中英文文献翻译论文-pid控制器

中北大学2013届毕业设计说明书第第页共20页附件1：外文原文PIDcontrollerZuoXinandSunJinming(ResearchInstituteofAutomation,UniversityofPetroleum,Belting102249,China)ReceivedApril2，2005Abstract:Performanceassessmentofaproportional-integral-derivative(PID)controllerisconduetedusingthePIDachievableminimumvarianceasabenchmark．Whentheprocessmodelisunknown，wecarlestimatetheP／D·achievableminimumvarianceandthecorrespondingparametersbyroutineclosed-loopoperationdata．Simulationresultsshowthattheprocessoutputvarianceisreducedbyretuningcontrollerparameters．Keywords：Performanceassessment，PIDcontrol，minimumvarianceAproportional–integral–derivativecontroller(PIDcontroller)isageneric.controlloopfeedbackmechanismwidelyusedinindustrialcontrolsystems.APIDcontrollerattemptstocorrecttheerrorbetweenameasuredprocessvariableandadesiredsetpointbycalculatingandthenoutputtingacorrectiveactionthatcanadjusttheprocessaccordingly.ThePIDcontrollercalculation(algorithm)involvesthreeseparateparameters;theProportional,theIntegralandDerivativevalues.TheProportionalvaluedeterminesthereactiontothecurrenterror,theIntegraldeterminesthereactionbasedonthesumofrecenterrorsandtheDerivativedeterminesthereactiontotherateatwhichtheerrorhasbeenchanging.Theweightedsumofthesethreeactionsisusedtoadjusttheprocessviaacontrolelementsuchasthepositionofacontrolvalveorthepowersupplyofaheatingelement.By"tuning"thethreeconstantsinthePIDcontrolleralgorithmthePIDcanprovidecontrolactiondesignedforspecificprocessrequirements.Theresponseofthecontrollercanbedescribedintermsoftheresponsivenessofthecontrollertoanerror,thedegreetowhichthecontrollerovershootsthesetpointandthedegreeofsystemoscillation.NotethattheuseofthePIDalgorithmforcontroldoesnotguaranteeoptimalcontrolofthesystemorsystemstability.Someapplicationsmayrequireusingonlyoneortwomodestoprovidetheappropriatesystemcontrol.Thisisachievedbysettingthegainofundesiredcontroloutputstozero.APIDcontrollerwillbecalledaPI,PD,PorIcontrollerintheabsenceoftherespectivecontrolactions.PIcontrollersareparticularlycommon,sincederivativeactionisverysensitivetomeasurementnoise,andtheabsenceofanintegralvaluemaypreventthesystemfromreachingitstargetvalueduetothecontrolaction.Note:Duetothediversityofthefieldofcontroltheoryandapplication,manynamingconventionsfortherelevantvariablesareincommonuse.1.ControlloopbasicsAfamiliarexampleofacontrolloopistheactiontakentokeepone'sshowerwaterattheidealtemperature,whichtypicallyinvolvesthemixingoftwoprocessstreams,coldandhotwater.Thepersonfeelsthewatertoestimateitstemperature.Basedonthismeasurementtheyperformacontrolaction:usethecoldwatertaptoadjusttheprocess.Thepersonwouldrepeatthisinput-outputcontrolloop,adjustingthehotwaterflowuntiltheprocesstemperaturestabilizedatthedesiredvalue.Feelingthewatertemperatureistakingameasurementoftheprocessvalueorprocessvariable(PV).Thedesiredtemperatureiscalledthesetpoint(SP).Theoutputfromthecontrollerandinputtotheprocess(thetapposition)iscalledthemanipulatedvariable(MV).Thedifferencebetweenthemeasurementandthesetpointistheerror(e),toohotortoocoldandbyhowmuch.Asacontroller,onedecidesroughlyhowmuchtochangethetapposition(MV)afteronedeterminesthetemperature(PV),andthereforetheerror.ThisfirstestimateistheequivalentoftheproportionalactionofaPIDcontroller.TheintegralactionofaPIDcontrollercanbethoughtofasgraduallyadjustingthetemperaturewhenitisalmostright.Derivativeactioncanbethoughtofasnoticingthewatertemperatureisgettinghotterorcolder,andhowfast,andtakingthatintoaccountwhendecidinghowtoadjustthetap.Makingachangethatistoolargewhentheerrorissmallisequivalenttoahighgaincontrollerandwillleadtoovershoot.Ifthecontrollerweretorepeatedlymakechangesthatweretoolargeandrepeatedlyovershootthetarget,thiscontrolloopwouldbetermedunstableandtheoutputwouldoscillatearoundthesetpointineitheraconstant,growing,ordecayingsinusoid.Ahumanwouldnotdothisbecauseweareadaptivecontrollers,learningfromtheprocesshistory,butPIDcontrollersdonothavetheabilitytolearnandmustbesetupcorrectly.Selectingthecorrectgainsforeffectivecontrolisknownastuningthecontroller.Ifacontrollerstartsfromastablestateatzeroerror(PV=SP),thenfurtherchangesbythecontrollerwillbeinresponsetochangesinothermeasuredorunmeasuredinputstotheprocessthatimpactontheprocess,andhenceonthePV.VariablesthatimpactontheprocessotherthantheMVareknownasdisturbancesandgenerallycontrollersareusedtorejectdisturbancesand/orimplementsetpointchanges.Changesinfeedwatertemperatureconstituteadisturbancetotheshowerprocess.Intheory,acontrollercanbeusedtocontrolanyprocesswhichhasameasurableoutput(PV),aknownidealvalueforthatoutput(SP)andaninputtotheprocess(MV)thatwillaffecttherelevantPV.Controllersareusedinindustrytoregulatetemperature,pressure,flowrate,chemicalcomposition,speedandpracticallyeveryothervariableforwhichameasurementexists.Automobilecruisecontrolisanexampleofaprocesswhichutilizesautomatedcontrol.Duetotheirlonghistory,simplicity,wellgroundedtheoryandsimplesetupandmaintenancerequirements,PIDcontrollersarethecontrollersofchoiceformanyoftheseapplications.2.PIDcontrollertheoryNote:Thissectiondescribestheidealparallelornon-interactingformofthePIDcontroller.ForotherformspleaseseetheSection"AlternativenotationandPIDforms".ThePIDcontrolschemeisnamedafteritsthreecorrectingterms,whosesumconstitutesthemanipulatedvariable(MV).Hence:WherePout,Iout,andDoutarethecontributionstotheoutputfromthePIDcontrollerfromeachofthethreeterms,asdefinedbelow.2.1.ProportionaltermTheproportionaltermmakesachangetotheoutputthatisproportionaltothecurrenterrorvalue.TheproportionalresponsecanbeadjustedbymultiplyingtheerrorbyaconstantKp,calledtheproportionalgain.Theproportionaltermisgivenby:WherePout:ProportionaloutputKp:ProportionalGain,atuningparametere:Error=SP−PVt:Timeorinstantaneoustime(thepresent)ChangeofresponseforvaryingKpAhighproportionalgainresultsinalargechangeintheoutputforagivenchangeintheerror.Iftheproportionalgainistoohigh,thesystemcanbecomeunstable(SeethesectiononLoopTuning).Incontrast,asmallgainresultsinasmalloutputresponsetoalargeinputerror,andalessresponsive(orsensitive)controller.Iftheproportionalgainistoolow,thecontrolactionmaybetoosmallwhenrespondingtosystemdisturbances.Intheabsenceofdisturbances,pureproportionalcontrolwillnotsettleatitstargetvalue,butwillretainasteadystateerrorthatisafunctionoftheproportionalgainandtheprocessgain.Despitethesteady-stateoffset,bothtuningtheoryandindustrialpracticeindicatethatitistheproportionaltermthatshouldcontributethebulkoftheoutputchange.2.2.IntegraltermThecontributionfromtheintegraltermisproportionaltoboththemagnitudeoftheerrorandthedurationoftheerror.Summingtheinstantaneouserrorovertime(integratingtheerror)givestheaccumulatedoffsetthatshouldhavebeencorrectedpreviously.Theaccumulatederroristhenmultipliedbytheintegralgainandaddedtothecontrolleroutput.Themagnitudeofthecontributionoftheintegraltermtotheoverallcontrolactionisdeterminedbytheintegralgain,Ki.Theintegraltermisgivenby:Iout:IntegraloutputKi:IntegralGain,atuningparametere:Error=SP−PVτ:TimeinthepastcontributingtotheintegralresponseTheintegralterm(whenaddedtotheproportionalterm)acceleratesthemovementoftheprocesstowardssetpointandeliminatestheresidualsteady-stateerrorthatoccurswithaproportionalonlycontroller.However,sincetheintegraltermisrespondingtoaccumulatederrorsfromthepast,itcancausethepresentvaluetoovershootthesetpointvalue(crossoverthesetpointandthencreateadeviationintheotherdirection).Forfurthernotesregardingintegralgaintuningandcontrollerstability,seethesectiononlooptuning.2.3DerivativetermTherateofchangeoftheprocesserroriscalculatedbydeterminingtheslopeoftheerrorovertime(i.e.itsfirstderivativewithrespecttotime)andmultiplyingthisrateofchangebythederivativegainKd.Themagnitudeofthecontributionofthederivativetermtotheoverallcontrolactionistermedthederivativegain,Kd.Thederivativetermisgivenby: Dout:DerivativeoutputKd:DerivativeGain,atuningparametere:Error=SP−PVt:Timeorinstantaneoustime(thepresent)Thederivativetermslowstherateofchangeofthecontrolleroutputandthiseffectismostnoticeableclosetothecontrollersetpoint.Hence,derivativecontrolisusedtoreducethemagnitudeoftheovershootproducedbytheintegralcomponentandimprovethecombinedcontroller-processstability.However,differentiationofasignalamplifiesnoiseandthusthisterminthecontrollerishighlysensitivetonoiseintheerrorterm,andcancauseaprocesstobecomeunstableifthenoiseandthederivativegainaresufficientlylarge.2.4SummaryTheoutputfromthethreeterms,theproportional,theintegralandthederivativetermsaresummedtocalculatetheoutputofthePIDcontroller.Definingu(t)asthecontrolleroutput,thefinalformofthePIDalgorithmis:andthetuningparametersareKp:ProportionalGain-LargerKptypicallymeansfasterresponsesincethelargertheerror,thelargertheProportionaltermcompensation.Anexcessivelylargeproportionalgainwillleadtoprocessinstabilityandoscillation.Ki:IntegralGain-LargerKiimpliessteadystateerrorsareeliminatedquicker.Thetrade-offislargerovershoot:anynegativeerrorintegratedduringtransientresponsemustbeintegratedawaybypositiveerrorbeforewereachsteadystate.Kd:DerivativeGain-LargerKddecreasesovershoot,butslowsdowntransientresponseandmayleadtoinstabilityduetosignalnoiseamplificationinthedifferentiationoftheerror.3.LooptuningIfthePIDcontrollerparameters(thegainsoftheproportional,integralandderivativeterms)arechosenincorrectly,thecontrolledprocessinputcanbeunstable,i.e.itsoutputdiverges,withorwithoutoscillation,andislimitedonlybysaturationormechanicalbreakage.Tuningacontrolloopistheadjustmentofitscontrolparameters(gain/proportionalband,integralgain/reset,derivativegain/rate)totheoptimumvaluesforthedesiredcontrolresponse.Theoptimumbehavioronaprocesschangeorsetpointchangevariesdependingontheapplication.Someprocessesmustnotallowanovershootoftheprocessvariablebeyondthesetpointif,forexample,thiswouldbeunsafe.Otherprocessesmustminimizetheenergyexpendedinreachinganewsetpoint.Generally,stabilityofresponse(thereverseofinstability)isrequiredandtheprocessmustnotoscillateforanycombinationofprocessconditionsandsetpoints.Someprocesseshaveadegreeofnon-linearityandsoparametersthatworkwellatfull-loadconditionsdon'tworkwhentheprocessisstartingupfromno-load.Thissectiondescribessometraditionalmanualmethodsforlooptuning.ThereareseveralmethodsfortuningaPIDloop.Themosteffectivemethodsgenerallyinvolvethedevelopmentofsomeformofprocessmodel,thenchoosingP,I,andDbasedonthedynamicmodelparameters.Manualtuningmethodscanberelativelyinefficient.Thechoiceofmethodwilldependlargelyonwhetherornottheloopcanbetaken"offline"fortuning,andtheresponsetimeofthesystem.Ifthesystemcanbetakenoffline,thebesttuningmethodofteninvolvessubjectingthesystemtoastepchangeininput,measuringtheoutputasafunctionoftime,andusingthisresponsetodeterminethecontrolparameters.ChoosingaTuningMethodMethodAdvantagesDisadvantagesManualTuningNomathrequired.Onlinemethod.Requiresexperiencedpersonnel.Ziegler–NicholsProvenMethod.Onlinemethod.Processupset,sometrial-and-error,veryaggressivetuning.SoftwareToolsConsistenttuning.Onlineorofflinemethod.Mayincludevalveandsensoranalysis.Allowsimulationbeforedownloading.Somecostandtraininginvolved.Cohen-CoonGoodprocessmodels.Somemath.Offlinemethod.Onlygoodforfirst-orderprocesses.3.1ManualtuningIfthesystemmustremainonline,onetuningmethodistofirstsettheIandDvaluestozero.IncreasethePuntiltheoutputofthelooposcillates,thenthePshouldbeleftsettobeapproximatelyhalfofthatvaluefora"quarteramplitudedecay"typeresponse.ThenincreaseDuntilanyoffsetiscorrectinsufficienttimefortheprocess.However,toomuchDwillcauseinstability.Finally,increaseI,ifrequired,untiltheloopisacceptablyquicktoreachitsreferenceafteraloaddisturbance.However,toomuchIwillcauseexcessiveresponseandovershoot.AfastPIDlooptuningusuallyovershootsslightlytoreachthesetpointmorequickly;however,somesystemscannotacceptovershoot,inwhichcasean"over-damped"closed-loopsystemisrequired,whichwillrequireaPsettingsignificantlylessthanhalfthatofthePsettingcausingoscillation.3.2Ziegler–NicholsmethodAnothertuningmethodisformallyknownastheZiegler–Nicholsmethod,introducedbyJohnG.ZieglerandNathanielB.Nichols.Asinthemethodabove,theIandDgainsarefirstsettozero.The"P"gainisincreaseduntilitreachesthe"criticalgain"Kcatwhichtheoutputoftheloopstartstooscillate.KcandtheoscillationperiodPcareusedtosetthegainsasshown:3.3PIDtuningsoftwareMostmodernindustrialfacilitiesnolongertuneloopsusingthemanualcalculationmethodsshownabove.Instead,PIDtuningandloopoptimizationsoftwareareusedtoensureconsistentresults.Thesesoftwarepackageswillgatherthedata,developprocessmodels,andsuggestoptimaltuning.Somesoftwarepackagescanevendeveloptuningbygatheringdatafromreferencechanges.MathematicalPIDlooptuninginducesanimpulseinthesystem,andthenusesthecontrolledsystem'sfrequencyresponsetodesignthePIDloopvalues.Inloopswithresponsetimesofseveralminutes,mathematicallooptuningisrecommended,becausetrialanderrorcanliterallytakedaysjusttofindastablesetofloopvalues.Optimalvaluesarehardertofind.Somedigitalloopcontrollersofferaself-tuningfeatureinwhichverysmallsetpointchangesaresenttotheprocess,allowingthecontrolleritselftocalculateoptimaltuningvalues.Otherformulasareavailabletotunetheloopaccordingtodifferentperformancecriteria.4ModificationstothePIDalgorithmThebasicPIDalgorithmpresentssomechallengesincontrolapplicationsthathavebeenaddressedbyminormodificationstothePIDform.OnecommonproblemresultingfromtheidealPIDimplementationsisintegralwindup.Thiscanbeaddressedby:InitializingthecontrollerintegraltoadesiredvalueDisablingtheintegralfunctionuntilthePVhasenteredthecontrollableregionLimitingthetimeperiodoverwhichtheintegralerroriscalculatedPreventingtheintegraltermfromaccumulatingaboveorbelowpre-determinedboundsManyPIDloopscontrolamechanicaldevice(forexample,avalve).Mechanicalmaintenancecanbeamajorcostandwearleadstocontroldegradationintheformofeitherstictionoradeadbandinthemechanicalresponsetoaninputsignal.Therateofmechanicalwearismainlyafunctionofhowoftenadeviceisactivatedtomakeachange.Wherewearisasignificantconcern,thePIDloopmayhaveanoutputdeadbandtoreducethefrequencyofactivationoftheoutput(valve).Thisisaccomplishedbymodifyingthecontrollertoholditsoutputsteadyifthechangewouldbesmall(withinthedefineddeadbandrange).Thecalculatedoutputmustleavethedeadbandbeforetheactualoutputwillchange.Theproportionalandderivativetermscanproduceexcessivemovementintheoutputwhenasystemissubjectedtoaninstantaneous"step"increaseintheerror,suchasalargesetpointchange.Inthecaseofthederivativeterm,thisisduetotakingthederivativeoftheerror,whichisverylargeinthecaseofaninstantaneousstepchange.5.LimitationsofPIDcontrolWhilePIDcontrollersareapplicabletomanycontrolproblems,theycanperformpoorlyinsomeapplications.PIDcontrollers,whenusedalone,cangivepoorperformancewhenthePIDloopgainsmustbereducedsothatthecontrolsystemdoesnotovershoot,oscillateor"hunt"aboutthecontrolsetpointvalue.Thecontrolsystemperformancecanbeimprovedbycombiningthefeedback(orclosed-loop)controlofaPIDcontrollerwithfeed-forward(oropen-loop)control.Knowledgeaboutthesystem(suchasthedesiredaccelerationandinertia)canbe"fedforward"andcombinedwiththePIDoutputtoimprovetheoverallsystemperformance.Thefeed-forwardvaluealonecanoftenprovidethemajorportionofthecontrolleroutput.ThePIDcontrollercanthenbeusedprimarilytorespondtowhateverdifferenceor"error"remainsbetweenthesetpoint(SP)andtheactualvalueoftheprocessvariable(PV).Sincethefeed-forwardoutputisnotaffectedbytheprocessfeedback,itcannevercausethecontrolsystemtooscillate,thusimprovingthesystemresponseandstability.Forexample,inmostmotioncontrolsystems,inordertoaccelerateamechanicalloadundercontrol,moreforceortorqueisrequiredfromtheprimemover,motor,oractuator.IfavelocityloopPIDcontrollerisbeingusedtocontrolthespeedoftheloadandcommandtheforceortorquebeingappliedbytheprimemover,thenitisbeneficialtotaketheinstantaneousaccelerationdesiredfortheload,scalethatvalueappropriatelyandaddittotheoutputofthePIDvelocityloopcontroller.Thismeansthatwhenevertheloadisbeingacceleratedordecelerated,aproportionalamountofforceiscommandedfromtheprimemoverregardlessofthefeedbackvalue.ThePIDloopinthissituationusesthefeedbackinformationtoeffectanyincreaseordecreaseofthecombinedoutputinordertoreducetheremainingdifferencebetweentheprocesssetpointandthefeedbackvalue.Workingtogether,thecombinedopen-loopfeed-forwardcontrollerandclosed-loopPIDcontrollercanprovideamoreresponsive,stableandreliablecontrolsystem.AnotherproblemfacedwithPIDcontrollersisthattheyarelinear.Thus,performanceofPIDcontrollersinnon-linearsystems(suchasHVACsystems)isvariable.OftenPIDcontrollersareenhancedthroughmethodssuchasPIDgainschedulingorfuzzylogic.Furtherpracticalapplicationissuescanarisefrominstrumentationconnectedtothecontroller.Ahighenoughsamplingrate,measurementprecision,andmeasurementaccuracyarerequiredtoachieveadequatecontrolperformance.AproblemwiththeDerivativetermisthatsmallamountsofmeasurementorprocessnoisecancauselargeamountsofchangeintheoutput.Itisoftenhelpfultofilterthemeasurementswithalow-passfilterinordertoremovehigher-frequencynoisecomponents.However,low-passfilteringandderivativecontrolcancanceleachotherout,soreducingnoisebyinstrumentationmeansisamuchbetterchoice.Alternatively,thedifferentialbandcanbeturnedoffinmanysystemswithlittlelossofcontrol.ThisisequivalenttousingthePIDcontrollerasaPIcontroller.6.CascadecontrolOnedistinctiveadvantageofPIDcontrollersisthattwoPIDcontrollerscanbeusedtogethertoyieldbetterdynamicperformance.ThisiscalledcascadedPIDcontrol.IncascadecontroltherearetwoPIDsarrangedwithonePIDcontrollingthesetpointofanother.APIDcontrolleractsasouterloopcontroller,whichcontrolstheprimaryphysicalparameter,suchasfluidlevelorvelocity.Theothercontrolleractsasinnerloopcontroller,whichreadstheoutputofouterloopcontrollerassetpoint,usuallycontrollingamorerapidchangingparameter,flowrateoraccelleration.ItcanbemathematicallyprovedthattheworkingfrequencyofthecontrollerisincreasedandthetimeconstantoftheobjectisreducedbyusingcascadedPIDcontroller.