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1、PIDControlIntroductionThePIDcontrolleristhemostcommonformoffeedback.Itwasanessentialelementofearlygovernorsanditbecamethestandardtoolwhenprocesscontrolemergedinthe1940s.Inprocesscontroltoday,morethan95%ofthecontrolloopsareofPIDtype,mostloopsareactuallyPIcontrol.PIDcontrollersaretodayfoundinallareasw

2、herecontrolisused.Thecontrollerscomeinmanydifferentforms.Therearestandalonesystemsinboxesforoneorafewloops,whicharemanufacturedbythehundredthousandsyearly.PIDcontrolisanimportantingredientofadistributedcontrolsystem.Thecontrollersarealsoembeddedinmanyspecialpurposecontrolsystems.PIDcontrolisoftencom

3、binedwithlogic,sequentialfunctions,selectors,andsimplefunctionblockstobuildthecomplicatedautomationsystemsusedforenergyproduction,transportation,andmanufacturing.Manysophisticatedcontrolstrategies,suchasmodelpredictivecontrol,arealsoorganizedhierarchically.PIDcontrolisusedatthelowestlevel;themultiva

4、riablecontrollergivesthesetpointstothecontrollersatthelowerlevel.ThePIDcontrollercanthusbesaidtobethe“breadandbutterofcontrolengineering.Itisanimportantcomponentineverycontrolengineer'stoolbox.PIDcontrollershavesurvivedmanychangesintechnology,frommechanicsandpneumaticstomicroprocessorsviaelectro

5、nictubes,transistors,integratedcircuits.ThemicroprocessorhashadadramaticinfluencethePIDcontroller.PracticallyallPIDcontrollersmadetodayarebasedonmicroprocessors.ThishasgivenopportunitiestoprovideThe AlgorithmWewill startThe “textbook ”additionalfeatureslikeautomatictuning,gainscheduling,andcontinuou

6、sadaptation.bysummarizingthekeyfeaturesofthePIDcontroller.versionofthePIDalgorithmisdescribedby:de t丁。三r the reference variable,1tutKete0whereyisthemeasuredprocessvariable,uisthecontrolsignalandeisthecontrolerror(e=ysp?y).Thereferencevariableisoftencalledthesetpoint.Thecontrolsignalisthusasumofthree

7、terms:theP-term(whichisproportionaltotheerror),theI-term(whichisproportionaltotheintegraloftheerror),andtheD-term(whichisproportionaltothederivativeoftheerror).ThecontrollerparametersareproportionalgainK,integraltimeTi,andderivativetimeTd.Theintegral,proportionalandderivativepartcanbeinterpretedasco

8、ntrolactionsbasedonthepast,thepresentandthefutureasisillustratedinFigure.Thederivativepartcanalsobeinterpretedaspredictionbylinearextrapolationasis川ustratedinFigure.Theactionofthedifferenttermscanbe川ustratedbythefollowingfigureswhichshowtheresponsetostepchangesinthereferencevalueinatypicalcase.Effec

9、tsofProportional,IntegralandDerivativeActionProportionalcontrolisillustratedinFigure.ThecontrollerisgivenbywithTi=andTd=0.Thefigureshowsthatthereisalwaysasteadystateerrorinproportionalcontrol.Theerrorwilldecreasewithincreasinggain,butthetendencytowardsosc川ationwillalsoincrease.Figure川ustratestheeffe

10、ctsofaddingintegral.ItfollowsfromthatthestrengthofintegralactionincreaseswithdecreasingintegraltimeTi.Thefigureshowsthatthesteadystateerrordisappearswhenintegralactionisused.Comparewiththediscussionofthe“magicofintegralaction“inSection.ThetendencyforoscillationalsoincreaseswithdecreasingTi.Theproper

11、tiesofderivativeactionareillustratedinFigure.Figure川ustratestheeffectsofaddingderivativeaction.TheparametersKandTarechosensothattheclosedloopsystemisoscillatory.Dampingincreaseswithincreasingderivativetime,butdecreasesagainwhenderivativetimebecomestoolarge.Recallthatderivativeactioncanbeinterpreteda

12、sprovidingpredictionbylinearextrapolationoverthetimeTd.UsingthisinterpretationitiseasytounderstandthatderivativeactiondoesnothelpifthepredictiontimeTdistoolarge.InFiguretheperiodofoscillationisabout6sforthesystemwithoutderivativeChapter6.PIDControlFigureFigureDerivativeactionsceasetobeeffectivewhenT

13、dislargerthana1s(onesixthoftheperiod).Alsonoticethattheperiodofosc川ationincreaseswhenderivativetimeisincreased.ThereismuchmoretoPIDthanisrevealedby().Afaithfulimplementationoftheequationwillactuallynotresultinagoodcontroller.ToobtainagoodPIDcontrolleritisalsonecessarytoconsider。FigureDifferentParame

