數(shù)字芯片相關(guān)課件：Lecture note 4 Digital Control In Power Electronics

DigitalControlInPowerElectronicsOutlineDeadbeatControllerPRControllerRepetitiveControllerPredictiveControllerOutlineDeadbeatControllerPRControllerRepetitiveControllerPredictiveControllerDeadbeatControllerThemainideaofdeadbeatcontrolleristotracktheinputasquickaspossible.ThepossibledelayTwopuredelayunitsarenecessaryPlantdiscretizationDesignD(z)Minimaldelayforis2TsOnethingismissinginthemodelAddonetermtodecouplethedisturbanceincontrol.SimulationSeethesimulationIntroductionofPRcontrollerPRcontrollermeansProportionalResonantcontrollerwhosetransferfunctioniswritteninsdomainasbelow:WhatPRcontrollerisusefor?WeknowthatPIcontrollercanachievezerostaticerrorwhentrackingDCreferencebecauseitcangetinfinitegaintoDCvalue.Soifacontrollergetsinfinitegainatω,thenitwilltracktheACvalueofωwithzerostaticerror.ThisiswhyPRcontrollerisadoptedininverter.

FromtheBodeplot,wecanseeitgetsinfinitegainatresonantfrequency.Butitalsohasphaseinverseatresonantfrequency.SomeotherformofPRcontrollerIntroductionofPRcontroller

Ifnecessary,onecanusethemtwojustbyaddingtherightone’sphasecompensationtotheleftone.Here,wewillintroducethedesignmethodofPRcontrollerwithphasecompensation,andthedesignmethodisawayinfrequencydomainusingNyquistplot.ReviewofNyquistPlotNyquistPlotBodePlotTherightpictureshowtherelationshipbetweenNyquistplotandBodeplot.Infact,NyquistplotcanreflectmoreinformationthanBodeplot.NyquistCriterion:Iftheopen-looptransferfunctionisstable,thecloseloopsystemisstableonlyiftheNyquistplotofopen-loopdonotcirclepoint(-1,0).(Forunitfeedbackandminimumphasesystem)Ingeneral,thefurtherthetrackisapartfrom(-1,0),themorestablethesystemis.

DesignProcedureParametersList2kW2mH30uF25Ω380V220V(RMS),50Hz10kHz0.20.01Again,wewillusethisexampletointroducethedesignprocedureindetails.

TopologyofInverterThemainstepsareshowedasbelow:1)DesigntheKpwithoutresonantpart.2)Designphasecompensationθ.3)DesignKIusingroot-locusmethod.First,designthecurrentloop.

