浙大电力电子系统建模及控制ch3-DC-DC变换器的电流峰值控制

Chapter3CurrentProgrammedControlConceptofCurrentProgrammedControlCurrentprogrammedcontrolvs.dutycyclecontrol•Simplerdynamics—inductorpoleismovedtohighfrequency•Simplerobustoutputvoltagecontrol,withlargephasemargin•currentlimitingability•Transformersaturationproblemsinbridgeorpush-pullconverterscanbemitigatedAdisadvantage:susceptibilitytonoiseAdvantagesofcurrentprogrammedcontrol:Buckconverter:inductorcurrentslopesInductorcurrentslopes,CCMInductorcurrentslopesm1and–m2buckconverterboostconverterbuck–boostconverterSteady-stateinductorcurrentwaveform,CPMSolveford:Insteadystate:)0()(LSLiTi11Mm22MmDdThenPerturbedinductorcurrentwaveformdˆIsnegativeChangeininductorcurrentperturbationoveroneswitchingperiodSteady-statewaveformPerturbedwaveformACBFromrectangletriangleABCDFromrectangletriangleABDChangeininductorcurrentperturbationovermanyswitchingperiodsForstability:Similarly1'DD11DDExample:unstableoperationforD=0.6Example:stableoperationforD=1/3StabilizationviaadditionofanartificialramptothemeasuredswitchcurrentwaveformNow,transistorswitchesoffwhenSteadystatewaveformswithartificialrampStabilityanalysis:perturbedwaveformSTdˆSTdˆam1m2m)0(ˆLi)(ˆSLTiSimilarlyStabilityanalysis:changeinperturbationovercompleteswitchingperiodsFirstsubinterval:Secondsubinterval:Netchangeoveroneswitchingperiod:Afternswitchingperiods:Characteristicvalue:Thecharacteristicvalueα•Forstability,require|α|1•Buckandbuck-boostconverters:m2=–v/LSoifviswell-regulated,thenm2isalsowell-regulated•Acommonchoice:ma=0.5m2Thisleadstoα=–1atD=1,and|α|1for0=D1.TheminimumαthatleadstostabilityforallD.•Anothercommonchoice:ma=m2.Thisleadstoα=0for0=D1.Deadbeatcontrol,finitesettlingtimeASimpleFirst-OrderModelConverterw/currentprogrammedcontrol?)(ˆ)(ˆ0)(ˆtvcgtitv?)(ˆ)(ˆ0)(ˆtigctvtvInductorcurrent)(tiLequalInductorcurrentfollowsthecommanddynamically)()(titicTsLThefirst-orderapproximation(simpleCPMmodel)•AccuratewhenconverteroperateswellintoCCM(sothatswitchingrippleissmall)andthemagnitudeoftheartificialrampisnottoolarge•Yieldsphysicalinsightandsimplefirst-ordermodelResultingsmall-signalrelation:Ifneglectswitchingrippleandartificialramp)(tiLCCMbuck-boostwithCPMexample)(tic)(tiLSmall-signalmodelofCCMbuck–boostwithdutycyclecontrolTransformationtosplaneTakeLaplacetransform:Solveforthedutycyclevariation:Theinductorequation)(ˆ)(ˆ')(ˆ)(ˆsdVVsvDsvDsisLggLUsefirst-orderapproximationDutycycledependsonciˆgvˆvˆ)(ˆ)(ˆ)(ˆ')(ˆsdIRsvsiDsvsCLLCapacitorvoltageequationinsertVVsvDsvDsisLIRsvsiDsvsCggcLc)(ˆ)(ˆ)(ˆ)(ˆ)(ˆ')(ˆ)(ˆ)(ˆ)(ˆsdIsiDsiLLgOutputequationinsertVVsvDsvDsisLIsiDsiggcLcg)(ˆ')(ˆ)(ˆ)(ˆ)(ˆSmall-signalmodelofCCMbuck–boostwithCPMVVsvDsvDsisLIRsvsiDsvsCggcLc)(ˆ)(ˆ)(ˆ)(ˆ)(ˆ')(ˆVVsvDsvDsisLIsiDsiggcLcg)(ˆ')(ˆ)(ˆ)(ˆ)(ˆ)(ˆ')(ˆ1)(ˆ'')(ˆ2svRDDsvRRDsiDRDsLDsvsCgc)(ˆ')(ˆ)(ˆ')(ˆ2svRDDsvRDsiDRDsLDsigcgCollectterms,simplifyusingsteady-staterelations:1stordersystemThestatevariableiscapacitorvoltageiLisnotstatevariableControlvariableisicandnotdEquivalentcircuit:inputport)(ˆ')(ˆ)(ˆ')(ˆ2svRDDsvRDsiDRDsLDsigcgEquivalentcircuit:outputport)(ˆ')(ˆ1)(ˆ'')(ˆ2svRDDsvRRDsiDRDsLDsvsCgcEquivalentcircuitofCCMbuck–boostwithCPM1stordersystemControlvariableisicandnotd)(ˆticTableCurrentprogrammedmodesmall-signalequivalentcircuitparametersCanonicalModelforbasicconverterswithCPMControltooutputtransferfunctionControl-to-outputtransferfunctionResultforbuck-boostexamplesCRrfsisvsGgvcvc1||||)(ˆ)(ˆ)(220ˆDRCsRDDLsDDRsGvc11'11')(2InputtooutputtransferfunctionResultforbuck-boostexampleLine-to-outputtransferfunctionOutputimpedanceOutputimpedanceResultforbuck-boostexampleAveragedswitchmodelingWiththefirst-orderapproximationAveragedterminalwaveforms,CCM:The1stapproximation:CPMaveragedswitchequationsTsTstvtv)()(d(t)12ssTTtvtdtv)()()(12ssTTtitdti)()()(21Insertd(t),andsssssTcTTTcTtitvtvtitdti)()()()()()(121•Outputportisacurrentsource•InputportisadependentcurrentsourcessssTTcTTtvtitvti)()()()(211PowerconservationforswitchnetworkCPMaveragedswitchmodelTsgtv)(Tsti)(2LTsLti)(Tstv)(CRTstv)(1Tsti)(1Tstv)(2平均开关网络TscTsTstitvtv)()()(12Tscti)(•largesignalmodelsuitedtobothstaticanddynamic•nonlinearPerturbationandlinearizationtoconstructsmall-signalmodelinputportequation:inputportsmallsignalmodel:Outputportsmallsignalmodel:Tsgtv)(Tsti)(2LTsLti)(Tstv)(CRTstv)(1Tsti)(1Tstv)(2平均开关网络TscTsTstitvtv)()()(12Tscti)(ssssTcTTTtitvtvti)()()()(12111112121)(ˆ)(ˆ)(ˆ)(ˆVItvVItvVVtiticcciiˆˆ2EquivalentcircuitofCPMBuckconverterinputportsmallsignalmodel:Outputportsmallsignalmodel:11112121)(ˆ)(ˆ)(ˆ)(ˆVItvVItvVVtiticcciiˆˆ2gvˆLLiˆvˆCRciˆDicˆ2DRRDv2ˆgiˆExpressingtheequivalentcircuitintermsoftheconverterinputandoutputvoltagesvisLvCˆˆˆ2gvˆLLiˆvˆCRciˆDicˆ2DRRDv2ˆgiˆApplyTransferfunctionsoftheCPMbuckconverter0ˆ0ˆ()1R()||()ˆ1()gvccvvsGsRZssCRCsis＝CPMcontrolBuckconverter