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1、模糊控制外文文献附录CONTROL, PID CONTROL, ANDADVANCED FUZZY CONTROLFOR SIMULATING A NUCLEARREACTOR OPERATIONXIAOZHONG LIand DA RUAN*elgian NuclearResearchCentre(SCKoCENBoeretang200, 8-2400 Mol, Belgium(Received 15 March1999)Basedonthebackgroundoffuzzycontrolapplications tothefirstnuclearreactorinBelgium (BRI)

2、atthe Belgian NuclearResearch Centre(SCK.CEN), wehavemade a real fuzzy logic control demo model. The demo modelis suitable for usto test and com- paresome newalgorithmsoffuzzy controlandintelligent systems, whichisadvantageous because it is always difficult and time-consuming, due to safety aspects,

3、 to do allexperiments in areal nuclear environment. Inthis paper, wefirst report briefly on theconstructionofthedemo model, andthenintroducetheresults of afuzzy control,a proportional-integral-derivative (PID)control and an advanced fuzzy control, in whichthe advancedfuzzy controlis a fuzzy control

4、with an adaptive function that canSelf-regulate thefuzzy control rules. Afterwards, we present a comparative study of thosethree methods. The results have shown that fuzzy control has more advantagesin termsof flexibility, robustness,and easily updated facilities withrespect to the PID control ofthe

5、 demo model, butthat PID control has muchhigher regulation resolution due to itsintegration term. The adaptive fuzzy control can dynamically adjust the rule base,therefore it is more robust and suitable tothose very uncertain occasions.Keywords:Fuzzycontrol; PIDcontrol;fuzzy adaptive control; nuclea

6、rreactorIINTRODUCTIONTodaythetechniquesof fuzzylogic control are very maturein mostengineeringareas, butnotinnuclearengineering, thoughsome research has been done(Bernard, 1988; Hah and Lee,1994; Lin et al. 1997; Matsuoka,1990). The mainreason isthatitisimpossibleto do experiments in nuclearengineer

7、ing as easily as inotherindustrial areas.Forexample, areactorisusuallynot available to any individual.Evenforspecialistsinnuclearengineering, anofficiallicence for doingany on-line testis necessary. Thatis whyweare still conducting projects such as fuzzylogic control applicationin BRl(the firstnucle

8、arreactorinBelgium)(Li andRuan,1997a; Ruan,1995; Ruan and Li, 1997; 1998;Ruan and van der Wal,1998).In the frameworkofthisproject, wefindthat althoughtherearealready many fuzzylogiccontrol applications,itis difficulttoselectthe mostsui-table for testing and comparison of our algorithms. Moreover, du

9、e to thesafetyregulationsof thenuclearreactor,itisnotrealisticto perform many experiments in BRl. Inthis situation, wehave to conduct part ofthe pre-processing experiments outsidethe reactor, e.g., com-parisons ofdifferentmethodsandthepreliminarychoicesofthe parameters.Onesolutionistomakeasimulation

10、programmeina computer,butthishasthedisadvantagethatinwhich,however, therealtimepropertycannotbewellreflected.Therefore another solutionhasadopted,thatis,wedesignedand madea water-levelcontrolsystem, referred toasthedemo model, whichissuitablefor ourtestingandexperiments.Inparticular,this demo model(

11、Fig.1) is designedto simulatethe powercontrol principle of BRl(Li et al., 1996a,b; Liand Ruan, 1997b).In this demo model, our goal was to control the water level in tower TI at a desired level bymeans oftuning VL(the valve for large control towerT2)and VS(the valveforsmallcontroltowerT3). The pump k

12、eeps on working to supply waterto T2andT3.Alltaps arefor manual tuning at thistime. VIandV2valves are usedto control the water levelsin T2and T3 respectively. For example, whenthe waterlevelin T2 is lower than photoelectric switchsensor 1 then the on-offvalve V, will be opened (on), and when the wat

13、er levelin T2is higherthan photoelectric switch sensor 2 then the on-offvalve Vl will be closed (off). The same istrue ofV2.Only whenbothVI andV2are closedV3 will beopened,because itcandecreasethepressureofthepumpand thereby prolongits working life. The pressure sensor is usedto detect the height of