NyquistPlotDesignProcedure1)DesignKpSincethedistancetopoint(-1,0)canrepresentthestability,anddistancedreducewithincreasingKp.Soifwechooseaproperd,thenKpwillbeobtained.DesignprocedureofKpisshowedhere.DesignprocedureofKp2)DesignθPhasecompensationisimportant,thephaseangleneededtoaddisnotaccordingtothesystem’sdelay,itisstillaccordingtotheprincipletomakewholesystemstable.Addarbitraryphasecompensationwillgetresultasshowedinleftside.Lineofdashedmeansinfinitegainatresonantfrequency.DesignProcedure2)DesignθTomakethesystemmorestable,wewanttheasymptote(greenline)isverticaltothepoint(-1,0),whichmeansthedistanceto(-1,0)willnotinfluencethedesignedoneinstepone.Thus,wecangetthewaytocalculatetheangle.G(s)meanstheopen-loopwithoutresonantpartThus,theanglecanbeobtained.Hereitisnotobvioustoseetheinfluenceofphasecompensation,butwhenapplyingtohighresonantfrequency,itwillbereallyimportant.Thisexample,wechoosed=0.8,andtheresultisDesignProcedureFromtheformofPRcontroller,thelastparameterisKI,sinceithasonlyoneunknownparameter,wecanfindthebestonebyroot-locusmethod.Usingpointdepictionmethod,wecandrawthesystem’sroot-locusasshowedintherightside.Seedetails,wewillfindthatthedominantrootswouldfirstgetmorestableandthenlessstablewithincreasingKISo,herewechooseasshowedinthepicture,whereKIis350.Tothisend,alltheParametersareobtained.Itseemsahardwaytocalculatealltheparameters,butusingmatlabwillmakeallworklesshard.DesignProcedureThelaststepistodiscretizeparametersinsdomaintozdomain.Unlikecommonuseddiscretizingmethod,werecommendpre-modifiedTustinmethodwhosetransformationislistedbelow:Thismethodisveryusefulespeciallywhenωislargeωheremeansresonantfrequency.DesignofExternalVoltageLoopNyquistplotwithoutPRcontrollerisshowedasbelow.DesignProcedureisthesameascurrentloop,parameterscanbeobtained.SimulationResultsHeregivessomesimulationresultsgotbymatlab\simulink.Simulationwaves.(a)isthesteadywaveoffullload(b)isthesteadywaveofnon-load(Redlinevrefmeansthevoltagereferencewhileblacklinevomeanstheoutputvoltage)(a)(b)Fromthesimulationresult,wecanseeithasverysmallstaticerror.Butatthesametime,thedynamicresponseisnotsoperfect.Inaword,theparametersdesignprocedurehasbeendone.Simulationwave.FromfullloadtoNon-loadRepetitivecontrollerThemainideaofrepetitivecontrolleristoeliminatetheperiodicalerrorbyusingintegrators.DCsystemDCsystemDecomposedIntegratorcanbeemployedtoeliminateDCerrorIntegratorHerethedelayisNsamplingpointsFordigitalsystem,theintegratorisintheboundaryofstableregionUsuallyrepetitivecontrollerhaslowdynamicresponse.IntroductionofRepetitiveControllerWhat’srepetitivecontroller?Theconceptofrepetitivecontroloriginatesfromtheinternalmodelcontrolprinciple,thegoalofitistomakethecontrolledsystemoutputtrackasetofpredefinedreferenceinputswithoutsteady-stateerror.Thedigitalimplementationofarepetitivecontrolleronlyrequiresthesetupofasuitablysizeddelaylineandofapositivefeedbackloop.GeneralimplementationoftherepetitivecontrollerTransferfunctionFrequencydomainTsissampletimeFromthetransferfunctioninfrequencydomain,wecanseethatitwillgetinfinitegainwhenWherekisintegerIntroductionofRepetitiveControllerTherearealsosomeotherstructuresforrepetitivecontroller,whicharewidelyusedinpracticalengineeringproject.Inthisstructure,addingfilterF1(z)inthepositivefeedbackpathandfilterF2(z)intheforwardpath,aimstolimittheamplificationofhigh-orderharmonics.Lherecanincreasethesystemphasemarginbutnottochangethegain.ThisstructureistheoreticallyequivalenttotheaboveonewhenF2(z)=1.Inaword,repetitivecontrollerisaimedtogetinfinitegainatpredefinedfrequencytorealizezerosteady-stateerror.IntroductionofRepetitiveControllerAlso,tomakesatisfactorytransientperformance,therepetitivecontrollerismoretypicallyemployedinparallelconnectionwithaconventionalregulator.ProportionalcontrollerparalleledtorepetitivecontrollerTodesignarepetitivecontroller,therearefourstepstodo:1)determineKP2)determineparameterM,3)determineparameterL,4)determineKREP5)determinestructureF1(z).Still,usethisexampletointroducethedesignprocedureindetails.Thestructureofcontrolleristheoneshowedinthefigurewhichincludesproportionalcontrollerandrepetitivecontroller.TopologyofInverterDesignProcedureStill,weneedtodesigncurrentloopandvoltageloop.CurrentLoopTosimplifytheprocedure,thecurrentcontrollerwillbeusedjustaproportionalKP,whereKPis0.8asdesignedbefore.Next,wewillintroducedesignprocedureofrepetitivecontrollerinVoltageloop.VoltageLoopinzdomainFirst,modelingtheloopinzdomainsincerepetitivecontrollerareexpressedinzdomain.ThemethodwewilluseisBodeplotinfrequencydomain.Stepone:DetermineKpWhendesigningKp,justignorerepetitivepart,andthedesignprocedureisassameaswhatindesigningPIcontroller.DesignProcedureFromtheBodeplotofopenvoltageloopwithoutcontroller,crossoverfrequencycanbeobtained,thendetermineanewcrossoverfrequency,soKPwillbeobtained.Here,crossoverfrequencyis400HzandKPis1.5.Steptwo:DetermineMAsaforementionedreasons,togetinfinitegain,Mshouldmeettheconditionshowedintherightside.SoMis400.Thus,itcangetinfinitegainwhenfrequencyis50Hzandharmonics.Here,someexplainneededtosay,afteraddingfilterF1(z)inthepositivefeedbackpath,thegainwouldchange.DesignProcedureStepthree:DetermineLInthisstructure,ifonewanttoincreasesystem’sphasemargin,hecandefineLbiggerthanM.Ifnot,justletLbeequaltoM.Here,sincethesamplingfrequencyishighcomparedtothecrossoverfrequency,justletL=M.Stepfour:DetermineKREPWhendesigningKREP,weneedacarefulconsiderationoftheopenloopgain.Justasshowedinthefigure,KREPwillinfluencethegain.Here,wejustsetKREPas1.Butonecanchangeitifnecessary.Inthisfigure,itcanalsobeseenthatthephasemarginisverysmallandthegainisreallybiginhighfrequency.Sotolimittheamplificationofhigh-orderharmonics,weneedtoaddafilterinthefeedbackpath.DesignProcedureFromthetransferfunction,wemayknowthataddaproperF1(z)canlimitthegainofrepetitivecontrollerbymakingdenominatornotbeequaltozero.Stepfive:DeterminestructureofF1(z)Tolimithigh-orderharmonics,oneeasywayistoaddlow-passfilter.ItcanalsouseamovingaveragefilterNismovingtapsHere,weadoptalow-passfilterwhoseparametersinsdomainareasbelow:TheBodeplothasbeenshowedintherightside,wecanseethatthegaininhighfrequencyislimited.DesignProcedureStepfive:DeterminestructureofF1(z)ThereisalsoadisadvantageofF1(z).Fromtheexpression,wecanseethatfrequencyofinfinitegaindifferfrompredefinedoneafteraddingfilter.Thereasonisthatlow-passfilteritselfhasdelayeffect.Usingamovingaveragefilterisbettercomparedtolow-passfilter,butitstillhastheproblem.Afterall,thedesignprocedurehasbeendone.Bodeplotisshowedintherightside.Itcomparesthetwosystem(oneonlyusesproportionalcontroller,theotherusesproportionalandrepetitivecontroller).SimulationResultsHeregivessomesimulationresultsgotbymatlab\simulink.Simulationwaves.(a)isthesteadywaveoffullload(b)isthesteadywaveofnon-load(Redlinevrefmeansthevoltagereferencewhileblacklinevomeanstheoutputvoltage)Fromthesimulationresultintherightside,wecanseethatthesettlingtimeisquitelong,usuallyaboutseveralfundamentalperiod.Itisdifficulttoimprovethissignificantly.Simulationwave.FromfullloadtoNon-loadExampleCircuitspecifications:Full-bridgetopologyOutputtransformerisolationFullydigitalcontrolMultipleloopfeedbackstrategyTheproblemwithabovecontrolschemeStageA:Reference>OutputvoltageStageB:Outputvoltage>ReferenceProblems:StageBistheovershootofthesystem.Bothtwostagesdeterioratetheperformanceseverely,especiallystageB.Thestructureoftheproposedcontroller

