PID控制器中英文对照外文翻译文献

中英文对照外文翻译文献(文档含英文原文和中文翻译)外文:Memory-BasedOn-LineTuningofPIDControllersforNonlinearSystemsAbstract—Sincemostprocesseshavenonlinearities,controllerdesignschemestodealwithsuchsystemsarerequired.Ontheotherhand,PIDcontrollershavebeenwidelyusedforprocesssystems.Therefore,inthispaper,anewdesignschemeofPIDcontrollersbasedonamemory-based(MB)modelingisproposedfornonlinearsystems.AccordingtotheMBmodelingmethod,somelocalmodelsareautomaticallygeneratedbasedoninput/outputdatapairsofthecontrolledobjectstoredinthedata-base.TheproposedschemegeneratesPIDparametersusingstoredinput/outputdatainthedata-base.ThisschemecanadjustthePIDparametersinanon-linemannerevenifthesystemhasnonlinearproperties.Finally,theeffectivenessofthenewlyproposedcontrolschemeisnumericallyevaluatedonasimulationexample.I.INTRODUCTIONInrecentyears,manycomplicatedcontrolalgorithmssuchasadaptivecontroltheoryorrobustcontroltheoryhavebeenproposedandimplemented.However,inindustrialprocesses,PIDcontrollers[1],[2],[3]havebeenwidelyemployedforabout80%ormoreofcontrolloops.Thereasonsaresummarizedasfollows.(1)thecontrolstructureisquitsimple;(2)thephysicalmeaningofcontrolparametersisclear;and(3)theoperators’know-howcanbeeasilyutilizedindesigningcontrollers.Therefore,itisstillattractivetodesignPIDcontrollers.However,sincemostprocesssystemshavenonlinearities,itisdifficulttoobtaingoodcontrolperformancesforsuchsystemssimplyusingthefixedPIDparameters.Therefore,PIDparameterstuningmethodsusingneuralnetworks(NN)[4]andgeneticalgorithms(GA)[5]havebeenproposeduntilnow.Accordingtothesemethods,thelearningcostisconsiderablylarge,andthesePIDparameterscannotbeadequatelyadjustedduetothenonlinearproperties.Therefore,itisquitedifficulttoobtaingoodcontrolperformancesusingtheseconventionalschemes.Bytheway,developmentofcomputersenablesustomemorize,fastretrieveandreadoutalargenumberofdata.Bytheseadvantages,thefollowingmethodhasbeenproposed:Whenevernewdataisobtained,thedataisstored.Next,similarneighborstotheinformationrequests,called’queries’,areselectedfromthestoreddata.Furthermore,thelocalmodelisconstructedusingtheseneighbors.Thismemory-based(MB)modelingmethod,iscalledJust-In-Time(JIT)method[6],[7],LazyLearningmethod[8]orModel-on-Demand(MoD)[9],andtheseschemehavelotsofattentioninlastdecade.Inthispaper,adesignschemeofPIDcontrollersbasedontheMBmodelingmethodisdiscussed.AfewPIDcontrollershavebeenalreadyproposedbasedontheJITmethod[10]andtheMoDmethod[11]whichbelongtotheMBmodelingmethods.Accordingtotheformermethod,theJITmethodisusedasthepurposeofsupplementingthefeedbackcontrollerwithaPIDstructure.However,thetrackingpropertyisnotguaranteedenoughduetothenonlinearitiesinthecasewherereferencesignalsarechanged,becausethecontrollerdoesnotincludesanyintegralactioninthewholecontrolsystem.Ontheotherhand,thelattermethodhasaPIDcontrolstructure.PIDparametersaretunedbyoperators’skills,andtheyarestoredinthedata-baseinadvance.Andalso,asuitablesetofPIDparametersisgeneratedusingthestoreddata.However,thegoodcontrolperformancecannotbenecessarilyobtainedinthecasewherenonlinearitiesareincludedinthecontrolledobjectand/orsystemparametersarechanged,becausePIDparametersarenottunedinanon-linemannercorrespondingtocharacteristicsofthecontrolledobject.Therefore,inthispaper,adesignschemeofPIDcontrollersbasedontheMBmodelingmethodisnewlyproposed.Accordingtotheproposedmethod,PIDparameterswhichareobtainedusingtheMBmodelingmethodareadequatelytunedinproportiontocontrolerrors,andmodifiedPIDparametersarestoredinthedata-base.Therefore,moresuitablePIDparameterscorrespondingtocharacteristicsofthecontrolledobjectarenewlystored.Moreover,analgorithmtoavoidtheexcessiveincreaseofthestoreddata,isfurtherdiscussed.Thisalgorithmyieldsthereductionofmemoriesandcomputationalcosts.Finally,theeffectivenessofthenewlyproposedcontrolschemeisexaminedonasimulationexample.II.PIDCONTROLLERDESIGNBASEDONMEMORY-BASEDMODELINGMETHODA.MBmodelingmethodFirst,thefollowingdiscrete-timenonlinearsystemisconsidered:,（1）wherey(t)denotesthesystemoutputandf(·)denotesthenonlinearfunction.Moreover,_(t−1)iscalled’informationvector’,whichisdefiedbythefollowingequation:,（2）whereu(t)denotesthesysteminput.Also,nyandnurespectivelydenotetheordersofthesystemoutputandthesysteminput,respectively.AccordingtotheMBmodelingmethod,thedataisstoredintheformoftheinformationvector_expressedinEq.(2).Moreover,_(t)isrequiredincalculatingtheestimateoftheoutputy(t+1)called’query’.Thatis,aftersomesimilarneighborstothequeryareselectedfromthedata-base,thepredictivevalueofthesystemcanbeobtainedusingtheseneighbors.B.ControllerdesignbasedonMBmodelingmethodInthispaper,thefollowingcontrollawwithaPIDstructureisconsidered:（3）（4）wheree(t)denotesthecontrolerrorsignaldefinedbye(t):=r(t)−y(t).（5）r(t)denotesthereferencesignal.Also,kc,TIandTDrespectivelydenotetheproportionalgain,theresettimeandthederivativetime,andTsdenotesthesamplinginterval.Here,KP,KIandKDincludedinEq.(4)arederivedbytherelations=，=/和=/。denotesthedifferencingoperatordefinedby..Here,itisquitedifficulttoobtainagoodcontrolperformanceduetononlinearities,ifPIDparameters(KP,KI,KD)inEq.(4)arefixed.Therefore,anewcontrolschemeisproposed,whichcanadjustPIDparametersinanon-linemannercorrespondingtocharacteristicsofthesystem.Thus,insteadofEq.(4),thefollowingPIDcontrollawwithvariablePIDparametersisemployed:（6）Now,Eq.