14、 waterlevelinTI.So for TI,itisa dynamic system with two entrancesand one exit for water flow.COMPARATIVE STUDY OFFUZZYCONTROLThe Demo Model StructureFIGURE 1The working principle of the demo model.BRI is a 42-year old research reactor, in which the control method is the simple on-off method. Many me

15、thods called traditional meth- ods, when compared to fuzzy logic, are still verynewto the BR1reactor. One ofthese,proportional-integral-derivative(PID) control, has to betestedas wellas fuzzy logic method. So far, wehavetestedthe normal fuzzy control, traditionalPID control, and an advanced fuzzy co

16、ntrol on this demo model. To obtain a better demonstration, these three approaches have been programmed and integrated into one con- roller system basedon theprogrammablelogic controller(PLC) of the OMRON company. The purposeof tluspaperistoreportcomparative experimentalresults of these three method

17、s from thedemo model.Section2simplyintroduces a normal fuzzy control and its result.Section3introducesaPIDcontrolandits result.Section4 introduces an advanced fuzzy control which is able to self-regulate the Fuzzycontrolrules. Section 5comparesthepreviousthree methods and their results.2 FUZZY CONTR

18、OLThe fuzzy control algorithm inthis demo model is a normal algorithm basedonthe Mamdanimodel.To simulatethe BRlreactor, weuse twofuzzy controllers(FLCl and FLC2)tocontrol VL and VSseparately(note:itispossibleto useonefuzzylogic controller withtwo outputs to control VL and VS and the relatedresult c

19、an bereferredto (LiandRuan,1997b). Let Dbethedifferencebetweentheactual value (P) of water level and the set value(S)and DD bethe derivative of D,inother words,the speed anddirection of the change ofwater level. VLand VSrepresentthe control signal to VL(Iarge valve) and VS (small valve),respectively

20、. When Dis too big, we use FLC1to control VL(main-tuning); When Dis small, weuse FLC2 to control VS(fine-tuning). Wechoose D and DD asinputs ofthe fuzzylogic con- troller, and VL or VS as theoutputof the fuzzylogic controller.DandDD mustbefuzzifiedbeforefuzzyinference.Supposethe universes of discour

21、se (orinputvariables intervals)of D andDDare -d,djand-dd,dd,respectively. Weuse7fuzzysetstopartitionhem,i.e.,NegativeLarge(NL),Negative Middle(NM),Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Middle (PM),and Positive Large(PL). Asfor VLand VS,becausetheresultoffuzzy reasoning is als

22、oa fuzzylinguistic value, the universes of discourse of VLand VS also needtobefuzzified. Weusethose 7 fuzzylinguistic erms too. Symmetrical trianglar-shapedfunctions are usedto definethe membership functions for input variables (Li et al., 1995; 1996a,b),and singletons are for outputvariables(Ornron

23、,1992). Eachfuzzycontrollerhasonerulebasewhichcontains49fuzzy control rules. The its rule can be represented as the followingform: ifD is Ai and DDis Bi,then VL(or VS)is Ci where A, Bi, and Ciare fuzzylinguistical values, such as NL, PS, and so on.Theabove rule is sometimes abbreviatedas (Ai,Bi:Ci).

24、 Figure 2 shows a control effect of asyntheticcontrol process. It first goes up from 0 to 20cmthen keeps on at 20 an,next drops downfrom 20 to 10 cmand finally keeps on at 10cm.Inviewofthisfigure,weknowthatthefuzzycontrolhasquickresponses(quicklyapproachingthesetvalue)andsmallovershoot (almostinvisi

25、ble),but withasmall steady error (notso smoothina steady state).COMPARATWE STUDY OF FUZZY CONTROLFIGURE2The control effect of fuzzycontrolto the demo model.3PID CONTROLIn the PID control, itis difficultto control VL and VSseparatelylike the previous fuzzy controlwith a good control result, because t

26、he integration term of the PID control needs some time, and this will result in an oscillation when switching control signal between VL and VS. From this point of view the PID control is worse than the fuzzy control. Therefore, in our tests, VL and VS have to be controlled by the same signal. We use

