PID中英文对照翻译Word文档下载推荐.docx

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ThePIDcontrollercanthusbesaidtobethe“breadandbutterofcontrolengineering.Itisanimportantcomponentineverycontrolengineer’stoolbox。

PIDcontrollershavesurvivedmanychangesintechnology，frommechanicsandpneumaticstomicroprocessorsviaelectronictubes，transistors,integratedcircuits.ThemicroprocessorhashadadramaticinfluencethePIDcontroller。

PracticallyallPIDcontrollersmadetodayarebasedonmicroprocessors。

Thishasgivenopportunitiestoprovideadditionalfeatureslikeautomatictuning,gainscheduling,andcontinuousadaptation.

6。

2TheAlgorithm

WewillstartbysummarizingthekeyfeaturesofthePIDcontroller。

The“textbook”versionofthePIDalgorithmisdescribedby：

6.1

whereyisthemeasuredprocessvariable，rthereferencevariable，uisthecontrolsignalandeisthecontrolerror（e=

−y）.Thereferencevariableisoftencalledthesetpoint。

Thecontrolsignalisthusasumofthreeterms：

theP—term（whichisproportionaltotheerror），theI-term（whichisproportionaltotheintegraloftheerror），andtheD—term（whichisproportionaltothederivativeoftheerror）.ThecontrollerparametersareproportionalgainK，integraltimeTi,andderivativetimeTd。

Theintegral，proportionalandderivativepartcanbeinterpretedascontrolactionsbasedonthepast，thepresentandthefutureasisillustratedinFigure2.2。

ThederivativepartcanalsobeinterpretedaspredictionbylinearextrapolationasisillustratedinFigure2.2.Theactionofthedifferenttermscanbeillustratedbythefollowingfigureswhichshowtheresponsetostepchangesinthereferencevalueinatypicalcase。

EffectsofProportional，IntegralandDerivativeAction

ProportionalcontrolisillustratedinFigure6。

1.ThecontrollerisgivenbyD6。

1EwithTi=

andTd=0。

Thefigureshowsthatthereisalwaysasteadystateerrorinproportionalcontrol。

Theerrorwilldecreasewithincreasinggain,butthetendencytowardsoscillationwillalsoincrease.

Figure6.2illustratestheeffectsofaddingintegral.ItfollowsfromD6.1EthatthestrengthofintegralactionincreaseswithdecreasingintegraltimeTi。

Thefigureshowsthatthesteadystateerrordisappearswhenintegralactionisused。

Comparewiththediscussionofthe“magicofintegralaction"

inSection2.2。

ThetendencyforoscillationalsoincreaseswithdecreasingTi.ThepropertiesofderivativeactionareillustratedinFigure6。

3.

Figure6。

3illustratestheeffectsofaddingderivativeaction.TheparametersKandTiarechosensothattheclosedloopsystemisoscillatory。

Dampingincreaseswithincreasingderivativetime，butdecreasesagainwhenderivativetimebecomestoolarge。

RecallthatderivativeactioncanbeinterpretedasprovidingpredictionbylinearextrapolationoverthetimeTd。

UsingthisinterpretationitiseasytounderstandthatderivativeactiondoesnothelpifthepredictiontimeTdistoolarge.InFigure6。

3theperiodofoscillationisabout6sforthesystemwithoutderivativeChapter6。

PIDControl

1

2

DerivativeactionsceasetobeeffectivewhenTdislargerthana1s（onesixthoftheperiod）.Alsonoticethattheperiodofoscillationincreaseswhenderivativetimeisincreased.

APerspective

ThereismuchmoretoPIDthanisrevealedby（6.1）。

Afaithfulimplementationoftheequationwillactuallynotresultinagoodcontroller。

ToobtainagoodPIDcontrolleritisalsonecessarytoconsider。

Figure6.3

∙Noisefilteringandhighfrequencyrolloff

∙Setpointweightingand2DOF

∙Windup

∙Tuning

∙Computerimplementation

InthecaseofthePIDcontrollertheseissuesemergedorganicallyasthetechnologydevelopedbuttheyareactuallyimportantintheimplementationofallcontrollers。

Manyofthesequestionsarecloselyrelatedtofundamentalpropertiesoffeedback,someofthemhavebeendiscussedearlierinthebook。

6.3FilteringandSetPointWeighting

Differentiationisalwayssensitivetonoise。

ThisisclearlyseenfromthetransferfunctionG（s）=sofadifferentiatorwhichgoestoinfinityforlarges。

Thefollowingexampleisalsoilluminating。

wherethenoiseissinusoidalnoisewithfrequencyw。

Thederivativeofthesignalis

Thesignaltonoiseratiofortheoriginalsignalis1/anbutthesignaltonoiseratioofthedifferentiatedsignalisw/an.Thisratiocanbearbitrarilyhighifwislarge。