(6)canberewrittenasthefollowingrelations:（7）（8）（9）whereg(·)denotesalinearfunction.BysubstitutingEq.(7)andEq.(8)intoEq.(1)andEq.(2),thefollowingequationcanbederived:（10）（11）whereny_3,nu_2,andh(·)denotesanonlinearfunction.Therefore,K(t)isgivenbythefollowingequations:（12）（13）whereF(·)denotesanonlinearfunction.Sincethefutureoutputy(t+1)includedinEq.(13)cannotbeobtainedatt,y(t+1)isreplacedbyr(t+1).Becausethecontrolsystemsothatcanrealizey(t+1)!r(t+1),isdesignedinthispaper.Therefore,¯_(t)includedinEq.(13)isnewlyrewrittenasfollows:（14）Aftertheabovepreparation,anewPIDcontrolschemeisdesignedbasedontheMBmodelingmethod.Thecontrollerdesignalgorithmissummarizedasfollows.[STEP1]Generateinitialdata-baseTheMBmodelingmethodcannotworkifthepastdataisnotsavedatall.Therefore,PIDparametersarefirstlycalculatedusingZieglar&Nicholsmethod[2]orChien,Hrones&Reswick(CHR)method[3]basedonhistoricaldataofthecontrolledobjectinordertogeneratetheinitialdatabase.Thatis,_(j)indicatedinthefollowingequationisgeneratedastheinitialdata-base:（15）whereandaregivenbyEq.(14)andEq.(9).Moreover,N(0)denotesthenumberofinformationvectorsstoredintheinitialdata-base.NotethatallPIDparametersincludedintheinitialinformationvectorsareequal,thatis,K(1)=K(2)=···=K(N(0))intheinitialstage.[STEP2]CalculatedistanceandselectneighborsDistancesbetweenthequeryandtheinformationvectorsarecalculatedusingthefollowingL1-normwithsomeweights:（16）whereN(t)denotesthenumberofinformationvectorsstoredinthedata-basewhenthequeryisgiven.Furthermore,denotesthel-thelementofthej-thinformationvector.Similarly,denotesthel-thelementofthequeryatt.Moreover,denotesthemaximumelementamongthel-thelementofallinformationvectorsstoredinthedata-base.Similarly,denotestheminimumelement.Here,kpieceswiththesmallestdistancesarechosenfromallinformationvectors.[STEP3]ConstructlocalmodelNext,usingkneighborsselectedinSTEP2,thelocalmodelisconstructedbasedonthefollowingLinearlyWeightedAverage(LWA)[12]: （17）wherewidenotestheweightcorrespondingtothei-thinformationvectorintheselectedneighbors,andiscalculatedby:（18）[STEP4]DataadjustmentInthecasewhereinformationcorrespondingtothecurrentstateofthecontrolledobjectisnoteffectivelysavedinthedata-base,asuitablesetofPIDparameterscannotbeeffectivelycalculated.Thatis,itisnecessarytoadjustPIDparameterssothatthecontrolerrordecreases.Therefore,PIDparametersobtainedinSTEP3areupdatedcorrespondingtothecontrolerror,andthesenewPIDparametersarestoredinthedata-base.ThefollowingsteepestdescentmethodisutilizedinordertomodifyPIDparameters: （19）（20）where_denotesthelearningrate,and饎hefollowingJ(t+1)denotestheerrorcriterion:（21）（22）yr(t)denotestheoutputofthereferencemodelwhichisgivenby:(23)(24)Here,T(z−1)isdesignedbasedonthereferenceliterature[13].Moreover,eachpartialdifferentialofEq.