27、 the following formula:U(t)K pee dtTddeTidtBy substitution,U(t)K peK ie dtK ddedtwhereU(I):control valueto VL and VS at time r;e:the proportional parameter and Kp=(1IPB)x loo%,Ki:theintegrationthe set value-the real value at timeI; Kp:wherePBistheproportionalband;parameterand Kd =usedFlGURE 3The tra

28、jectoryofthe water level by the PID control.and Ki=l/Tiwhere Tiis the integrationtime; Kd:the differentialparameterTd where Tdis the differential time. In practice, a discrete form of the above formula isU(t)K Pe(t)K i Tse(1)e(2).e(t)K d e(t)e(t1)Tswhere T,isthe sample period. Figure 3 shows a resul

29、t of the PID control,where PB= l5%, Ti=30s,Td=10s. Inviewofthis figure,thePIDcontrolis verystable(verysmooth insteadystates),andhasquickresponses too,butwithvisible overshoots.4 ADVANCED FUZZY CONTROLThekernel partofthefuzzylogic controlisthefuzzyrulebase withlinguisticterms,thoughthe membershipfunc

30、tionsandscale factors also have animportant effect onthefuzzylogiccontroller.Therearesomepaperswhichdiscusshowtoadjustmembershipfunctions and/or scale factors(Baturand Kasparian,1991;Chouand Lu,1994;Tonshoffand Walter,1994;Zheng,1992).Thissectionfocuseson rules. Normallythemethodsofderivingrulescan

31、bebroadlydividedintotwotypes,sourceableandnon-sourceable.Thesourceable methodmeanstherules are obtained fromsome informationsource, such as human experience or historicalinput-outputdata. Experience hasbeenwidelyused by the fuzzy engineers,especiallybytheearly fuzzy engineers. The problemofusing hum

32、anexperience is thatit is time-consuming,and to some degree subjective.Inorder toovercome these problems,particularlyavoidingthesubjectivity,historicalinput-outputdata-ifavailable can be used. To obtainrules from such data, many methods are used, one ofthe popularapproaches is neural net- works(NN)(

33、Berenjiand Khedkar,1992; HalgamugeandGlesner,1994; Jang, 1992; Kosko, 1992; Li et al.,1995; Lin ezal., 1995; Takagiand Hayashi,1991; Wangand Mendel,1992). One problemofthe sourceable methodisthatit depends strictly on the source which will be transformedinto rules. Inthe case that the source isnoisy

34、, then the rules mightbebiased. Anotherproblemofthesourceable methodis thatitis usually non-adaptive,i.e., alltherules are fixed,therefore it cannot perform wellunderadynamic environment. The non-source- ablemethodsaresource-freeandtheyproduceandchoose rules accordingtoaperformance measurementofthec

35、ontroller,suchasgeneticalgorithms(GA)(Karr,1991;Limetal.,1996;QiandChin,1997) (mostlyalsogenerating membership functions and scale factors) and self-organizing controllers (SOC) (Heer al.,1993; Li et al., 1996a,b; Linetal.,1997, Procykand Mamdani,1979; Shao,1988; Tanscheitand Scharf,1988;Wuetal.,199

36、2). WithGAitis possible tofindintegratedlyoptimalparametersbutGAisverycomputationrich,andfurthermore,it is almost impossible toapplyGAin a real complex system withouta simulationmodel. Perhapsthe SOCis the onlymethod which has the followingadvantages: objective,adaptive,less computationrequired, mor

37、eerror-tolerant, and simple.FIGURE 4An adaptive functionis incorporatedinto a fuzzycontrol system.ThegeneralprincipleoftheSOCisthatthecontrollermonitorsitsownperformanceandadjustsitscontrolrulestoimproveperformance for time-varyingandunknown plants. The problem of the SOC showto performthe performan

38、ce measurement. Thebasic wayisto design a performancemeasurement tablewhichlooks like a fuzzy control ruletable and to useitto assess the performance of the controller rules)(ProcykandMamdani,1979), but to designsuchaperformancemeasurementtableisalsoverydifficult(Chung and Oh, 1993) anditissystem-de

39、pendent. Basedon the SOC, this section willintroduce an adaptivemethod which uses a set of new norms to replace the ormerperformancemeasurement.Thenewnormsareverysimpleandsystem-independent,thereforetheycanbe easily appliedto most fuzzy controllers. Inthis section, the advancedfuzzy control means th

