Fuzzy inference system | My Assignment Tutor

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