[vague]7.PhysicalimplementationofPIDcontrolIntheearlyhistoryofautomaticprocesscontrolthePIDcontrollerwasimplementedasamechanicaldevice.Thesemechanicalcontrollersusedalever,springandamassandwereoftenenergizedbycompressedair.Thesepneumaticcontrollerswereoncetheindustrystandard.Electronicanalogcontrollerscanbemadefromasolid-stateortubeamplifier,acapacitorandaresistance.ElectronicanalogPIDcontrolloopswereoftenfoundwithinmorecomplexelectronicsystems,forexample,theheadpositioningofadiskdrive,thepowerconditioningofapowersupply,oreventhemovement-detectioncircuitofamodernseismometer.Nowadays,electroniccontrollershavelargelybeenreplacedbydigitalcontrollersimplementedwithmicrocontrollersorFPGAs.MostmodernPIDcontrollersinindustryareimplementedinsoftwareinprogrammablelogiccontrollers(PLCs)orasapanel-mounteddigitalcontroller.SoftwareimplementationshavetheadvantagesthattheyarerelativelycheapandareflexiblewithrespecttotheimplementationofthePIDalgorithm.References[1]Byung，S.K.(2000)OnPerformanceAssessmentofFeedbackControlLoops．Austin：TheUniversityofTexasAustin[2]Desborough，L．andHarris，T.(1992)PerformanceAssessmentMeasuresforUnivariateFeedbackControl.TheCanadianJournalofChemicalEngineering,70(12)．1186-1197[3]Ender,D.B.(1993)ProcessControlPerformance：NotasGoodasYouThink．ControlEngineering，40(10)[4]Harris,T(1993)PefformanceAssessmentMeasllresforUnivariateFeedforward/FeedbackControl．TheCanadianJournalofChemicalEngineering，71(8)，1186-1197[5]Qin，S．J．(1998)Contr01PerformanceMonitoring：AReviewandAssessment．Com．Chem．Eng．，(23)，173．186[6]Sun,Jinming(2004)PIDPerformanceAssessmentandParametersTuning．Beijing：ChinaUniversityofPetroleum[7]Xu，Xi；Li，TaoandBo，Xiaochen(2000)MatlabToolboxApplication--ControlEngineering．Bering：ElectronIndustryPress附件2：外文资料翻译译文PID控制器左信孙金明（石油大学自动化研究所，北京，102249，中国）发表于2005.4.2摘要：一个比例积分微分（PID）控制器的性能评价进行使用PID实现的最小方差作为参照。在过程模型是未知的，我们估计PID可达到的最小方差和常规的闭环操作数据的相应参数。仿真结果表明，系统输出方差是通过重新调谐控制器参数减少。关键词：绩效考核，PID控制，最小方差比例积分微分控制器（PID调节器）是一个控制环，广泛地应用于工业控制系统里的反馈机制。PID控制器通过调节给定值与测量值之间的偏差，给出正确的调整，从而有规律地纠正控制过程。PID控制器算法涉及到三个部分：比例，积分，微分。比例控制是对当前偏差的反应，积分控制是基于新近错误总数的反应，而微分控制则是基于错误变化率的反应。这三种控制的结合可用来调节过程系统，例如调节阀的位置，或者加热系统的电源调节。根据具体的工艺要求，通过PID控制器的参数整定，从而提供调节作用。控制器的响应可以被认为是对系统偏差的响应。注意一点的是，PID算法不一定就是系统或系统稳定性的最佳控制。一些应用可能只需要运用一到两种方法来提供适当的系统控制。这是通过把不想要的控制输出置零取得。在控制系统中存在P,PI,PD,PID调节器。PI调节器很普遍，因为微分控制对测量噪音非常敏感。积分作用的缺乏可以防止系统根据控制目标而达到它的目标值。注释：由于控制理论和应用领域的差异，很多相关变量的命名约定是常用的。控制环基础一个关于控制环类似的例子就是保持水在理想温度，涉及到两个过程，冷、热水的混合。人可以凭触觉估测水的温度。基于此他们设计一个控制行为：用冷水龙头调整过程。