# Fuzzy Logic Control | My Assignment Tutor

ECTE441/841/941Intelligent ControlLecture 04 12Subject Outline Introduction to intelligent control and fuzzy sets Fuzzy operations and rules Fuzzy inference and PID control Fuzzy logic controller design Fuzzy logic controller tuning and fuzzy extension TSK fuzzy control13Objectives of This Lecture Explain basics of FLC system Design a Mamdani Fuzzy Controller manually. Design a Mamdani Fuzzy Controller using Matlab14Lecture Structure Introduction to FLC Mamdani FLC Example15Fuzzy Logic Control Fuzzy logic control (FLC) attempts to develop analternative method of designing a control system. The most basic FLC method is known as Mamdanimethod in which FLC is viewed as directly translatingexternal performance specifications and observations ofplant behavior into a rule-based linguistic controlstrategy. An alternative approach is the architecture proposed byTakagi and Sugeno (TSK method) in which acombination of linguistic rules and linear functions isused to form a fuzzy logic control strategy.16Mamdani Architecture Basic AssumptionThe basic assumption underlying the approach to fuzzylogic control proposed by Mamdani (1974) is this:In the absence of an explicit plant model and/or clearstatement of control design objectives, informalknowledge of the operation of the given plant can becodified in terms of if-then, or condition-action, rules.This forms the basis for a linguistic control strategy.17Mamdani Architecture Design IssuesIn Mamdani architecture, the design procedure for therule-base is not well defined. To this end Sugeno andTakagi have suggested the following methods to designthe rule base: Interrogation of human operator Observance of human operator in action Fuzzy model of processThe first two of the above methods are applicable insituations in which prior knowledge of the operation ofthe given physical system is available. In general onemay rely on intuitive model of the behaviour of the givenphysical system.18Mamdani Architecture: Basic ParadigmThe basic paradigm for fuzzy logic control that has emerged followingMamdani’s original work is a linguistic or rule-based strategy in theform:If OA1 is — and OA2 is .—- and . . . Then CA1 is — and CA2 is —. . .If OA1 is — and OA2 is —- and . . . Then CA1 is —and CA2 is — . . .This maps the observable attributes of a system (OA1 OA2…) to itscontrollable attributes (CA1, CA2…). InferenceEngine(CA1CA2…)Rule Base PhysicalSystem InputsOutputs(OA1OA2…)19Continuous CasePlant uh2.dt y FISen –+r dtdh1e h0unen1InputSet pointReferenceDesired outputCommandOutputResponse 20Generic Mamdani Controller in Discrete TimeLet’s consider a control strategy that maps the error, e=yd -y into thecontrol action, u. At the heart of the control strategy is a fuzzy logiccontrol algorithm that operates in discrete time steps of period T andmaps the normalized values of error, en(t), and change in error, cen (t)where ne and nce are the corresponding normalization factors, intochanges in the control action, dun (t), via rules of the form:If en(t) is P and cen (t) is N then dun (t ) is Z.Here P, N and Z are short for Positive, Negative, and Zero. In theintegrator the value of du is denormalized again byen(t)  nee(t), cen(t)  nce(e(t)  e(t  T ))u t T uu t u t T de u tu nddd    ( )( ) ( ) ( )PlantZ-1FIS duee+ –ydDerivative Controllern n dedu du+ +IntegratornceZ-1–nen+u yce ce21Control Rules for Speed Control of a Car 14tnPNNPZNPPPNZP 2 3T0 P N ZIf en(t) is P and cen (t) is N then dun (t ) is Z.-1 1mN Z P-1 1mN Z Pencendun en cendun-0.5 0.5y   y euen yd ynd 0yn,yd,en=1-yn If dun (t ) is P then cen is NIf dun (t ) is N then cen is P22Rules for the Generic Fuzzy Controller Observable AttributeError, enChange-in-error, cenControllable AttributesChange-in-input, dunI: Starting up, change the input inresponse to the setpoint changeIf en is P and cen is P then dun is PIf en is N and cen is N then dun is NII: Plant is not responding: adjust inputIf en is P and cen is Z then dun is PIf en is N and cen is Z then dun is NIII: Plant is responding normally, keepinput the sameIf en is P and cen is N then dun is ZIf en is N and cen is P then dun is ZIV: Reached equilibriumIf en is Z and cen is Z then dun is ZV: Error is nil but changing, takeactionIf en is Z and cen is N then dun is NIf en is Z and cen is P then dun is P 23Rules for the Generic Fuzzy Controller ce e(du)N0PNNN00N0PP0PP 24Comparison with a PD Controller Observable AttributeError, enChange-in-error, cenControllable AttributesChange-in-input, dunI:Starting up, change the input inresponse to the setpoint changeIf en>0 and cen>0 then dun>0If en

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