基于内模控制的模糊pid参数的整定外文文献翻译【完稿】

毕业设计（论文）外文文献译文及原文基于内模控制的模糊PID参数的整定XIAOGANGDUAN,HANXIONGLI,ANDHUADENGSCHOOLOFMECHANICALANDELECTRICALENGINEERING,CENTRALSOUTHUNIVERSITY,CHANGSHA410083,CHINA,ANDDEPARTMENTOFMANUFACTURINGENGINEERINGANDENGINEERINGMANAGEMENT,CITYUNIVERSITYOFHONGKONG,HONGKONG摘要在本文中将利用内模控制的整定方法实现模糊PID控制。此种控制方式首次应用于模糊PID控制器，它包括一个线性PID控制器和非线性补偿部分。非线性补偿部分可视为一个干扰过程，模糊PID控制器的参数可在分析的基础上确定内模结构。模糊PID控制系统利用李亚谱诺夫稳定性理论进行稳定性分析。仿真结果表明利用内模控制整定模糊PID控制参数是有效的。1引言一般而言，传统的PID控制器对于十分复杂的被控对象控制效果不太理想,如高阶时滞系统。在这种复杂的环境下,众所周知,模糊控制器由于其固有的鲁棒性可以有更好的表现，因此，在过去30年中，模糊控制器，特别是,模糊PID控制器因其对于线性系统和非线性系统都能进行简单和有效的控制，已被广泛用于工业生产过程14。模糊PID控制器有多种形式5,如单输入模糊PID控制器,双输入模糊PID控制器和三个输入的模糊PID控制器。一般情况下，没有统一的标准。单输入可能会丢失派生信息,三输入模糊PID控制器会产生按指数增长的规则。在本文中所采用的双输入模糊PID控制器有一个适当的结构并且实用性强，因此在各种研究和应用中,是最流行的模糊PID类型。尽管业界对于应用模糊PID有越来越大的兴趣，但从控制工程的主流社会的角度来看,它仍然是一个极具争议的话题。原因之一是模糊PID参数整定的基本理论分析方法至今仍不明确。因此，模糊PID控制器不得不进行两个级别的整定。在较低层次上，该整定是由调整增益获得线性控制性能。在更高层次上的调整，是由改变知识库参数以提高控制性能,然而调整知识库参数很难,此外，很难通过改变参数特性改善瞬态响应。根据知识库传达一般控制规则倾向于保持成员函数不变，通过离线设计和调试工作扩大增益，然而，由于由模糊PID控制器生成非线性控制表面的复杂性，调整机制的衡量因素和稳定性分析仍然是艰巨的任务。如果非线性能得到适当的利用，模糊PID控制器可能得到比传统PID控制器更好的系统性能。一些非常规的调整方法已进行了介绍912。虽然非线性被认为是在增益裕度和相位裕度基础上获得的，但是由于非线性因素，模糊PID控制器可能会产生比常规PID控制器较高的增益。而高增益可能使控制系统的稳定性变差。常规PID控制器很容易实现，大量的整定规则可以涵盖广泛的进程规格。在常规PID控制器的整定方法中，内模控制基础整定是在商业PID控制软件包中流行的方法之一，因为只需调整一个参数，便可以生产更好的设置点响应15。本文提出了一种基于内模控制的PID控制器的整定分析方法，模糊PID控制器可分解为线性PID控制器加上非线性补偿部分的控制器。把非线性补偿部分近似看作一个过程干扰，模糊PID参数就可以分析设计使用内模控制。模糊PID控制器的稳定性分析是根据李亚谱诺夫稳定性理论。最后，通过仿真来证明此种调整方法是有效的。2问题的提出21常规PID控制器常规PID控制器通常被描述为下列方程810DPEKTEIPIDUI1T（1）其中E是跟踪误差，KP是比例增益，KI是积分增益，KD是微分增益，TI和TD分别是积分时间常数和微分时间常数，这些控制参数的关系是KIKP/TI和KDKPTD。PID控制器的传递函数可以表示如下S1TTSDI）（CKG（2）在根轨迹中，PID控制器有两个零点和,一个极点是原点。条件是两个零点满足大于4。ITDITDTCPPUDEYY_YR图1内模控制配置图AMICPREUDYY图2内模控制配置图B22内模控制原则基本的内模控制原则如图1所示，其中P是被控对象，P是名义上的模型对象，C是控制器，R和D是设置点和干扰，Y和YK分别是被控对象的输出和模型对象的输出。内模控制结构相当于古典单闭环反馈控制器如图1（B）所示，如果单闭环控制器如下S1SPCIM（3）及SFP1S_C（4）其中S是被控模型的最小相位部分，包含任何时间延迟和右零点，FS是一个低通滤波P_SP器，一般形式是NCST1F（5）调整参数TC是理想闭环时间常数N是一个待定的正整数。EKKIKDRULEBASESERUEPIDUE图3模糊PID控制器结构23模糊PID控制器模型模糊PID控制器如图2所示，形式为10PUKUPID_及UK1BSA（6）是一种非线性的时间变量参数,A和B分别是每个输入和输出的成员函数一半的外延。32模糊PID控制实际上有两个层次的增益。扩大增益KE,KD,K0,和K1处于较低的水平。扩大增益的调整将会影响模糊PID控制器效果，造成控制参数的不断变化。作为控制行为的模糊耦合控制，KE,KD,K0,和K1以何种不同的控制行动仍然没有非常清楚，这使得实际设计和调试过程相当困难。