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模糊控制外文文献
模糊控制外文文献
附录
CONTROL,PIDCONTROL,AND
ADVANCEDFUZZYCONTROL
FORSIMULATINGANUCLEAR
REACTOROPERATION
XIAOZHONGLIandDARUAN*
elgianNuclearResearchCentre(SCKoCEN
Boeretang200,8-2400Mol,Belgium
(Received15March1999)
BasedonthebackgroundoffuzzycontrolapplicationstothefirstnuclearreactorinBelgium(BRI)attheBelgianNuclearResearchCentre(SCK.CEN),wehavemadearealfuzzylogiccontroldemomodel.Thedemomodelissuitableforustotestandcom-paresomenewalgorithmsoffuzzycontrolandintelligentsystems,whichis
advantageousbecauseitisalwaysdifficultandtime-consuming,duetosafetyaspects,todoall
experimentsinarealnuclearenvironment.Inthispaper,wefirstreportbrieflyonthe
constructionofthedemomodel,andthenintroducetheresultsofafuzzycontrol,
aproportional-integral-derivative(PID)controlandanadvancedfuzzycontrol,inwhich
theadvancedfuzzycontrolisafuzzycontrolwithanadaptivefunctionthatcan
Self-regulatethefuzzycontrolrules.Afterwards,wepresentacomparativestudyofthose
threemethods.Theresultshaveshownthatfuzzycontrolhasmoreadvantagesinterms
offlexibility,robustness,andeasilyupdatedfacilitieswithrespecttothePIDcontrolof
thedemomodel,butthatPIDcontrolhasmuchhigherregulationresolutionduetoits
integrationterm.Theadaptivefuzzycontrolcandynamicallyadjusttherulebase,
thereforeitismorerobustandsuitabletothoseveryuncertainoccasions.
Keywords:
Fuzzycontrol;PIDcontrol;fuzzyadaptivecontrol;nuclearreactor
IINTRODUCTION
Todaythetechniquesoffuzzylogiccontrolareverymatureinmost
engineeringareas,butnotinnuclearengineering,thoughsomeresearchhasbeendone(Bernard,1988;HahandLee,1994;Linetal.1997;Matsuoka,1990).Themainreasonisthatitisimpossibletodoexperimentsinnuclearengineeringaseasilyasinotherindustrialareas.Forexample,areactorisusuallynotavailabletoanyindividual.Evenforspecialistsinnuclearengineering,anofficiallicencefordoinganyon-linetestisnecessary.Thatiswhywearestillconductingprojectssuchas"fuzzylogiccontrolapplication"inBRl(thefirstnuclearreactorinBelgium)(LiandRuan,1997a;Ruan,1995;RuanandLi,1997;1998;RuanandvanderWal,1998).Intheframeworkofthisproject,wefindthatalthoughtherearealreadymanyfuzzylogiccontrolapplications,itisdifficulttoselectthemostsui-
tablefortestingandcomparisonofouralgorithms.Moreover,duetothesafetyregulationsofthenuclearreactor,itisnotrealistictoperformmanyexperimentsinBRl.Inthissituation,wehavetoconductpartofthepre-processingexperimentsoutsidethereactor,e.g.,com-
parisonsofdifferentmethodsandthepreliminarychoicesoftheparameters.Onesolutionistomakeasimulationprogrammeinacomputer,butthishasthedisadvantagethatinwhich,however,therealtimepropertycannotbewellreflected.Thereforeanothersolutionhasadopted,thatis,wedesignedandmadeawater-level
controlsystem,referredtoasthedemomodel,whichissuitableforourtestingandexperiments.Inparticular,thisdemomodel(Fig.1)isdesignedtosimulatethepowercontrolprincipleofBRl(Lietal.,1996a,b;LiandRuan,1997b).
Inthisdemomodel,ourgoalwastocontrolthewaterlevelintowerTIatadesiredlevelbymeansoftuningVL(thevalveforlargecontroltowerT2)andVS(thevalveforsmallcontroltowerT3).ThepumpkeepsonworkingtosupplywatertoT2andT3.Alltapsareformanualtuningatthistime.VIandV2valvesareusedtocontrolthewaterlevelsinT2andT3respectively.Forexample,whenthewaterlevelinT2islowerthanphotoelectricswitchsensor1thentheon-offvalveV,willbeopened(on),andwhenthewaterlevelinT2ishigherthanphotoelectricswitchsensor2thentheon-offvalveVlwillbeclosed(off).ThesameistrueofV2.OnlywhenbothVIandV2areclosedV3willbeopened,becauseitcandecreasethepressureofthepumpandtherebyprolongitsworkinglife.ThepressuresensorisusedtodetecttheheightofwaterlevelinTI.SoforTI,itisadynamicsystemwithtwoentrancesandoneexitforwaterflow.
COMPARATIVESTUDYOFFUZZYCONTROL
TheDemoModelStructure
FIGURE1Theworkingprincipleofthedemomodel.
BRIisa42-yearoldresearchreactor,inwhichthecontrolmethodisthesimpleon-offmethod.Manymethodscalledtraditionalmeth-ods,whencomparedtofuzzylogic,arestillverynewtotheBR1reactor.Oneofthese,proportional-integral-derivative(PID)control,hastobetestedaswellasfuzzylogicmethod.Sofar,wehavetestedthenormalfuzzycontrol,traditionalPIDcontrol,andanadvancedfuzzycontrolonthisdemomodel.Toobtainabetterdemonstration,thesethreeapproacheshavebeenprogrammedandintegratedintoonecon-rollersystembasedontheprogrammablelogiccontroller(PLC)oftheOMRONcompany.Thepurposeoftluspaperistoreportcomparativeexperimentalresultsofthesethreemethodsfromthedemomodel.Section2simplyintroducesanormalfuzzycontrolanditsresult.