Inapracticalcontrollerwithderivativeactionitistherefornecessarytolimitthehighfrequencygainofthederivativeterm.Thiscanbedonebyimplementingthederivativetermas

6.2

insteadofD=sTdY。

Theapproximationgivenby（6。

2）canbeinterpretedastheidealderivativesTdfilteredbyafirst—ordersystemwiththetimeconstantTd/N。

Theapproximationactsasaderivativeforlow—frequencysignalcomponents。

Thegain,however，islimitedtoKN。

Thismeansthathigh-frequencymeasurementnoiseisamplifiedatmostbyafactorKN.TypicalvaluesofNare8to20。

Furtherlimitationofthehigh-frequencygain

ThetransferfunctionfrommeasurementytocontrolleroutputuofaPIDcontrollerwiththeapproximatederivativeis

Thiscontrollerhasconstantgain

athighfrequencies。

ItfollowsfromthediscussiononrobustnessagainstprocessvariationsinSection5。

5thatitishighlydesirabletorolloffthecontrollergainathighfrequencies。

Thiscanbeachievedbyadditional

lowpassfilteringofthecontrolsignalby

whereTfisthefiltertimeconstantandnistheorderofthefilter.ThechoiceofTfisacompromisebetweenfilteringcapacityandperformance。

ThevalueofTfcanbecoupledtothecontrollertimeconstantsinthesamewayasforthederivativefilterabove。

Ifthederivativetimeisused，Tf=Td/Nisasuitablechoice。

IfthecontrollerisonlyPI,Tf=Ti/Nmaybesuitable。

Thecontrollercanalsobeimplementedas

6。

3

ThisstructurehastheadvantagethatwecandevelopthedesignmethodsforanidealPIDcontrolleranduseaniterativedesignprocedure。

ThecontrollerisfirstdesignedfortheprocessP（s）。

ThedesigngivesthecontrollerparameterTd.AnidealcontrollerfortheprocessP（s）/（1+sTd/N）2isthendesignedgivinganewvalueofTdetc。

Suchaprocedurewillalsogiveaclearpictureofthetradeoffbetweenperformanceandfiltering。

SetPointWeighting

Whenusingthecontrollawgivenby（6.1）itfollowsthatastepchangeinthereferencesignalwillresultinanimpulseinthecontrolsignal。

Thisisoftenhighlyundesirablethereforderivativeactionisfrequentlynotappliedtothereferencesignal.Thisproblemcanbeavoidedbyfilteringthereferencevaluebeforefeedingittothecontroller。

Anotherpossibilityistoletproportionalactionactonlyonpartofthereferencesignal。

Thisiscalledsetpointweighting。

APIDcontrollergivenby（6。

1）thenbecomes

4

wherebandcareadditionalparameter。

Theintegraltermmustbebasedonerrorfeedbacktoensurethedesiredsteadystate。

ThecontrollergivenbyD6。

4Ehasastructurewithtwodegreesoffreedombecausethesignalpathfromytouisdifferentfromthatfromrtou。

Thetransferfunctionfromrtouis

6.5

Timet

4Responsetoastepinthereferenceforsystemswithdifferentsetpointweightsb=0dashed,b=0.5fullandb=1.0dashdotted。

TheprocesshasthetransferfunctionP（s）=1/（s+1）3andthecontrollerparametersarek=3,ki=1.5andkd=1.5。

andthetransferfunctionfromytouis

6

Setpointweightingisthusaspecialcaseofcontrollershavingtwodegreesoffreedom.

Thesystemobtainedwiththecontroller（6.4）respondtoloaddisturbancesandmeasurementnoiseinthesamewayasthecontroller（6.1）。

Theresponsetoreferencevaluescanbemodifiedbytheparametersbandc。

ThisisillustratedinFigure6。

4,whichshowstheresponseofaPIDcontrollertoset—pointchanges，loaddisturbances,andmeasurementerrorsfordifferentvaluesofb。

Thefigureshowsclearlytheeffectofchangingb。

Theovershootforset-pointchangesissmallestforb=0,whichisthecasewherethereferenceisonlyintroducedintheintegralterm，andincreaseswithincreasingb。

Theparametercisnormallyzerotoavoidlargetransientsinthecontrolsignalduetosuddenchangesintheset—point.

4DifferentParameterizations

ThePIDalgorithmgivenbyEquation（6。

1）canberepresentedbythetransferfunction

6.7

8

9

AninteractingcontrolleroftheformEquationD6。

8Ethatcorrespondstoanon—interactingcontrollercanbefoundonlyif

Theparametersarethengivenby

10

Thenon—interactingcontrollergivenbyEq