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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-output