重复这个过程，调节热水流直到温度处于期望的稳定值。感觉水温就是对过程值或变量的测量。期望得到的温度称为给定值。控制器的输出对象和过程的输入对象称为控制参数。测量值与给定值之间的差就是偏差值，太高、太低或正常。作为一个控制器，在确定温度给定值后，就可以粗略决定改变阀门位置多少，以及怎样改变偏差值。首次估计即是PID 控制器的比例度的确定。当它几乎正确时，PID控制器的积分作用就是起着逐渐调整温度的作用。微分作用就是根据水温变得更热、更冷，以及变化速率来决定什么时候、怎样调整那些阀门。当偏差小时而做了一个大变动，相当于一个大的调整控制器，会导致超调。如果控制器反复进行大的变动并且反复越过给定值的改变，控制环将会不稳定。输出值将在期望值或一常量周围摆动，甚至破坏系统稳定性。人不会这样做，因为我们是有智慧的控制人员，可以从历史经验中学习，但PID控制器没有学习能力，必须正确的设定。为有效的控制系统选择正确的参数被称为整定控制器。如果控制器在零偏差从稳定开始，然后进一步的变化将导致其它一些影响过程的能测量、不能测量值的变化，并且作用于偏差值上。除主过程以外，其他的对扰动有影响的过程可以用来抑制扰动或实现对目标值的改变。供给水温的变化就构成了对过程的一个扰动。理论上，控制器能用来控制可测量对象，以及可以影响偏差的输出、输入标准值的所有过程参数。控制器在工业中被用来调节温度，压力，流速，化学组成，速度以及其它任何存在可测量的对象。汽车游览控制就是一个自动化的过程控制的例子。由于它们悠久的历史，简易，良好的理论基础以及简单的设置、维护要求，PID控制器被许多应用实践所采纳。2.PID控制器理论注释：这部分描述PID控制器理想平行或非相互作用的形式。关于其他形式，请看“其它的表达式和PID形式”这部分。PID控制是根据它的三个参数而命名的，三参数结合起来就形成控制参数。因此：Pout，Iout和Dout是控制器的三个参数，下面分别予以确定。2.1比例度比例度是根据当前的错误值而做出的变动。比例度可以通过恒定的Kp增加来调整，称为比例增益。比例度计算如下：Pout:比例度Kp：比例系数，协调参数。e:偏差=SP-PVt:时间或瞬时时间（当前的）一个高的比例增益产生于一种输出值的大的变化。如果比例增益太高，系统将变得不稳定。响应地，一个小的调整产生于一小的输出变化，而如果比例增益太低，当对系统振荡作出反映时，控制作用可能太小。缺少扰动的情况下，纯粹的比例控制不能完全解决问题，但是将保留从过程中获得的具有比例增益的功能的稳态偏差。尽管有稳态补偿，理论和工业实践都表明比例度在输出控制中起到大部分的作用。2.2积分值积分值的大小与偏差的大小及持续时间成正比。根据即时的超时的错误改正，进行积累补偿。积累的误差通过积分调节后再作用于输出。对总的控制作用的积分大小由积分时间常数来决定，即Ki，积分值计算如下：Iout：积分值Ki:积分时间常数，协调参数e:偏差=SP-PVζ：积分时间积分值加速面向设定值的过程运动并且消除残余的只与控制器发生作用的稳态偏差。然而，因为积分从过去的积累误差作出反应，引起当前的值越过设定值（跨过设定值向其它方向改变）。想了解更多的关于积分和控制器稳定度的知识，请参见关于环路调谐的部分。2.3微分值过程偏差的变化率通过超时错误的斜率来计算（即它第一个关于调节的微分），并增加由微分时间常数Kd引起的变化的速率。对整个控制行为的微分作用的大小称为微分值Kd。微分值计算如下：Dout:微分输出值Kd:微分时间常数，协调参数e:偏差=SP-PVt:时间或瞬时时间（当前的）微分作用减缓了控制器输出的变化率，这种效果最接近于控制器的给定值。因此，微分控制用来降低由积分部分产生的因素并改进控制器过程控制的稳定度。但是，信号噪音对偏差值非常敏感，而且如果噪音和微分度足够大的话，将使系统变得不稳定。2.4摘要三种参数控制的输出值，比例，积分和微分综合起来能够计算出PID调节器的输出，计算控制器输出时，PID算法的最终形式u(t)为：协调参数分别是：Kp:比例增益—偏差愈大时，Kp也愈大，比例期补偿更大。过大的比例增益会导致系统的不稳定乃至崩溃。Ki:积分，Ki越大时，稳态偏差会更迅速地被消除。在达到稳态之前，在瞬态响应期间组合的任何误差必须分开。Kd：微分。Kd越大时，越容易超调，但是不同扰动区域的信号噪音的瞬态响应可能导致系统的不稳定。3.环路调谐如果PID控制器参数选择的不正确，控制过程输入可能是不稳定的，即：它的输出有分歧，有或没有动摇，并且只通过饱和或者机械破损是有限的。控制环的协调根据那些期望控制过程的最佳值来调整它的控制参数。最佳控制行为就是过程能根据应用作出相应的变化。一些过程不允许在设定值以外易变的过程超限，如果发生了，将是不安全的。其它过程必须在达到新设定值过程前把用掉的能量减到最小。通常，过程要求稳定，不可因为过程条件和给定值的任何变化而摆动。一些过程有一定的非线性，因此在系统满负荷下正常工作的参数在系统零负荷下将停止工作。这部分为环路调谐描述了一些传统的手工方法。PID环的调节有几种方法。最有效的方法一般与某种形式的过程模型的发展有关，然后选择的P,I和基于动态模型参数的D。手工协调方法相对来说可能没有效率。方法的选择基本依赖于控制环是否可以协调，以及系统的响应时间。如果系统可被离线工作，最好的协调方法经常与输入的阶跃变化系统有关，输出值的测量作为一个时间函数，并用来确定控制参数。3.1手工调节如果系统必须保持在线，一种协调方法把积分和微分时间常数置零。增加P值直到环的输出值摆动，然后，P值应该大约被设为标准值的四分之一。然后增加D直到过程补偿在足够的时间内是正确的。不过，D值太大将引起不稳定。最后，增加I值，如果需要的话，直到那些环在负荷扰动之后可迅速到达给定值。不过，I值太大将引起过度的反应并且超调。快速PID环路调谐通常越过微小扰动并且能更迅速地达到给定值；但是，一些系统不能承受超调，这时，采用超调闭环系统是有必要的，这个要求P值确定为引起系统摆动的P值的一半。3.2Ziegler–Nichols方法另一种调节方式方法正式被称为Ziegler–Nichols方法，由约翰·G.齐格勒和纳撒尼尔·B.尼科尔斯发明。如同在上面的方法内，I和D常数开始时先被置零。P值增加直至达到Kc值，此时闭环输出值稳定。Kc和Pc用来象显示的那样设定目标值：3.3PID调节软件现在大多数的现代工业设备自动控制环不再使用以上介绍的各种手工计算方法。相应地，PID协调和循环优化软件被用来保证结果的确定。这些软件自动收集数据，构建过程模型，并且建立最佳的调节方式。一些软件包甚至能根据参考值的变化规律来开发数据库。数学PID环路调节在系统里引起一个推动，然后根据被控制的系统的频率响应设计PID环标准值。在有几分钟响应时间的环、数学环路调谐中被推荐，因为反复试验要花费数天，而仅仅是为了找到一套稳定的环价值。而最佳的控制值更难