Section3introducesaPIDcontrolanditsresult.
Section4introducesanadvancedfuzzycontrolwhichisabletoself-regulatetheFuzzycontrolrules.Section5comparesthepreviousthreemethodsandtheirresults.
2FUZZYCONTROL
ThefuzzycontrolalgorithminthisdemomodelisanormalalgorithmbasedontheMamdanimodel.TosimulatetheBRlreactor,weusetwofuzzycontrollers(FLClandFLC2)tocontrolVLandVSseparately(note:
itispossibletouseonefuzzylogiccontrollerwithtwooutputstocontrolVLandVSandtherelatedresultcanbereferredto(LiandRuan,1997b)).LetDbethedifferencebetweentheactualvalue(P)ofwaterlevelandthesetvalue(S)andDDbethederivativeofD,inotherwords,thespeedanddirectionofthechangeofwaterlevel.VLandVSrepresentthecontrolsignaltoVL(Iargevalve)andVS(smallvalve),respectively.WhenDistoobig,weuseFLC1tocontrolVL(main-tuning);WhenDissmall,weuseFLC2tocontrolVS
(fine-tuning).WechooseDandDDasinputsofthefuzzylogiccon-troller,andVLorVSastheoutputofthefuzzylogiccontroller.DandDDmustbefuzzifiedbeforefuzzyinference.Supposetheuniversesofdiscourse(orinputvariables'intervals)ofDandDDare-d,djand[-dd,dd],respectively.Weuse7fuzzysetstopartitionhem,i.e.,NegativeLarge(NL),NegativeMiddle(NM),NegativeSmall(NS),Zero(ZE),PositiveSmall(PS),PositiveMiddle(PM),andPositiveLarge(PL).AsforVLandVS,becausetheresultoffuzzyreasoningisalsoafuzzylinguisticvalue,theuniversesofdiscourseofVLandVSalsoneedtobefuzzified.Weusethose7fuzzylinguisticermstoo.Symmetricaltrianglar-shapedfunctionsareusedtodefinethemembershipfunctionsforinputvariables(Lietal.,1995;1996a,b),andsingletonsareforoutputvariables(Ornron,1992).Eachfuzzycontrollerhasonerulebasewhichcontains49fuzzycontrolrules.Theitsrulecanberepresentedasthefollowingform:
ifDisAiandDDisBi,thenVL(orVS)isCiwhereA,Bi,andCiarefuzzylinguisticalvalues,suchasNL,PS,andsoon.Theaboveruleissometimesabbreviatedas(Ai,Bi:
Ci).Figure2showsacontroleffectofasyntheticcontrolprocess.Itfirstgoesupfrom0to20cmthenkeepsonat20an,nextdropsdownfrom20to10cmandfinallykeepsonat10cm.
Inviewofthisfigure,weknowthatthefuzzycontrolhasquickresponses(quicklyapproachingthesetvalue)andsmallovershoot(almostinvisible),butwithasmallsteadyerror(notsosmoothinasteadystate).
COMPARATWESTUDYOFFUZZYCONTROL
FIGURE2Thecontroleffectoffuzzycontroltothedemomodel.
3PIDCONTROL
InthePIDcontrol,itisdifficulttocontrolVLandVSseparatelylikethepreviousfuzzycontrolwithagoodcontrolresult,becausetheintegrationtermofthePIDcontrolneedssometime,andthiswillresultinanoscillationwhenswitchingcontrolsignalbetweenVLandVS.FromthispointofviewthePIDcontrolisworsethanthefuzzycontrol.Therefore,inourtests,VLandVShavetobecontrolledbythesamesignal.Weusethefollowingformula:
Bysubstitution,
whereU(I):
controlvaluetoVLandVSattimer;e:
thesetvalue-therealvalueattimeI;Kp:
theproportionalparameterandKp=(1IPB)xloo%,wherePBistheproportionalband;Ki:
theintegration
FlGURE3ThetrajectoryofthewaterlevelbythePIDcontrol.
parameterandKi=l/TiwhereTiistheintegrationtime;Kd:
thedifferentialparameterandKd=TdwhereTdisthedifferentialtime.Inpractice,adiscreteformoftheaboveformulaisused
whereT,isthesampleperiod.Figure3showsaresultofthePIDcontrol,wherePB=l5%,Ti=30s,Td=10s.Inviewofthisfigure,thePIDcontrolisverystable(verysmoothinsteadystates),andhasquickresponsestoo,butwithvisibleovershoots.
4ADVANCEDFUZZYCONTROL
Thekernelpartofthefuzzylogiccontrolisthefuzzyrulebasewithlinguisticterms,thoughthemembershipfunctionsandscalefactorsalsohaveanimportanteffectonthefuzzylogiccontroller.Therearesomepaperswhichdiscusshowtoadjustmembershipfunctionsand/orscalefactors(BaturandKasparian,1991;ChouandLu,1994;TonshoffandWalter,1994;Zheng,1992).Thissectionfocusesonrules.Normallythemethodsofderivingrulescanbebroadlydividedintotwotypes,sourceableandnon-sourceable.Thesourceablemethodmeanstherulesareobtainedfromsomeinformationsource,suchashumanexperienceorhistoricalinput-outputdata.Experiencehasbeenwidelyusedbythefuzzyengineers,especiallybytheearlyf