Objectives:Conventionalcontrollerfordynamicresponse.Repetitivecontrollerfordealingwithperiodicdisturbances.RepetitivecontrollerAnalysisofthehybridcontrolsystem

(1)(2)SystemStableconditions:(1)(2)Therootsofarelocatedinsidetheunitcircle.Analysisofdisturbancerejectingability:periodicdisturbanceinput.

:trackingerror

isstable(1)(2)(3)Experimentspecifications:Filterinductance0.3mHInductorESR0.1ΩCapacitorESR0.05ΩFiltercapacitor20uFDCinputvoltage220VReferencevoltage220Vrms50HzSamplingfrequency20KHzSwitchingfrequency10KHzSamplingperiod50usRatedoutputpower2KWModulationmodeDoublePWM

PWMINVERTERPARAMETERS

ParameterDescriptionsymbolValueProportionandintegralOfvoltageloopcontrollerKp0.3Ki3120ProportionofcurrentcontrollerKpi1.5VoltageFeedbackCoefficientKa59.2CurrentFeedbackCoefficientKb140.2ModulationratioKpwm0.02PARAMETERSOFTHECONTROLSYSTEMCharacteristicsofconventionalopenlooptransferfunctionOpenloopbodediagramofthesystemwithouttherepetitivecontrol

RepetitivecontroldesignEXPERIMENTALRESULTS

Experimentalresultsofdynamicresponseofconventionalcontrolfora100%stepchangesintheload.OutputVoltageandcurrentwaveformunderRCDrectifierloadwithconventionalcontrol.ThecorrespondingspectrumwithTHD=5.4%

ConventionalController(1)(2)(3)Proposedcontroldynamicresponseoftheproposedcontrolfora100%stepchangesintheresistiveload.OutputVoltageandcurrentwaveformunderRCDrectifierloadOutputvoltageandoutput