A y ‘‘we have‘ { | ( ) *}Forwhich the MF reach a maximum *.average of the maximizing atMean of maximum is theYYMOMAMOMdyydyyY y yyy 2thenIf ( ) reaches its maximum wheneverIf ( ) has a single maximum at , thenleft rightMOMA left rightA MOMy yyy y [y ,y ]y y y* y y*. 13More on Defuzzification Definition “It refers to the way a crisp value is extracted from a fuzzyset as a representative value” There are five methods of defuzzifying a fuzzy set A of auniverse of discourse Z Centroid of area zCOA Mean of maximum zMOM Smallest of maximum zSOM Largest of maximum zLOM Bisector of area zBOA14More on Defuzzification Bisector of area zBOAthis operator satisfies the following;where = min {z; z Z} & = max {z; z Z}. zBOAzBOAA (z)dz A (z)dz, 1A y15 Smallest of maximum zSOMAmongst all z that belong to [z1, z2], the smallest is called zSOM Largest of maximum zLOMAmongst all z that belong to [z1, z2], the largest value is calledzLOMMore on Defuzzification16Information Flow of Fuzzy Inference System171. Fuzzify inputs:Resolve all fuzzy statements in the antecedent to a degree of membershipbetween 0 and 1. If there is only one part to the antecedent, this is the degreeof support for the rule.2. Apply fuzzy operator to multiple part antecedents:If there are multiple parts to the antecedent, apply fuzzy logic operators andresolve the antecedent to a single number between 0 and 1. This is thedegree of support for the rule.3. Apply implication method:Use the degree of support for the entire rule to shape the output fuzzy set.The consequent of a fuzzy rule assigns an entire fuzzy set to the output. Thisfuzzy set is represented by a membership function that is chosen to indicatethe qualities of the consequent. If the antecedent is only partially true, (i.e., isassigned a value less than 1), then the output fuzzy set is truncated accordingto the implication method.4. Aggregation:The combination of the consequents of each rule in preparation fordefuzzification.5. Defuzzification.Steps of FIS18Fuzzy Approach Essentials It would be ideal if we could just capture the essentialsof this problem, leaving aside all the factors that couldbe arbitrary. Let’s make a list of what really matters inthis problem: If service is poor, then tip is cheap If service is good, then tip is average If service is excellent, then tip is generous The order of rules is arbitrary. We might add two morerules: If food is rancid, then tip is cheap If food is delicious, then tip is generous19Crisp Inference SystemIf a

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