(19)isdevelopedasfollows:.（25）NotethataprioriinformationwithrespecttothesystemJacobianisrequiredinordertocalculateEq.(25).Here,usingtherelationx=|x|sign(x),thesystemJacobiancanbeobtainedbythefollowingequation:（26）wheresign(x)=1(x>0),−1(x<0).Now,ifthesignofthesystemJacobianisknowninadvance,byincludingin,theusageofthesystemJacobiancanmakeeasy[14].Therefore,itisassumedthatthesignofthesystemJacobianisknowninthispaper.[STEP5]RemoveredundantdataInimplementingtorealsystems,thenewlyproposedschemehasaconstraintthatthecalculationfromSTEP2toSTEP4mustbefinishedwithinthesamplingtime.Here,storingtheredundantdatainthedata-baseneedsexcessivecomputationaltime.Therefore,analgorithmtoavoidtheexcessiveincreaseofthestoreddata,isfurtherdiscussed.Theprocedureiscarriedoutinthefollowingtwosteps.First,theinformationvectorswhichsatisfythefollowingfirstcondition,areextractedfromthedata-base:[Firstcondition]（27）whereisdefinedby（28）Moreover,theinformationvectorswhichsatisfythefollowingsecondcondition,arefurtherchosenfromtheextracted:（29）whereisdefinedby（30）Ifthereexistplural,theinformationvectorwiththesmallestvalueinthesecondconditionamongall,isonlyremoved.Bytheaboveprocedure,theredundantdatacanberemovedfromthedata-base.Here,ablockdiagramsummarizedmentionedabovealgorithmsareshowninFig.rr_+ModelPIDTunerTunerTunerPID整定DatabaseModelMemory-BasedPIDControllerCControllerControllerSystemControllerSystemIII.SIMULATIONEXAMPLEInordertoevaluatetheeffectivenessofthenewlyproposedscheme,asimulationexampleforanonlinearsystemisconsidered.Asthenonlinearsystem,thefollowingHammersteinmodel[15]isdiscussed:[System1]（31）[System2]（32）wheredenotesthewhiteGaussiannoisewithzeromeanandvariance.StaticpropertiesofSystem1andSystem2areshowninFig.2.Fig.2FromFig.2,itisclearthatgainsofSystem2arelargerthanonesofSystem1at.Here,thereferencesignalr(t)isgivenby:（33）Theinformationvector¯_isdefinedasfollows:（34）Thedesiredcharacteristicpolynomialincludedinthereferencemodelwasdesignedasfollows:（35）whereT(z−1)wasdesignedbasedonthereferenceliterature[13].Furthermore,theuser-specifiedparametersincludedintheproposedmethodaredeterminedasshowninTableI.TABLEIUSER-SPECIFIEDPARAMETERSINCLUDEDINTHEPROPOSEDMETHOD(HAMMERSTEINMODEL).OrdersoftheinformationvectorNumberofneighborsLearningrateCoefficientstoinhibitthedataInitialnumberofdataForthepurposeofcomparison,thefixedPIDcontrolschemewhichhaswidelyusedinindustrialprocesseswasfirstemployed,whosePIDparametersweretunedbyCHRmethod[3].Then,PIDparameterswerecalculatedas（36）Moreover,thePIDcontrollerusingtheNN,calledNN-PIDcontroller,wasappliedforthepurposeofthecomparison,wheretheNNwasutilizedinordertosupplementthefixedPIDcontroller.ThecontrolresultsforSystem1aresummarizedinFig.3,wherethesolidlineanddashedlinedenotethecontrolresultsoftheproposedmethodandthefixedPIDcontroller,respectively.Furthermore,trajectoriesofPIDparametersusingtheproposedmethodareshowninFig.4.FromFig.3,owingtononlinearitiesofthecontrolledobject,thecontrolresultbythefixedPIDcontrollerisnotgood.Ontheotherhand,fromFig.3andFig.4,thegoodcontrolresultcanbeobtainedusingtheproposedmethod,becausePIDparametersareadequatelyadjusted.Moreover,thenumberofdatastoredinthedatabasewas49.Usingthealgorithmtoremoveneedlessdata,thenumberofdatastoredinthedata-basecanbeeffectively（37）whereNdenotesthenumberofstepsper1[epoc].Furthermore,thenumberofiterationwassetas1,becausePIDparameterscanbeadjustedinanon-linemannerbytheproposedmethod.Moreover,theNN-PIDcontrollerwasappliedtoSystem1.Errorbehaviorsof_expressedinEq.(37)areshowninFig.5,andcontrolresultsareshowninFig.6.Fig.5Fig.6FromFig.5,thenecessarynumberforlearningiterationswas86[epoc]untilthecontrolresultusingtheNN-PIDcontrollercouldbeobtainedthesamecontrolperformancesastheproposedmethod,thatis,untilwassatisfied.Therefore,theeffectivenessoftheproposedmethodisalsoverifiedincomparisonwiththeNN-PIDcontrollerfornonlinearsystems.Next,thecasewherethesystemhastime-variantparametersisconsidered.Thatis,thesystemchangesfromEq.(31)Fig.5.ErrorbehaviorsusingthecontrollerfusedthefixedPIDwiththeNN-PIDforHammersteinmodel.Fig.6.ControlresultusingthecontrollerfusedthefixedPIDwiththeNN-PIDforHammersteinmodel.toEq.(32)att=70.First,thecontrolresultwiththefixedPIDcontroller,isshowninFig.7,wherePIDparametersaresetasthesameparametersasshowninEq.(36).Sincethegainofthecontrolledobjectbecomeshighgainaroundr(t)=2.0,thefixedPIDcontrollerdoesnotworkwell.Ontheotherhand,theproposedcontrolschemewasemployedinthiscase.ThecontrolresultandtrajectoriesofPIDparametersareshowninFig.8andFig.9.Fig.8Fromthesefigures,agoodcontrolperformancecanbealsoobtainedbecausePIDparametersareadequatelyadjustedusingtheproposedmethod.Theusefulnessforthenonlinearsystemwithtime-variantparametersissuggestedinthisexample.IV.CONCLUSIONSInthispaper,anewdesignschemeofPIDcontrollersusingtheMBmodelingmethodhasbeenproposed.ManyPIDcontrollerdesignschemesusingNNsandGAshavebeenproposedfornonlinearsystemsuptonow.Inemployingtheseschemeforrealsystems,however,itisaseriousproblemthatthelearningcostbecomesconsiderablylarge.Ontheotherhand,accordingtotheproposedmethod,suchcomputationalburdenscanbeeffectivelyreducedusingthealgorithmforremovingtheredundantdata.Inaddition,theeffectivenessoftheproposedmethodhavebeenverifiedbyanumericalsimulationexample.Theapplicationofthenewlyproposedschemeforrealsystemsandtheextensiontomultivariablecasesarecurrentlyunderconsideration.