Fuzzy control

Introduction

ThefuzzymathematicscreatedbyZadehhasmadeagreatcontributiontothecontrolofambiguoussystems.Sincethe1970s,somepracticalfuzzycontrollershaveappearedoneafteranother,makingusAnotherbigstepforwardinthefieldofcontrol.

FuzzyLogicControlisabbreviatedasFuzzyControl,whichisacomputerdigitalcontroltechnologybasedonfuzzysettheory,fuzzylinguisticvariablesandfuzzylogicinference.In1965,L.A.ZadehoftheUnitedStatesfoundedthefuzzysettheory;in1973,hegavethedefinitionoffuzzylogiccontrolandrelatedtheorems.In1974,BritishE.H.Mamdaniformedafuzzycontrollerbasedonfuzzycontrolstatementsforthefirsttime,andappliedittothecontrolofboilersandsteamengines,whichachievedsuccessinthelaboratory.Thispioneeringworkmarkedthebirthoffuzzycybernetics.

Fuzzycontrolisessentiallyanonlinearcontrol,whichbelongstothecategoryofintelligentcontrol.Amajorfeatureoffuzzycontrolisthatithasbothasystematictheoryandalargeamountofpracticalapplicationbackground.ThedevelopmentoffuzzycontrolinitiallyencounteredgreaterresistanceintheWest;however,ithasbeenquicklyandwidelyusedintheEast,especiallyinJapan.

Inthepast20years,fuzzycontrolhasmadegreatprogressbothintheoryandtechnology,andhasbecomeaveryactiveandfruitfulbranchinthefieldofautomaticcontrol.Itstypicalapplicationsinvolvemanyaspectsofproductionandlife,suchasfuzzywashingmachines,airconditioners,microwaveovens,vacuumcleaners,camerasandcamcordersinhouseholdappliances;inthefieldofindustrialcontrol,therearewaterpurificationtreatments,fermentationprocesses,andchemicalreactors.,Cementkilns,etc.;inspecialsystemsandotheraspects,therearesubwayparkingatstations,cardriving,elevators,escalators,steamengines,androbotfuzzycontrol.

Basicprinciples

Inordertoachievehigh-precisioncontroloflinearmotormotion,thesystemadoptsafullyclosed-loopcontrolstrategy.However,inthespeedloopcontrolofthesystem,becausetheloaddirectlyactsonthemotorHowever,ifonlyPIDcontrolisusedforthedisturbance,itisdifficulttomeettherapidresponserequirementsofthesystem.Becausethefuzzycontroltechnologyhasthecharacteristicsofwideapplicationrangeandcertainrobustnesstotime-varyingloads,thelinearmotorservocontrolsystemisasystemthatrequiresfastresponseandcanrealizedynamicadjustmentinaveryshorttime.Therefore,thispaperconsidersdesigningaPIDfuzzycontrollerinthespeedloop,usingthefuzzycontrollertocontrolthespeedofthemotor,andrealizestheprecisecontrolofthelinearmotortogetherwiththeclassiccontrolstrategyofthecurrentloopandthepositionloop.

Thefuzzycontrollerconsistsoffourparts:

(1)Fuzzy.Themainfunctionistoselecttheinputquantityofthefuzzycontrollerandconvertitintothefuzzyquantitythatcanberecognizedbythesystem,whichspecificallyincludesthefollowingthreesteps:

First,theinputquantityisprocessedtomeettherequirementsoffuzzycontrol;

Secondly,scaletheinputquantity;

Thirdly,determinethefuzzylanguagevalueofeachinputquantityandthecorrespondingmembershipfunction.

(2)Rulebase.Establishfuzzyrulebasebasedontheexperienceofhumanexperts.Fuzzyrulelibrarycontainsmanycontrolrules,whichisakeystepinthetransitionfromactualcontrolexperiencetofuzzycontroller.

(3)Fuzzyreasoning.Mainlyrealizeknowledge-basedreasoninganddecision-making.