3基于内模控制的模糊PID整定在模糊PID控制器整定的基础上的内模控制方法，通过分析模糊PID控制模型得到第一个简单推导。然后，参数模糊PID控制器可在内模控制的基础上确定参数。假设一个工业过程可以模仿成一阶加上延迟（FOPDT）环节，传递函数如下LSTKPE1S7其中K、T和L分别是稳态增益，时间常数，和延迟时间，这些参数通过阶跃响应法，频率响应，和闭环继电反馈等方法来描述的，FOPDT是一种最常见最实用的模型，尤其是在过程控制中18。通过式（6）可以得到10KPSABUPID（8）SUSNPIDPI（9）SABKSUN10（10）是一个非线性项，没有明确的分析表达。显然，模糊PID控制可视为常规PID的非线性补偿。常规PID控制部分是UPIDS，非线性补偿部分是UNS。基于内模控制的模糊PID整定。如果我们考虑非线性补偿UNS作为一个过程的干扰，并设置为GFS如图3，基于内模控制的模糊PID控制器可简化如下S21ESL11因此，为可以分解为，其中SPSPSS21SLTKP12从而得到ST12SCKLTCIM（13）模糊PID在第K水平上的带宽可以通过适合的来控制。带宽和快速的反应，的值越小可得到较大的带宽和较快的响应速度，否则带宽变小，响应缓慢，因此，为了提高上升时间，的值应该小，所以，两个参数和可得到确定。备注模糊PID控制实际上是一个传统PID控制器UPID加上滑动控制。由于滑模控制是一种鲁棒控制所以模糊PID控制是力的比传统的PID控制有更好的鲁棒性。4控制仿真在这一节中，通过上述方法进行模糊PID整定的控制性能与常规PID的比较，选择IEA和ITAE作为标准，数值越小意味着控制性能越好。DTEDTEITAEIE，（14）在所有控制仿真中常规PID控制参数是由内模控制方法决定的，模糊PID控制参数是由上述整定方法确定的。范例1考虑一个工业过程，所描述的一阶延迟环节，模型函数如下S10ESP（15）线性部分在过程中占主导地位。小延迟时间意味着弱非线性特性。由图5可以看出，由于延迟时间小，常规PID控制和模糊PID控制差异不大。然而，当延迟时间增加至L06，如图6，模糊PID控制实现了优于常规PID控制控制性能。此外模糊PID控制器增益低于常规PID控制器。图4范例1中模糊PID控制（实线）和常规图5延迟时间增加至L06，模糊PID控PID控制（虚线）性能比较制（实线）和常规PID控制（虚线）性能比较范例2假设一工业过成描述如下8AS1P（16）其中A1，假设不存在建模误差，在阶跃响应和奈奎斯特工业过程曲线基础上可获得逼近模型如下S34E1SP（17）如图7所示，常规PID控制和模糊PID控制差异不大。因为该模型是正确的。但是，假设有建模误差和参数A的实际值是095。如图8，模糊PID控制比常规PID控制实现更好的控制性能。此外，由图8可以看出模糊PID控制器增益低于常规PID控制器。图6A1时，模糊PID控制（实线）和常规图7A095时，模糊PID控制（实线）和常规PID控制（虚线）性能比较PID控制（虚线）性能比较5结论本文介绍了一种基于内模控制的模糊PID控制器的整定分析方法。解析模型是第一次应用于模糊PID控制器的整定。分析模型包括一个线性PID控制及非线性补偿部分。在内模控制方法基础上，模糊PID控制器的参数可由过程干扰的补偿部分来分析确定。虽然扩大收益和是耦合的，这一程序是在解耦基础上的滑动模型控制。稳定性分析表明，该控制系统是全局渐近稳定的。模糊PID控制器采用此种整定方法比传统的PID控制器有更的鲁棒性强大。仿真结果表明，模糊PID控制器通过此种整定方法，与传统的PID控制器相比在动态和静态上都实现更好的控制性能和更好的鲁棒性。参考文献1SUGENOMINDUSTRIALAPPLICATIONSOFFUZZYCONTROLELSEVIERAMSTERDAM,THENETHERLANDS,19852MANEL,AALBERT,AJORDI,AMANEL,PWASTEWATERNEUTRALIZATIONCONTROLBASEDONFUZZYLOGICEXPERIMENTALRESULTSINDENGCHEMRES1999,38,270927193ZHANG,JANONLINEARGAINSCHEDULINGCONTROLSTRATEGYBASEDONNEUROFUZZYNETWORKSINDENGCHEMRES2001,40,316431704HOJJATI,HSHEIKHZADEH,MROHANI,SCONTROLOFSUPERSATURATIONINASEMIBATCHANTISOLVENTCRYSTALLIZATIONPROCESSUSINGAFUZZYLOGICCONTROLLERINDENGCHEMRES2007,46,123212405GEORGE,KIMHU,BGRAYMOND,GGANALYSISOFDIRECTACTIONFUZZYPIDCONTROLLERSTRUCTURESIEEETRANSSYST,MAN,CYBERNETICS,PARTB1999,293,3713886LI,HXGATLAND,HCONVENTIONALFUZZYLOGICCONTROLANDITSENHANCEMENTIEEETRANSSYST,MAN,CYBERNETICS1996