Fuzzy-control-system

LOGOFuzzycontrolsystemCAOJIANPENGPartoneFuzzycontroldefinitionFuzzycontrolcharacteristicsThecompositionofthefuzzycontrolFuzzyset4123FuzzycontroldefinitionFuzzycontrolprovidesaformalmethodologyforrepresenting,manipulating,andimplementingahuman’sheuristicknowledgeabouthowtocontrolasystem.AfuzzycontrolsystemisacontrolsystembasedonfuzzylogicBasedonZedehprofessor’sfuzzysettheory.Simplifiedreasoningisusedinfuzzycontrolthusfuzzycontrolisanintelligentcontrol.Duewiththefuzzyvariablewhichcannoteasytodividetocrispvalue.UsingthelanguagetodescribethevariableofthecontrolFuzzycontrolcharacteristicsUsefulcases:(1)Thecontrolprocessesaretoocomplextoanalyzebyconventionalquantitativetechniques.(2)Theavailablesourcesofinformationareinterpretedqualitatively,inexactly,oruncertainly.AdvantagesofFLC(FuzzyLogiccontroller):(1)Parallelordistributedcontrolmultiplefuzzyrules-complexnonlinearsystem.(2)Linguisticcontrol.Linguisticterms-humanknowledge.(3)Robustcontrol.Morethan1controlrules-aerrorofaruleisnotfatal.ThecompositionofthefuzzycontrolFourmaincomponentsofafuzzycontroller:Theknowledgebase:containsaknowledgeoftheapplicationdomainandthecontrolgoals.Thefuzzificationinterface:transformsinputcrispvaluesintofuzzyvaluesThedecision-makinglogic:performsinferenceforfuzzycontrolactionsThedefuzzificationinterface:transformsfuzzyvaluesintocrispvalues.ExampleSetallthepersonconsiderthe60°CwaterisHOT.Butifthetemperatureisbelowthan60°C,notallthepersonconsiderthat,sohowtoexpressthatwithfuzzy?FuzzysetCrispsetSetSisasetofXdomain.If𝒙∈𝑺,then𝝁𝒔𝒙=𝟏;if,then𝝁𝒔𝒙=𝟎;.xS:,Xμ01FuzzysetSetFisasetofXdomain.If𝒙∈𝑭,thenmembershipfunction𝝁𝑭𝒙willgivecorrespondencemembershipvaluetoeach𝒙.:,Xμ01𝝁𝒔𝒙ischaracteristicfunction.𝝁𝑭𝒙ismembershipfunction.FuzzycontroldefinitionFuzzysetbxbxmmbxbmxaamaxaxxA00)(mba()Axxaxaaxbbabxcdxcxddcxd0μ10abcdxxFuzzyset()()xaFxe222σμ()()FFxxc21μ1xxFuzzysetDifferencewiththenormalset.ParttwoMembershipfunctionFuzzificationFuzzyinferenceDefuzzification5134Knowledgebase2MembershipfunctionDefinition:amembershipfunctionforafuzzysetAontheuniverseofdiscourseXisdefinedas,whereeachelementofXismappedtoavaluebetween0and1.Thisvalue,calledmembershipvalueordegreeofmembership,quantifiesthegradeofmembershipoftheelementinXtothefuzzysetA.]1,0[:XA5070901103010Temp.(F°)FreezingCoolWarmHot01360.70.336F°is30%Cooland70%FreezingMembershipfunctionMembershipfunctiondesignFirstischoosingthecontroller'sinputandoutputvariable.Basedonthecontrolprecisionandrealneededtodecidethefuzzysetsnumber.Basedontherealcontrolsystemperformancemadedecideoftheeachfuzzyset’sdomain.Basedonthecontrolplantperformancetodecidethetypesofthemembershipfunctiontypes.Whentheinputvaluehastherandomnoisewhatmainstheinputvalueshouldbefuzzy,inthisconditionitsbettertousetriangularmembershipfunction.(Temperaturecontrolsystem)MembershipfunctionEachmembershipshouldoverlapsonlywiththeclosestneighboringmembershipfunctions;Foranypossibleinput,itsmembershipvaluesinallrelevantfuzzysetsshouldsumto1(ornearly)KnowledgebaseDatabasePartitionofthevariablespaces.InputRangeFreezingCoolWarmHotDomainInput(°C)MembershipvalueFreezing3050≥x≥01000400.50.500Cool5070≥x≥3001006000.50.50Warm7090≥x≥50001080000.50.5Hot90110≥x≥7000011100001KnowledgebaseRulebaseFuzzycontrolrules.FuzzyrulesarelinguisticIF-THEN-constructionsthathavethegeneralformIFATHENBwhereAandBare(collectionsof)propositionscontaininglinguisticvariables.AiscalledthepremiseandBistheresultoftherule.•Iftemperatureishot,thenairmotorspeedisblast.•Iftemperatureiswarm,thenairmotorspeedisfast.•Iftemperatureiscool,thenairmotorspeedisslow.•Iftemperatureiscold,thenairmotorspeedisstop.KnowledgebaseFordesigntherulebaseshouldcare:Expertknowledgeandcontrolengineeringknowledge.Observationofoperator’sactions.Fuzzymodeloftheprocess:linguisticdescriptionofthedynamicperformance.ExpertisemethodObservationalmethodBasedonfuzzymodelSelforganicmethodFuzzificationFuzzificationThisistheprocessthattransformthecrispvaluetothecrispvalue.bxbxmmbxbmxaamaxaxxA00)(5070901103010Temp.(F°)FreezingCoolWarmHot01360.70.3baxmFuzzylogicFuzzylogicConnectives:FuzzyConjunction(AND),FuzzyDisjunction(OR),Operateondegreesofmembershipinfuzzysets.ABmax(A,B)AB=CQualityCisthedisjunctionofQualityAandB010.375A010.75B(AB=C)(C=0.75)ORFuzzylogicABmin(A,B)AB=CQualityCistheconjunctionofQualityAandB010.375A010.75B(AB=C)(C=0.375)ConjunctionANDFuzzyinferenceMamdanimethodUsingminimuminferencingFuzzyinferenceMamdanimethodDefuzzificationForthedefuzzificationwecanusethecentroidmethodtotransformthemembershipvaluetocrispvalue.Thecentroidmethodisverypopular,inwhichthecenterofmassoftheresultprovidesthecrispvalue.MeanscrispoutputoffuzzyinferenceIndicatescenterofrealofamembershipfunctionThemembershipvalueoutputoffuzzyinferencecrispoUibi()()icrispoibUiΣμΣμ=