(4)Deblurring.Themainfunctionistoconvertthecontrolquantityobtainedbyreasoningintocontroloutput.

3.2Speed​​loopfuzzycontrollerdesign

First,thespeederrorEandthedeviationchangerateΔEarebothfuzzyquantized,andthequantizeddataisusedasthetwofuzzycontrollers.Input;then,performfuzzyinferenceaccordingtothefuzzyrules,anddefuzzifytheinferencefuzzyvalueandthenmultiplyitbyascalefactortoconverttoΔKp,ΔKi,ΔKd;third,addthevalueobtainedinstep2totheoriginalvalueGetthelatestsetofPIDvalues;finally,obtainthecontroldegreeu(t)accordingtothenewPIDvalues​​tocompletethecontroltask.

Concept

Thegeneralcontrolsystemarchitectureconsistsoffivemainparts,namely:definitionofvariables,fuzzification,knowledgebase,logicaljudgmentandde-fuzzification.ThefollowingwilldiscusseachpartAbriefexplanation:

Definevariables

Thatistodeterminethestatusoftheprogrambeingobservedandconsidertheactionsofcontrol.Forexample,ingeneralcontrolproblems,inputvariableshaveoutputerrorsEandoutputErrorrateofchangeEC,andfuzzycontrolwillalsocontrolthevariableastheinputUofthenextstate.Amongthem,E,EC,andUarecollectivelycalledfuzzyvariables.

Fuzzification

Theinputvalueisconvertedintothenumericalvalueoftheuniverseinanappropriateproportion,andthespokenvariableisusedtodescribetheprocessofmeasuringthephysicalquantity,accordingtotheappropriatelinguisticvalue(linguisticvalue)Findtherelativemembershipdegreeofthisvalue.Thiscolloquialvariableiscalledfuzzysubsets.

KnowledgeBase

Includestwoparts:adatabase(database)andarulebase(rulebase).Thedatabaseprovidesdefinitionsfordealingwithfuzzydata;andtherulebaseusesagroupoflanguagesControlrulesdescribecontrolobjectivesandstrategies.

LogicJudgment

Imitatethefuzzyconceptofhumanjudgment,usefuzzylogicandfuzzyinferencemethodtomakeinferences,andgetthefuzzycontrolsignal.Thispartistheessenceofthefuzzycontroller.

Defuzzify

Defuzzify:Convertthefuzzyvalueobtainedbyinferenceintoaclearcontrolsignalastheinputvalueofthesystem.

Variableselection

Theselectedcontrolvariablemusthavesystemcharacteristics.Whetherthecontrolvariableisselectedcorrectlywillhaveagreatimpactontheperformanceofthesystem.Forexample,whendoingpositioncontrol,theerroramountbetweenthesystemoutputandthesetvaluecanbeusedastheinputvariableofthefuzzycontroller.Generallyspeaking,thesystemoutput,outputvariation,outputerror,outputerrorvariation,andtotaloutputerrorcanbeselectedasthelanguagevariablesofthefuzzycontroller.Thespecificchoicedependsontheengineer’sunderstandingofthesystemanditsprofessionalknowledge..Therefore,experienceandengineeringknowledgeplayaveryimportantroleintheselectionofcontrolvariables.

Domaindivision

Afterthecontrolvariablesaredetermined,thenextstepistowritethecontrolrulesbasedonexperience.Beforemakingthefuzzycontrolrules,theinputandoutputvariablespaceofthefuzzycontrollermustbedividedintofuzzycontrol.Forexample,whentheinputspacehasonlyasinglevariable,threeorfivefuzzysetscanbeusedtodividethespaceintothreeorfiveregions.Whentheinputspaceisabinaryvariable,usingfourfuzzycontrolrules,thespacecanbedividedintofourregions.