基于记忆的在线非线性系统PID控制器整定摘要由于大部分控制过程具有非线性，所以设计一种能够处理具有非线性系统的控制器就显得尤为重要。另一方面，PID控制器也被广泛应用于过程控制系统中。因此，在本文中提出了一种基于记忆的MB模型用来处理非线性PID控制器设计方案。通过MB方法，可以自动产生基于存储在数据中的控制对象的输入/输出数据对的本地模型。这种设计方案，通过存储在数据库中的输入/输出数据产生变量。即使系统具有非线性，该设计方案。同样能在线调整PID变量。最后，我们通过一个仿真系统的数据演化过程来证明该方案的有效性。Ⅰ引言近年来，像自适应控制理论，鲁棒控制理论等一些复杂的控制算法被提出和应用。但是，在工业过程中PID控制器依然占80%甚至更多的比例，其原因如下所述：（1）控制结构简单；（2）控制参数物理意义清晰；（3）能够很好地满足客户要求。因此，PID控制器的设计自然具有强大的吸引力。但是由于大部分控制系统具有非线性，简单地应用固定PID参数很难得到交好的控制效果。所以到现在为止已经提出了神经网络（NN）和遗传算法（GA）等PID参数整定方法。使用这些方法的学习代价是很大的，而且PID参数由于系统的非线性特征不能得到充分的调整。因而通过这些方便的方法不能得到很好的控制效果。不过，计算机的发展让我们能够记忆，快速检索以及读取大量数据。基于这些优点我们提出了以下方案：无论何时获得的新数据都被保存下来。被称为“询问”的信息要求从保存的数据中提取出来。这种基于记忆模型（MB）的方法叫做JIT方法。懒散学习方法或MOD方法。并且在过去的十年中，这些方法被给予了大量的关注。在本文中讨论了一种基于MB模型的PID控制器设计方案。一些基于用属于MB模型方法的JIT方法的PID控制器已经被提出。基于以前的方法，用JIT方法的目的是应用PID结构的辅助反馈控制器，但是，在相关信号改变的情况下的非线性，将会导致跟踪特性没有足够的保证，因为在整个控制系统中控制器不包含任何的积分行为。另一方面，后一种方法具有一个PID控制结构。PID参数不是通过与控制对象的特征相一致的在线方式整定的。因此，在本文中我们设计提出了一种基于MB模型的方法。通过这种新方法，有MB模型方法得到的PID参数在比例环节中得到了充分的整定，这主要是为了控制误差。规划后的PID参数被保存在数据库中。因此，回游更多的与空话子对象特征相一致的适当的PID参数被保存。再者，我们进一步提出了一种避免存储数据过分增长的算法。这种算法可以减少记忆和计算机花费。最后，这种新方法的有效度通过一个仿真模型来检测。Ⅱ基于记忆模型的PID控制器设计方法AMB模型方法第一，我们引入了如下时间递减非线性系统（1）其中，表示系统输出，表示非线性函数，被称为‘信息矢量’通过下式定义：（2）其中，表示系统输入，另外，和分别表示系统的输出和输入的阶数。在MB模型方法中数据一等式（2）中的信息矢量的形式被存储。在估计输出时，需要，因此被叫做询问。一些相似相邻数被从数据库中选出后，我们可以通过这些相邻数而获得系统的预测值。B基于MB模型方法的控制器设计在本文中我们引用了具有如下PID结构的控制规律：（3）（4）其中表示误差控制信号，有如下定义：（5）其中表示相关信号，另外，，和分别表示比例增益，调节时间和微分时间，表示采样时间。在这里等式（4）中的,和有如下联系：=，=/和=/。表示操作者的区别，并被定义为：。在这里由于非线性的存在我们将很难获得好的控制效果，这是在式（4）中的，，确定不变的假设下才成立的。因此，一种新的控制方案被提出来，这种方法能够通过与系统特征保持一致的在线方式调整PID参数。因而有了如下取代等式（4）的具有可变PID参数的PID控制规律：（6）现在等式（6）可以重新变成如下形式：（7）（8）（9）其中表示一个线性函数，将式（1）和式（2）带入式（7）和式（8）中我们可以得到如下等式：（10）（11）其中，ny≥3,nu≥2,h(1)表示一个非线性函数，因而通过下面等式给出：（12）（13）其中，表示非线性函数，既然下一个输出不能在t时刻得到我们就用来代替。为了使控制系统能够识别本文中所定义的—>，等式（13）中的可以被重新写成如下形式：（14）经过以上的准备工作以后，一种基于MB模型方法的PID控制被设计出来了。下面对控制器的设计算法作简单阐述。第一步：产生初试数据库如果以前的数据没有被全部保存，MB模型方法将不能工作。因此首先通过Z-N方法或CHR方法计算出PID参数。这两种方法都是在原有历史记录的基础上初始化数据库。在下面等式中存在的被称为初试数据库。（15）其中，和分别由式（14）和式（9）获得。表示存储在初始数据库中的信息矢量的数量。注意它在初始信息矢量中的PID参数是相等的，即：。第二步：计算距离，选择相邻数询问和信息矢量之间的距离通过下述具有一定重复的—一范数计算出（16）表示当询问给出时，数据库中存储的信息矢量数量表示第个信息矢量的第个元素。类似地，表示在t时刻询问第个元素。表示在数据库中所存储的所有信息矢量的第个元素的最大值。类似地，则表示最小元素，在这里具有最小距离的被从所有的信息矢量中选择出来。第三步：建立本地模型接下来，使用第一步中所选择的，然后基于如下线性平均质量建立本地模型： （17）其中，表示和第个信息矢量相一致的重量。取自于所选择的邻居，并且通过下式计算：（18）第四步：数据调整在和控制对象相一致的现在状态不能有效保存到数据库中的情况下，一个适当的PID参数不可能被有效的计算出来。为了减少控制误差，必须调整PID参数。因此在步骤3中所得出来的PID参数将作和控制误差一致的更新。然后这些新的PID参数被保存到数据库中。如下悬崖递减法被用来规范PID参数。（19）（20）其中表示学习率。下式所示表示误差指标：（21）（22）表示相关模型的输出，该模型如下所示：(23)(24)在这里，是基于文献[13]而设计的。与等式（19）的每一部分区别描述如下：（25）注意到为了计算等式（25）要求一个考虑系统雅可比行列式的优先信息。在这里通过关系式，系统的雅可比行列式可以通过如下等式获得：