,2610,7917977GEORGE,KIMHU,BGRAYMOND,GGTWOLEVELTUNINGOFFUZZYPIDCOTROLLERSIEEETRANSSYST,MAN,CYBERNETICS,PARTB2001,312,2632698WOO,ZWCHUNG,HYLIN,JJAPIDTYPEFUZZYCONTROLLERWITHSELFTUNINGSCALINGFACTORSFUZZYSETSSYST2000,115,3213269VEGA,PPRADA,CALEIXANDER,VSELFTUNINGPREDICTIVEPIDCONTROLLERIEEPROD1991,1383,30331110RAJANI,KMNIKHIL,RPAROBUSTSELFTUNINGSCHEMEFORPIANDPDTYPEFUZZYCONTROLLERSIEEETTRANSFUZZYSYST1999,71,21611RAJANI,KMNIKHIL,RPASELFTUNINGFUZZYPICONTROLLERFUZZYSETSSYST2000,115,32733812YESIL,EGUZELKAYA,MEKSIN,ISELFTUNINGFUZZYPIDTYPELOADANDFREQUENCYCONTROLLERENERGYCONVERSMANAGE2004,45,37739013XU,JXPOK,YMLIU,CHANG,CCTUNINGANDANALYSISOFAFUZZYPICONTROLLERBASEDONGAINANDPHASEMARGINSIEEETRANSSYST,MAN,CYBERNETICS,PARTA1998,285,68569114XU,JXHANG,CCLIU,CPARALLELSTRUCTUREANDTUNINGOFAFUZZYPIDCONTROLLERAUTOMATICA2000,36,67368415KAYA,IOBTAININGCONTROLLERPARAMETERSFORANEWPIPDSMITHPREDICTORUSINGAUTOTUNINGJPROCESSCONTROL2000,13,46547216LI,YKIAM,HAGREGORY,CYPATENTS,SOFTWARE,ANDHARDWAREFORPIDCONTROLIEEECONTROLSYSTMAG2006,425417CHA,SYCHUN,DWLEE,JTTWOSTEPIMCPIDMETHODFORMULTILOOPCONTROLSYSTEMDESIGNINDENGCHEMRES2002,41,3037304118LI,HXGATLAND,HBGREEN,AWFUZZYVARIABLESTRUCTURECONTROLIEEETRANSSYST,MAN,CYBERNETICS,PARTB1997,272,306312EFFECTIVETUNINGMETHODFORFUZZYPIDWITHINTERNALMODELCONTROLXIAOGANGDUAN,HANXIONGLI,ANDHUADENGSCHOOLOFMECHANICALANDELECTRICALENGINEERING,CENTRALSOUTHUNIVERSITY,CHANGSHA410083,CHINA,ANDDEPARTMENTOFMANUFACTURINGENGINEERINGANDENGINEERINGMANAGEMENT,CITYUNIVERSITYOFHONGKONG,HONGKONGANINTERNALMODELCONTROLIMCBASEDTUNINGMETHODISPROPOSEDTOAUTOTUNETHEFUZZYPROPORTIONALINTEGRALDERIVATIVEPIDCONTROLLERINTHISPAPERANANALYTICALMODELOFTHEFUZZYPIDCONTROLLERISFIRSTDERIVED,WHICHCONSISTSOFALINEARPIDCONTROLLERANDANONLINEARCOMPENSATIONITEMTHENONLINEARCOMPENSATIONITEMCANBECONSIDEREDASAPROCESSDISTURBANCE,ANDTHENPARAMETERSOFTHEFUZZYPIDCONTROLLERCANBEANALYTICALLYDETERMINEDONTHEBASISOFTHEIMCSTRUCTURETHESTABILITYOFTHEFUZZYPIDCONTROLSYSTEMISANALYZEDUSINGTHELYAPUNOVSTABILITYTHEORYTHESIMULATIONRESULTSDEMONSTRATETHEEFFECTIVENESSOFTHEPROPOSEDTUNINGMETHOD1INTRODUCTIONGENERALLYSPEAKING,CONVENTIONALPROPORTIONALINTEGRALDERIVATIVEPIDCONTROLLERSMAYNOTPERFORMWELLFORTHECOMPLEXPROCESS,SUCHASTHEHIGHORDERANDTIMEDELAYSYSTEMSUNDERTHISCOMPLEXENVIRONMENT,ITISWELLKNOWNTHATTHEFUZZYCONTROLLERCANHAVEABETTERPERFORMANCEDUETOITSINHERENTROBUSTNESSTHUS,OVERTHEPASTTHREEDECADES,FUZZYCONTROLLERS,ESPECIALLY,FUZZYPIDCONTROLLERSHAVEBEENWIDELYUSEDFORINDUSTRIALPROCESSESDUETOTHEIRHEURISTICNATURESASSOCIATEDWITHSIMPLICITYANDEFFECTIVENESSFORBOTHLINEARANDNONLINEARSYSTEMS14THEREARETOOMANYVARIATIONSOFFUZZYPIDCONTROLLERS,SUCHAS,ONEINPUT,TWOINPUT,ANDTHREEINPUTPIDTYPEFUZZYCONTROLLERSINGENERAL,THEREISNOSTANDARDBENCHMARKTHEONEINPUTMAYMISSMOREINFORMATIONONTHEDERIVATIVEACTION,ANDTHETHREEINPUTFUZZYPIDCONTROLLERSMAYCAUSEEXPONENTIALGROWTHOFRULESTHETWOINPUTFUZZYPID,ASWEUSEDINTHEPAPER,HASAPROPERSTRUCTUREANDTHEMOSTPRACTICALUSE,ANDTHUSISTHEMOSTPOPULARTYPEOFFUZZYPIDUSEDINVARIOUSRESEARCHANDAPPLICATIONDESPITETHEFACTTHATINDUSTRYSHOWSGREATERANDGREATERINTERESTINTHEAPPLICATIONSOFFUZZYPID,ITISSTILLAHIGHLYCONTROVERSIALTOPICFROMTHEPOINTOFVIEWOFTHEMAINSTREAMCONTROLENGINEERINGCOMMUNITYONEREASONISTHATTHEFUNDAMENTALTHEORYFORTHEANALYTICALTUNINGMETHODSOFFUZZYPIDISSTILLMISSINGTHEREFORE,FUZZYPIDCONTROLLERSHADTOBETUNEDQUALITATIVELYBYTWOLEVELTUNINGATALOWERLEVEL,THETUNINGISPERFORMEDBYADJUSTINGTHESCALINGGAINSTOOBTAINOVERALLLINEARCONTROLPERFORMANCEATAHIGHERLEVEL,THETUNINGISPERFORMEDBYCHANGINGTHEKNOWLEDGEBASEPARAMETERSTOENHANCETHECONTROLPERFORMANCEHOWEVER,ITISDIFFICULTTOTUNETHEKNOWLEDGEBASEPARAMETERSMOREOVER,ITISHARDTOIMPROVETHETRANSIENTRESPONSEBYCHANGINGTHEMEMBERFUNCTIONASTHEKNOWLEDGEBASECONVEYSAGENERALCONTROLPOLICY,ITISPREFERREDTOKEEPTHEMEMBERFUNCTIONUNCHANGEDANDTOLEAVETHEDESIGNANDTUNINGEXERCISESTOSCALINGGAINSHOWEVER,THETUNINGMECHANISMOFSCALINGFACTORSANDTHESTABILITYANALYSISARESTILLDIFFICULTTASKSDUETOTHECOMPLEXITYOFTHENONLINEARCONTROLSURFACETHATISGENERATEDBYFUZZYPIDCONTROLLERSIFTHENONLINEARITYCANBESUITABLYUTILIZED,FUZZYPIDCONTROLLERSMAYPOSETHEPOTENTIALTOACHIEVEBETTERSYSTEMPERFORMANCETHANCONVENTIONALPIDCONTROLLERSSOMENONANALYTICALTUNINGMETHODSWEREINTRODUCED912ALTHOUGHTHENONLINEARITYWASCONSIDEREDONTHEBASISOFGAINMARGINANDPHASEMARGINSPECIFICATIONS,THEFUZZYPIDCONTROLLERMAYPRODUCEHIGHERGAINSTHANCONVENTIONALPIDCONTROLLERSDUETOTHENONLINEARFACTORAHIGHGAINCOULDDETERIORATETHESTABILITYOFTHECONTROLSYSTEM15THECONVENTIONALPIDCONTROLLERISEASYTOIMPLEMENT,ANDLOTSOFTUNINGRULESAREAVAILABLETOCOVERAWIDERANGEOFPROCESSSPECIFICATIONSAMONGTUNINGMETHODSOFTHECONVENTIONALPIDCONTROLLER,THEINTERNALMODELCONTROLIMCBASEDTUNINGISONEOFTHEPOPULARMETHODSINCOMMERCIALPIDSOFTWAREPACKAGESBECAUSEONLYONETUNINGPARAMETERISREQUIREDANDBETTERSETPOINTRESPONSECANBEPRODUCED17ANANALYTICALTUNINGMETHODBASEDONIMCTOTUNEFUZZYPIDCONTROLLERSISPROPOSEDINTHISPAPERTHEFUZZYPIDCONTROLLERISFIRSTDECOMPOSEDASALINEARPIDCONTROLLERPLUSANONLINEARCOMPENSATIONITEMWHENTHENONLINEARCOMPENSATIONITEMISAPPROXIMATEDASAPROCESSDISTURBANCE,THEFUZZYPIDSCALINGPARAMETERSCANTHENBEANALYTICALLYDESIGNEDUSINGTHEIMCSCHEMETHESTABILITYANALYSISOFTHEFUZZYPIDCONTROLLERSISGIVENONTHEBASISOFTHELYAPUNOVSTABILITYTHEORYFINALLY,THEEFFECTIVENESSOFTHETUNINGMETHODOLOGYISDEMONSTRATEDBYSIMULATIONS2PROBLEMFORMULATION21CONVENTIONALPIDCONTROLLERTHECONVENTIONALPIDCONTROLLERISOFTENDESCRIBEDBYTHEFOLLOWINGEQUATION20,21DPEKTEIPIDUI1T（1）WHEREEISTHETRACKINGERROR,KPISTHEPROPORTIONALGAIN,KIISTHEINTEGRALGAIN,KDISTHEDERIVATIVEGAIN,ANDTIANDTDARETHEINTEGRALTIMECONSTANTANDTHEDERIVATIVETIMECONSTANT,RESPECTIVELYTHERELATIONSHIPSBETWEENTHESECONTROLPARAMETERSAREKIKP/TIANDKDKPTDTHETRANSFERFUNCTIONOFTHEPIDCONTROLLER1CANBEEXPRESSEDASFOLLOWSS1TSDI）（CKG（2）ONTHEROOTLOCUSPLANE,THEPIDCONTROLLERHASTWOZEROSTIANDTD,ANDONEPOLEATTHEORIGINTHECONDITIONTOHAVEREALZEROSISTHATTI4TDCPPUDEYY_YR_FIGURE1IMCCONFIGURATION（A）MICPRE_UDYYFIGURE2IMCCONFIGURATIONB22PRINCIPLEOFIMCTHEBASICIMCPRINCIPLEISSHOWNINFIGURE1A,WHEREPISTHEPLANT,PISANOMINALMODELOFTHEPLANT,CISACONTROLLERRANDDARETHESETPOINTANDTHEDISTURBANCE,ANDYANDYKARETHEOUTPUTSOFTHEPLANTANDITSNOMINALMODEL,RESPECTIVELYTHEIMCSTRUCTUREISEQUIVALENTTOTHECLASSICALSINGLELOOPFEEDBACKCONTROLLERSHOWNINFIGURE1BIFTHESINGLELOOPCONTROLLERCIMCISGIVENBYS1SPCIM（3）WITHSFP1S_C（4）WHEREPSPSPS,PSISTHEMINIMUMPHASEPARTOFTHEPLANTMODEL,PSCONTAINSANYTIMEDELAYSANDRIGHTHALFPLANEZEROS,ANDFSISALOWPASSFILTERWITHASTEADYSTATEGAINOFONE,WHICHTYPICALLYHASTHEFORMNCST1F（5）THETUNINGPARAMETERTCISTHEDESIREDCLOSEDLOOPTIMECONSTANT,ANDNISAPOSITIVEINTEGERTOBEDETERMINEDFIGUREEKKIKDRULEBASESERUEPIDUFIGURE3FUZZYPIDCONTROLLERSTRUCTURE23MODELOFFUZZYPIDCONTROLLERTHEFUZZYPIDCONTROLLER,ASSHOWNINFIGURE2,ISDESCRIBEDASFOLLOWS10PUKUPID6WITHUK1BSAISANONLINEARTIMEVARYINGPARAMETER,AANDBAREHALFOFTHESPREADOFEACHINPUTANDOUT32MEMBERFUNCTION,RESPECTIVELYTHEFUZZYPIDCONTROLACTUALLYHASTWOLEVELSOFGAINS6THESCALINGGAINSKE,KD,K0,ANDK1AREATTHELOWERLEVELTHETUNINGOFTHESESCALINGGAINSWILLAFFECTTHEGAINSOFFUZZYPIDTHEFUZZYPIDCONTROLACTUALLYHASTWOLEVELSOFGAINS6THESCALINGGAINSKE,KD,K0,ANDK1AREATTHELOWERLEVELTHETUNINGOFTHESESCALINGGAINSWILLAFFECTTHEGAINSOFFUZZYPIDCONTROLLERS,RESULTINGINTHECHANGINGOFTHECONTROLPERFORMANCEASTHECONTROLACTIONSAREFUZZILYCOUPLED,THECONTRIBUTIONOFEACHKE,KD,K0,ANDK1TODIFFERENTCONTROLACTIONSISSTILLNOTVERYCLEAR,WHICHMAKESTHEPRACTICALDESIGNANDTUNINGPROCESSRATHERDIFFICULT3TUNINGFUZZYPIDBASEDONTHEIMCTOTUNETHEFUZZYPIDCONTROLLERBASEDONTHEIMCMETHOD,ANANALYTICALMODELOFTHEFUZZYPIDCONTROLLERISOBTAINEDFIRSTBYSIMPLEDERIVATIONTHEN,THEPARAMETERSOFTHEFUZZYPIDCONTROLLERCANBEDETERMINEDONTHEBASISOFTHEIMCPRINCIPLESUPPOSETHATANINDUSTRIALPROCESSCANBEMODELEDBYAFIRSTORDERPLUSDELAYTIMEFOPDTSTRUCTURETHATHASTHETRANSFERFUNCTIONASFOLLOWSLSTKPE1S7WHEREK,T,ANDLARETHESTEADYSTATEGAIN,THETIMECONSTANT,ANDTHETIMEDELAY,RESPECTIVELYTHEESTIMATIONOFTHESEPARAMETERSUSINGTHESTEPRESPONSEMETHOD,FREQUENCYRESPONSE,ANDCLOSEDLOOPRELAYFEEDBACK,ETC,ISWELLDESCRIBEDTHEFOPDTMODELISONEOFTHEMOSTCOMMONANDADEQUATEONESUSED,ESPECIALLYINTHEPROCESSCONTROLINDUSTRIES18ONEOBTAINSFROM610KPSABUPID（8）SUSNPIPID（9）SABKSUN10（10）WITHSBEINGANONLINEARTERMWITHOUTANEXPLICITANALYTICALEXPRESSIONOBVIOUSLY,THEFUZZYPIDCONTROLCANBECONSIDEREDASACONVENTIONALPIDWITHANONLINEARCOMPENSATIONTHECONVENTIONALPIDCONTROLTERMISUPIDSANDTHENONLINEARCOMPENSATIONISUNSTUNINGOFFUZZYPIDCONTROLLERBASEDONIMCIFWECONSIDERTHENONLINEARCOMPENSATIONUNASAPROCESSDISTURBANCEANDSETGFSCIMCS,WHICHISSHOWNINFIGURE3,THEIMCBASEDTUNINGFORFUZZYPIDCONTROLLERSCANBESIMPLIFIEDASFOLLOWSBYTHEFIRSTORDERPADEAPPROXIMATION,THEDELAYTIMEISAPPROXIMATEDASFOLLOWSS21ESL11THEREFORE,THEPSCANBEFACTORIZEDASPSPSPS,其中S21SLTKP12WECANACHIEVEST12SCKLTCIM（13）THEBANDWIDTHOFTHEFUZZYPIDATTHEKTHLEVELCANBECONTROLLEDBYADJUSTINGRASMALLVALUEOFRGIVESWIDEBANDWIDTHANDFASTRESPONSEOTHERWISE,ITGIVESALOWBANDWIDTHANDSLUGGISHRESPONSETOIMPROVETHERISETIME,THEVALUEOFRSHOULDBESMALLTHEREFORE,THETWOPARAMETERSANDCANBEDETERMINEDREMARKTHEFUZZYPIDCONTROL11ISACTUALLYACONVENTIONALPIDCONTROLUPIDPLUSAPSEUDOSLIDINGMODECONTROLBECAUSETHESLIDINGMODECONTROLISAROBUSTCONTROL,THEFUZZYPIDCONTROLISMOREROBUSTTHANACONVENTIONALPIDCONTROL4CONTROLSIMULATIONSINTHISSECTION,THECONTROLPERFORMANCEOFFUZZYPIDTUNEDBYTHEPROPOSEDMETHODISCOMPAREDWITHTHATOFCONVENTIONALPIDCONTROLQUANTITATIVECRITERIAFORMEASURINGTHEPERFORMANCEARECHOSENASIAEANDITAESMALLERNUMBERSIMPLYBETTERPERFORMANCEDTEDTEITAEIE，14INALLCONTROLSIMULATIONS,PARAMETERSOFCONVENTIONALPIDCONTROLAREDETERMINEDBYIMCBASEDMETHODANDTHEPARAMETERSOFFUZZYPIDCONTROLAREDETERMINEDBYTHEPROPOSEDTUNINGMETHODEXAMPLE1CONSIDERANINDUSTRIALPROCESSTHATISAPPROXIMATELYDESCRIBEDBYAFIRSTORDERRATIONALTRANSFERFUNCTIONMODELWITHADELAYTIMEASFOLLOWSS10ESP15THELINEARPARTISTHEDOMINANTPROCESSTHESMALLDELAYTIMEIMPLIESWEAKNONLINEARFEATURESASSHOWNINFIGURE5,LITTLEDIFFERENCEISOBSERVEDBETWEENTHECONVENTIONALPIDCONTROLANDFUZZYPIDCONTROLDUETOTHESMALLDELAYTIMEHOWEVER,WHENTHEDELAYTIMEISINCREASEDTOL06,THEREWILLBELARGEMODELERRORCAUSEDBYAPPROXIMATINGTHEDELAYTIMEWITHAFIRSTORDERPADEAPPROXIMATIONIN15ASSHOWNINFIGURE6,FUZZYPIDCONTROLACHIEVESBETTERCONTROLPERFORMANCETHANCONVENTIONALPIDCONTROLMOREVER,THEGAINOFTHEFUZZYPIDCONTROLLERISLOWERTHANTHATOFCONVENTIONALPIDCONTROLLERFIGURE4CONTROLPERFORMANCEOFFUZZYPIDFIGURE5PERFORMANCEOFFUZZYPIDANDPIDANDPIDFOREXAMPLE1,FUZZYPIDSOLIDLINE,FORDELAYL06,FUZZYPIDSOLIDLINE,ANDCONVENTIONALPIDDOTTEDLINEANDCONVENTIONALPIDDOTTEDLINEEXAMPLE2ASSUMETHATANINDUSTRIALPROCESSISDESCRIBEDBY8AS1P16WHEREA1,SUPPOSETHATTHEREISNOMODELINGERRORINTHEPROCESSONTHEBASISOFSTEPRESPONSEANDNYQUISTCURVESOFTHEINDUSTRIALPROCESS,THEAPPROXIMATIONMODELCANBEOBTAINEDASFOLLOWSS34E1SP17ASSHOWNINFIGURE7,LITTLEDIFFERENCEISOBSERVEDBETWEENTHECONVENTIONALPIDCONTROLANDFUZZYPIDCONTROLBECAUSETHEMODELISACCURATEHOWEVER,SUPPOSETHATTHEREISMODELINGERRORANDTHEPRACTICALVALUEOFTHEPARAMETERAIS095ASSHOWNINFIGURE8,FUZZYPIDCONTROLACHIEVESBETTERCONTROLPERFORMANCETHANCONVENTIONALPIDCONTROLMOREVER,THEGAINOFTHEFUZZYPIDCONTROLLERISLOWERTHANTHATOFTHECONVENTIONALPIDCONTROLLER,WHICHISSHOWNINFIGURE8FIGURE6CONTROLPERFORMANCEOFFUZZYPIDFIGURE7CONTROLPERFORMANCEOFFUZZYPIDANDPIDANDPIDFORA1FUZZYPIDSOLIDLINEANDFORPROCESSA095FUZZYPIDCONVENTIONALPIDDOTTEDLINESOLIDLINEANDCONVENTIONALPIDDOTTEDLINE5CONCLUSIONANEFFECTIVETUNINGMETHODFORFUZZYPIDCONTROLLERSBASEDONIMCISPRESENTEDINTHISPAPERANANALYTICALMODELISFIRSTDEVELOPEDFORTHETUNINGOFFUZZYPIDCONTROLLERSTHEANALYTICALMODELINCLUDESALINEARPIDCONTROLANDANONLINEARCOMPENSATIONITEMONTHEBASISOFTHEIMCMETHOD,THEPARAMETERSOFFUZZYPIDCONTROLLERCANBEANALYTICALLYDETERMINEDBYREGARDINGTHECOMPENSATIONITEMASAPROCESSDISTURBANCEALTHOUGHTHESCALINGGAINSANDARECOUPLED,APROCEDUREISUSEDTODECOUPLETHEMONTHEBASISOFTHESLIDINGMODECONTROLTHESTABILITYANALYSISSHOWSTHATTHECONTROLSYSTEMISGLOBALLYASYMPTOTICALLYSTABLEFUZZYPIDCONTROLLERSTUNEDBYTHEPROPOSEDMETHODAREMOREROBUSTTHANTHECONVENTIONALPIDCONTROLLERTHESIMULATIONRESULTSSHOWTHATFUZZYPIDCONTROLLERSTUNEDBYTHEPROPOSEDMETHODACHIEVEBETTERCONTROLPERFORMANCEINBOTHTHETRANSIENTANDSTEADYSTATESANDAREMOREROBUSTTHANCONVENTIONALPIDCONTROLLERSLITERATURECITED1SUGENOMINDUSTRIALAPPLICATIONSOFFUZZYCONTROLELSEVIERAMSTERDAM,THENETHERLANDS,19852MANEL,AALBERT,AJORDI,AMANEL,PWASTEWATERNEUTRALIZATIONCONTROLBASEDONFUZZYLOGICEXPERIMENTALRESULTSINDENGCHEMRES1999,38,270927193ZHANG,JANONLINEARGAINSCHEDULINGCONTROLSTRATEGYBASEDONNEUROFUZZYNETWORKSINDENGCHEMRES2001,40,316431704HOJJATI,HSHEIKHZADEH,MROHANI,SCONTROLOFSUPERSATURATIONINASEMIBATCHANTISOLVENTCRYSTALLIZATIONPROCESSUSINGAFUZZYLOGICCONTROLLERINDENGCHEMRES2007,46,123212405GEORGE,KIMHU,BGRAYMOND,GGANALYSISOFDIRECTACTIONFUZZYPIDCONTROLLERSTRUCTURESIEEETRANSSYST,MAN,CYBERNETICS,PARTB1999,293,3713886LI,HXGATLAND,HCONVENTIONALFUZZYLOGICCONTROLANDITSENHANCEMENTIEEETRANSSYST,MAN,CYBERNETICS1996,2610,7917977GEORGE,KIMHU,BGRAYMOND,GGTWOLEVELTUNINGOFFUZZYPIDCOTROLLERSIEEETRANSSYST,MAN,CYBERNETICS,PARTB2001,312,2632698WOO,ZWCHUNG,HYLIN,JJAPIDTYPEFUZZYCONTROLLERWITHSELFTUNINGSCALINGFACTORSFUZZYSETSSYST2000,115,3213269VEGA,PPRADA,CALEIXANDER,VSELFTUNINGPREDICTIVEPIDCONTROLLERIEEPROD1991,1383,30331110RAJANI,KMNIKHIL,RPAROBUSTSELFTUNINGSCHEMEFORPIANDPDTYPEFUZZYCONTROLLERSIEEETTRANSFUZZYSYST1999,71,21611RAJANI,KMNIKHIL,RPASELFTUNINGFUZZYPICONTROLLERFUZZYSETSSYST2000,115,32733812YESIL,EGUZELKAYA,MEKSIN,ISELFTUNINGFUZZYPIDTYPELOADANDFREQUENCYCONTROLLERENERGYCONVERSMANAGE2004,45,37739013XU,JXPOK,YMLIU,CHANG,CCTUNINGANDANALYSISOFAFUZZYPICONTROLLERBASEDONGAINANDPHASEMARGINSIEEETRANSSYST,MAN,CYBERNETICS,PARTA1998,285,68569114XU,JXHANG,CCLIU,CPARALLELSTRUCTUREANDTUNINGOFAFUZZYPIDCONTROLLERAUTOMATICA2000,36,67368415KAYA,