Thedegreeofoverlapbetweenvariousfieldsduringfuzzysegmentationaffectstheperformanceofcontrol;generallyspeaking,thereisnoclearmethodtodeterminethedegreeofoverlapofthemodelset,andmostofthemrelyontheadjustmentofsimulationandexperimenttodeterminethesegmentationmethod,butSomereportssuggestthatabout1/3~1/2isideal.Thesizeoftheoverlapmeansthedegreeofblurbetweenfuzzycontrolrules,sofuzzysegmentationisanimportantfeatureoffuzzycontrol.

Functiontype

ThefuzzyvariableusedbyProfessorMamdaniatthebeginningisdividedintotwotypes:continuoustypeanddiscretetype.Therefore,thetypeofmembershipfunctioncanalsobedividedintocontinuoustypeanddiscretetype.kind.Duetothedifferentchoiceoflanguagevariablesandcorrespondingmembershipfunctions,manydifferentfuzzycontrollerarchitectureswillbeformed;thefollowingwillintroducethetypesofmembershipfunctions:

1.ContinuoustypeMembershipfunction

Therearethreecommoncontinuousmembershipfunctionsinfuzzycontrollers:

(1)Bell-shaped(2)Triangle(3)Trapezoid

2.DiscretetypeMembershipfunction

ProfessorMamdaniusesacontinuoustotalsetInaddition,adiscretecombinationcomposedof13elementsisalsoused.Becauseitismoreconvenienttouseintegerswhencalculatingwithmicroprocessorsthandecimalsbetween[0,1],themembershipdegreesoffuzzysetsareallexpressedasintegers.

Atthebeginningofthedevelopmentoffuzzycontroltheory,mostlybell-shapedmembershipfunctionswereused.Inrecentyears,triangularmembershipfunctionshavealmostbeenused.Thisisbecausethecalculationoftriangularmembershipfunctionsisrelativelysimple.Theperformanceisalmostthesameasthebellshape.

Controlrules

Controlrulesarethecoreofthefuzzycontroller.Itscorrectnessdirectlyaffectstheperformanceofthecontroller.Thenumberofthemisalsoanimportantmeasureoftheperformanceofthecontroller.Factors,thecontrolruleswillbefurtherdiscussedbelow.

Rulesource

Howtoobtainfuzzycontrolrules:

(1)Expertexperienceandknowledge

FuzzycontrolisalsocalledIntheexpertsystemofthecontrolsystem,theexpert'sexperienceandknowledgehavecluestoitsdesign.Humanbeingsoftenuselanguagequalitativeanalysisratherthannumericalquantitativeanalysistojudgethingsindailylife;andfuzzycontrolrulesprovideanaturalframeworkfordescribinghumanbehavioranddecisionanalysis;expertknowledgecanusuallybeexpressedintheformofif...then.

Byaskingexperiencedexpertstoobtaintheknowledgeofthesystem,andchangetheknowledgetotheformofif...then,thefuzzycontrolrulescanbeformed.Inaddition,inordertoobtainthebestsystemperformance,itisoftennecessarytousethetrialanderrormethodmultipletimestomodifythefuzzycontrolrules.

(2)Operator'soperationmode

Thecurrentpopularexpertsystemonlyconsiderstheacquisitionofknowledge.Expertscanskillfullymanipulatecomplexcontrolobjects,butitisnoteasytologicalizeexpertknow-how,whichrequiresconsiderationoftheacquisitionofskillsincontrol.Manyindustrialsystemscannotbecontrolledcorrectlywithgeneralcontroltheory,butskilledoperatorscansuccessfullycontrolthesesystemswithoutmathematicalmode:Thisinspiredustorecordtheoperator'soperatingmodeandorganizeitintoif...Thetypeof.thencanconstituteasetofcontrolrules.

(3)Learning

Inordertoimprovetheperformanceofthefuzzycontroller,itmustbecapableofself-learningorself-organization,sothatthefuzzycontrollercanincreaseOrmodifythefuzzycontrolrules.