14、terizations() can be represented by theThePIDalgorithmgivenbyEquationtransferfunction-,1GsK1sTdsKKTTiTiTdTdAninteractingcontrolleroftheformEquationthatcorrespondstoanon-interactingcontrollercanbefoundonlyifTi4TdTheparametersarethengivenbyK21J4TdTiTi1114TJTd十114TdThenon-interactingcontrollergivenbyEq

15、uation()ismoregeneral,andwewillusethatinthefuture.Itis,however,sometimesclaimedthattheinteractingcontrolleriseasiertotunemanually.ItisimportanttokeepinmindthatdifferentcontrollersmayhavedifferentstructureswhenworkingwithPIDcontrollers.Ifacontrollerisreplacedbyanothertypeofcontroller,thecontrollerpar

16、ametersmayhavetobechanged.Theinteractingandthenon-interactingformsdifferonlywhenbothIandtheDpartsofthecontrollerareused.IfweonlyusethecontrollerasaP,PI,orPDcontroller,thetwoformsareequivalent.YetanotherrepresentationofthePIDalgorithmisgivenbyGsk工skdsTheparametersarerelatedtotheparametersofstandardfo

17、rmthroughKkKkikdKTdIiTherepresentationEquation()isequivalenttothestandardform,buttheparametervaluesarequitedifferent.Thismaycausegreatdifficultiesforanyonewhoisnotawareofthedifferences,particularlyifparameter1/kiiscalledintegraltimeandkdderivativetime.Itisevenmoreconfusingifkiiscalledintegrationtime

18、.TheformgivenbyEquation()isoftenusefulinanalyticalcalculationsbecausetheparametersappearlinearly.Therepresentationalsohastheadvantagethatitispossibletoobtainpureproportional,integral,orderivativeactionbyfinitevaluesoftheparameters.PID介紹PID控制器是反饋控制的最常見形式。因?yàn)樵缭?0年代它就成為了過程控制的標(biāo)準(zhǔn)工具。在今天的過程控制業(yè)中,超過95%勺控制回路是P

19、ID類型,多數(shù)實(shí)際上是PI控制。PID控制是分布控制系統(tǒng)的一種重要組成部分??刂破鞅浑[藏在許多其他控制系統(tǒng)下面。PID控制與邏輯控制經(jīng)常結(jié)合在一起,連續(xù)作用、選擇器,和簡(jiǎn)單的功能模塊一起構(gòu)成復(fù)雜自動(dòng)化系統(tǒng),可以應(yīng)用在發(fā)電、運(yùn)輸,以及制造業(yè)。許多經(jīng)典的控制策略,譬如模型有預(yù)測(cè)性的控制。PID控制是使用在要求水平較低的場(chǎng)合;PID控制器應(yīng)用在底層。PID控制器在每個(gè)控制工程師的應(yīng)用實(shí)例里都能經(jīng)常見到。近年來PID控制器在技術(shù)生產(chǎn)上也產(chǎn)生了許多變化,從機(jī)械到微處理器控制由電子管,晶體管,組合電路組成的控制系統(tǒng)。微處理器對(duì)PID控制器有著強(qiáng)烈的影響。實(shí)際上今天制作的所有PID控制器都是建立在微處理器的

20、基礎(chǔ)上的。這就有機(jī)會(huì)擴(kuò)展其他的特點(diǎn):像自動(dòng)定調(diào),獲取預(yù)定,和連續(xù)的適應(yīng)。算法我們開始講解PID控制器的主要特點(diǎn)PID算法的描述:de tT,u是控制信號(hào),e是控制誤差itutKete(0這里y是被測(cè)量的處理可變量,r參考可變量eyspyo參考變量經(jīng)??梢员环Q為是固定的點(diǎn)??刂菩盘?hào)包含三個(gè)量,P-term,I-term,D-term,控制器的參數(shù)包括比例系數(shù)K,整體時(shí)間Ti,和Td。以過去,現(xiàn)在和未來為基礎(chǔ)的控制軌跡可解釋整體,比例項(xiàng)和輸出部份的關(guān)系。圖中舉例。在不同時(shí)間的運(yùn)動(dòng)可以表示輸出部分的一個(gè)典型的例子。在參數(shù)值方面作一下改變,即可預(yù)測(cè)下一時(shí)間的走向問題。PID的作用圖說明的是典型的比例控制。控制器給定Ti=8,Td=0。表示在比例控制中總存在有一種穩(wěn)定狀態(tài)誤差。獲取值增加誤差將減少,但系統(tǒng)穩(wěn)定性將受到影響。圖說明增加積分式的作用。它跟隨圖而來增加時(shí)間Ti.當(dāng)積分式運(yùn)行使用。穩(wěn)定狀態(tài)誤差將逐漸的消失。相比較,說明在圖減少Ti,波動(dòng)繼續(xù)增大。圖舉例說明增加輸出的方法的效果。參數(shù)K和Ti被選定以便閉環(huán)系統(tǒng)是振動(dòng)的。當(dāng)輸出時(shí)間過長(zhǎng)時(shí),導(dǎo)出時(shí)間將被阻值再一次增加,減少也

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