40、e above SOC,in other words, a fuzzy controlwith an adaptive function, where the adaptive function contains two steps: performancejudgementandchangingfuzzycontrolrules.Figure4illustrates howanadaptivefunctionisincorporatedintothefuzzy control system. Atthebeginning ofeach cycle, the controllerslastbe

41、haviourisjudgedandthentherulebase ischanged accordingly. Inthis cycle, thecontrollerwillusethe newrulebase andoutput theresulttothe controlledobject. Thebehaviourof the new rule base will be judgedand changed again inthe next cycle.4.1ThePrincipleofthe Adaptive FunctionLet D and DD represent error (

42、the difference between the actual value and the desired value)and change inerror, respectively. Let D(t) and DD(t) represent error and change in error at time t,respectively. They are two input variables. LetUbe an outputvariable,and assume thetotalnumber of the rules is n,then every rule has the fo

43、llowing form: if Dis A, DD isBi,thenUisC;,i=1,2 ,.,n, whereA,Bi,andCiare fuzzy linguistic values andiis anindexpointingouteach rulespositioninthe rule table (or the ruledata file). Useri to representthe fuzzy control magnitude (conclusionfuzzy set) of the ith rule, and let simplyr i 1,2,3,4,5,6,7whe

44、re1=NL,2=NM,3=NS,4=ZE,5=PS,6=PMY7=PL.In general, a control locus may be expressed with Fig. 5, and it can be regardedashavinguptofourfeaturesectionsandfourfeature points. Foreachfeaturepart,we offeranorm to guide the regulation of the fuzzy control rules. For example,the current waterlevel P(t)isint

45、hefeaturepart(I),thenafterthefuzzycontrollingusingthecurrentcontrolrules, we measure the waterlevel P(t +l) at the nexttime which has three possibilities:P(l) P(t + 1) S;P(t + 1) S and P(t + 1) S.FIGURE 5Any trajectory has up to four feature sections and four feature points.The related norm to guide

46、 how to change rules is the following:(i)if D(I +1) 5 0 and DD(t +I) 0,that is, P(t) P(t +1)5 S, then ri =ri(ii)if D(i f 1) 0and DD(t + 1) 0,that is, P(t +1) S and P(t + 1) 0, that is, P(t + 1) S, then ri = ri - a,where a is a step size and a =1,2,3,4,5,6. In case (i), thefuzzy con-troller makes the

47、 water level P(t f 1) closer to the set value S, therefore thebehaviourofthe fuzzycontrollerisgood,norulesshouldbe changed;Incase (ii), thefuzzy controllermakes thewater level P(t + 1) further fromthe set value S, therefore the behaviour of the fuzzy con- troller isnot good, the strength is too weak

48、 and the action of the correspondingrules shouldbestronger;In case(iii),thefuzzycontroller makes the waterlevelP(t $1)overpassthe set value S,thereforethe behaviourofthe fuzzycontrollerisnotgood, the strengthistoo strongand the action of the corresponding rules should be weakened. Not all rules but

49、some of those that areactivatedinlast cycle should be regulated. Weusethefollowingformula to describe whichshouldbe adjusted:A i( D ) Bi (DD )(A j ( D ) Bj ( DD )C jCiwhichmeansthe ithruleis changedonlyifitisthe largestactivated amongthoseactivatedrules which havethe same conclusion part. Forexample

50、,(NL,NM : PL) and (NM,NM :PL) are two activated rules and have the same conclusion part,i.e., PL. Comparing NL(D)A NM(DD)with NM(D) A NM(DD),the larger one correspondstothe rule which should be adjusted.4.2 AnExperimental ResultTo guarantee no overshoot, the best way is toinitialize all rules as the

51、 same conclusion part: NL, asshown in Table I. In this table, for example, NL at the row 2 and column 3 means: if D is NM and DDis NL then VL or VS is NL. All rules have the same conclusionpart though condition partsaredifferent.Figure 6 illustratesTABLE IThe initialruletable for both FLCland FLC2FIGURE6Comparison between adaptivefuzzy control and fuzzycont