Ruletype

Therearetwomainformsoffuzzycontrolrules:

(1)Stateevaluationfuzzycontrolrules

Stateevaluation(stateevaluation)fuzzycontrolrulesaresimilartohumanintuitionthinking,itisusedbymostfuzzycontrollers,anditstypeisasfollows:Ri:ifx1isAi1andx2isAi2….andxnisAin

thenyisCi

wherex1,x2,…….,xnandyarelinguisticvariablesorcalledfuzzyvariables,representingthestatevariablesandcontrolvariablesofthesystem;Ai1,Ai2,...,AinandCiarelinguisticvalues,representingfuzzysetsintheuniverseofdiscourse.Thereisanotherrepresentationofthisform,whichistochangetherearparttothefunctionofthesystemstatevariable.Itsformisasfollows:

Ri:ifx1isAi1andx2isAi2….andxnisAin

theny=f1(x1,x2,…….,xn)

(2)Fuzzycontrolrulesfortargetevaluation

ObjectevaluationFuzzycontrolrulescanevaluatecontroltargetsandpredictfuturecontrolsignals.Itsformisasfollows:

Ri:if(UisCi→(xisA1andyisB1))thenUisCi

Features

• Simplifiesthecomplexityofsystemdesign,especiallysuitableforthecontrolofnonlinear,time-varying,lagging,andincompletemodelsystems.

• Doesnotdependontheprecisemathematicalmodelofthecontrolledobject.

• Usingcontrollawstodescribetherelationshipbetweensystemvariables.

• Thesystemisdescribedbyverbalfuzzyvariablesinsteadofnumericalvalues.Thefuzzycontrollerdoesnotneedtoestablishacompletemathematicalmodelforthecontrolledobject.

• Thefuzzycontrollerisalanguagecontroller,whichisconvenientforoperatorstousenaturallanguageforman-machinedialogue.

• Fuzzycontrollerisanidealnonlinearcontrollerthatiseasytocontrolandmaster.Ithasbetterrobustness,adaptabilityandbetterFaultTolerance.

Disadvantages

1.Thedesignoffuzzycontrolstilllackssystemicity,whichisdifficulttocontrolthecomplexsystem.Itisdifficulttoestablishasystematicfuzzycontroltheorytosolveaseriesofproblemsoffuzzycontrolmechanism,stabilityanalysis,systematicdesignmethod,etc.;

2.Howtoobtainfuzzyrulesandmembershipfunctions,thatis,thedesignofthesystemThemethodiscompletelybasedonexperience;

3.Simplefuzzyprocessingofinformationwillleadtoadecreaseinthecontrolaccuracyofthesystemandadeteriorationindynamicquality.Ifyouwanttoimprovetheaccuracy,youwillinevitablyincreasethenumberofquantizationlevels,whichwillleadtotheexpansionoftherulesearchrange,reducethespeedofdecision-making,andevenfailtoimplementreal-timecontrol;

4.HowtoensurethestabilityofthefuzzycontrolsystemishowtosolvethefuzzycontrolThestabilityandrobustnessissueshaveyettoberesolved.

System

Fuzzycontrolisbasedonmoderncontroltheory,combinedwithadaptivecontroltechnology,artificialintelligencetechnology,andneuralnetworktechnology,andhasbeenunprecedentedlyappliedinthefieldofcontrol.

• Fuzzy-PIDcompoundcontrol

Fuzzy-PIDcompoundcontrolcombinesfuzzytechnologywithconventionalThePIDcontrolalgorithmiscombinedtoachievehighercontrolaccuracy.Whenthetemperaturedeviationislarge,Fuzzycontrolisused,whichhasfastresponsespeedandgooddynamicperformance;whenthetemperaturedeviationissmall,PIDcontrolisused,whichhasgoodstaticperformanceandmeetsthecontrolaccuracyofthesystem.Therefore,ithasbettercontrolperformancethanasinglefuzzycontrollerandasinglePIDregulator.

• Adaptivefuzzycontrol

Thiscontrolmethodhastheabilityofadaptiveself-learning,Itcanautomaticallymodifyandimprovetheadaptivefuzzycontrolrules,whichimprovestheperformanceofthecontrolsystem.Ithasbettercontrolperformanceforthosecomplexsystemswithnonlinearity,largetimedelay,andhighorder.

• Parameterself-tuningfuzzycontrol

Itisalsocalledproportionalfactorself-tuningfuzzycontrol.Thiscontrolmethodhasstrongadaptabilitytoenvironmentalchanges,andcanautomaticallycalibratethecontrollerinarandomenvironment,sothatthecontrolsystemcanmaintaingoodperformanceevenwhenthecharacteristicsofthecontrolledobjectchangeoraredisturbed.

• ExpertFuzzyControlEFC(ExpertFuzzyController)

Thecombinationoffuzzycontrolandexpertsystemtechnologyfurtherimprovestheintelligencelevelofthefuzzycontroller.Thiscontrolmethodnotonlymaintainsthevalueoftherule-basedmethodandtheflexibilitybroughtaboutbythefuzzysetprocessing,butalsocombinestheexpressionofexpertsystemtechnologywiththeadvantagesofusingknowledgetodealwithawiderrangeofcontrolproblems.

• Human-likeintelligentfuzzycontrol

ICalgorithmhastwokindsofproportionalmodeandholdmodeThecharacteristicsofthebasicmode.Thesetwocharacteristicsenablethesystemtobeintwostatesofclosed-loopoperationandopen-loopoperationwhentheabsolutevalueoftheerrorchanges.Thiscanproperlyresolvethecontradictionbetweenstability,accuracy,andrapidity,andisbetterappliedtopurelagobjects.

• Neuro-FuzzyControl(Neuro-FuzzyControl)

Thiscontrolmethodisbasedonneuralnetworksandusesfuzzylogictohavestrongstructuralknowledgeexpressioncapabilities,thatis,theabilitytodescribethequalitativeknowledgeofthesystem,thepowerfullearningcapabilitiesofneuralnetworks,andthedirectprocessingcapabilitiesofquantitativedata.

• Multivariablefuzzycontrol

Thiskindofcontrolissuitableformultivariablecontrolsystems.Amultivariablefuzzycontrollerhasmultipleinputvariablesandoutputvariables.

Fuzzyinference

Uptonow,thefuzzycontroltheorycanbedividedintothreemethods.Thefirstkindofinferenceisbasedonthesynthesisruleoffuzzyrelations,andthesecondkindofinference.Themethodissimplifiedbasedontheinferencemethodoffuzzylogic.Thethirdmethodofinferenceissimilartothefirstmethod,exceptthatthesubsequentpartischangedtoagenerallinearformula.Fuzzyinferencesmostlyadoptsyllogism,whichcanbeexpressedasfollows:

Conditionalproposition:IfxisAthenyisB

Fact:xisA

Conclusion:yisB

Theconditionalpropositioninthenotationisequivalenttothefuzzycontrolrulesinfuzzycontrol.Therelationshipbetweenthefrontpartandthebackpartcanbeexpressedbyafuzzyrelationship;asfortheinferencecalculation,itisThefuzzyrelationshipandfuzzysetAarecombinedandcalculatedtoobtainfuzzysetB.

Iftheantecedentpartcontainsmultiplepropositions,itcanbeexpressedasfollows:

Conditionalproposition:Ifx1isA1….andxnisAn

thenyisB

Fact:xisA1and….andxnisA'n

Conclusion:yisB

De-fuzzificationmethod

Intheimplementationoffuzzycontrol,manycontrolrulesaresubjectedtotheaboveinferencecalculations,andthenthecontroloutputisobtainedbycombiningtheinferenceresultsobtainedfromthecalculations;inordertoobtaintheoutputofthecontrolledsystem,thefuzzysetBmustbedefuzzified,Methodsofdefuzzificationinclude:

(1)Centerofgravitymethod

(2)Heightmethod

(3)Areamethod