IEEE TRANSACTIONS ON POWER ELECTRONICS VOL - PDF document

IEEETRANSACTIONSONPOWERELECTRONICS,VOL.18,NO.1,JANUARY2003PredictiveDigitalCurrentProgrammedControlJingquanChen,Member,IEEE,AleksandarProdic,StudentMember,IEEE,RobertW.Erickson,Fellow,IEEEandDraganMaksimovic,Member,IEEEThispaperexplorespredictivedigitalcurrentpro-grammedcontrolforvalley,peakoraveragecurrent.Thecontrollawsarederivedforthethreebasicconverters:buck,boost,andbuck–boost.Itisfoundthatforeachvariableofinterest(valley, IEEETRANSACTIONSONPOWERELECTRONICS,VOL.18,NO.1,JANUARY2003Inthispaper,anaccuratepredictivedigitalcontroltechniqueisproposedbasedoninductorcurrentwaveformpredictedbysampledinputandoutputvoltageandinductorcurrentinforma-tion.Inadditiontothepredictivevalleycontrol,wealsoconsiderrealizationofapredictivepeakcurrentandapredictiveaveragecurrentcontroltechniqueinthreebasicconverters,includingtheboost,thebuck,andthebuck–boostconverters.Theproposeddigitalcontroltechniquescanbeusedinarangeofpowercon-versionapplications,includingrectifierswithpowerfactorcor-rectionanddc–dcapplicationswithcurrentmodecontrol.Itisfoundthatthe“period-doubling”oscillationissues,whicharewellknowninanalogcurrentprogrammedcontrol[1]–[4],alsoexistindigitalpredictivecurrentcontrollers.Weshowhowtheoscillationproblemcanbeeliminatedbyproperlyselectingthemodulationmethodaccordingtothecontrolobjective(valley,peak,oraveragecurrent).Thepaperisorganizedasfollows.Predictivecurrentcon-trolunderthemostcommonlyusedtrailingedgepulse-widthmodulationisfirstintroducedfortheboostconverterinSec-tionII,followedbyananalysisoftheoscillationproblemsinaverageandpeakcurrentcontrol.Thecorrelationsbetweendif-ferentpulse-widthmodulationmethodsandcurrentcontrolob-jectivesarethenidentifiedinSectionIII.RobustnessanddesignconsiderationsarediscussedinSectionIV.Derivationofthepre-dictivecontrollawforothernonisolatedconvertersisgiveninSectionV.Finally,inSectionVI,thepredictiveaveragecurrentcontrollerisimplementedandexperimentallyverifiedinaboostPFCrectifier,andhighperformanceisdemonstratedunderstrictrequirementsforavionicsapplications.II.PROGRAMMEDONTROLODULATIONInthissection,threepredictivecurrentprogrammedcontroltechniquesarediscussed:valleycurrentcontrol,peakcurrentcontrol,andaveragecurrentcontrol.Thecommonlyusedtrailing-edgepulse-widthmodulationmethodillustratedinFig.2isassumed.Thepulsatingswitchcontrolsignal isproducedbycomparingthecontrolvariable withatrailingedgesaw-toothsignal .Underthismodulation,thetransistorswitchisturnedonatthebeginningofeachswitchingcycle,andturnedoffaftertime ,where istheswitchdutyratio.Theswitchthenstaysofffortheremainderoftheswitchingcycle.Allthreeconsideredcurrentcontroltechniquesarebasedonthesameapproachofusingthesampledinductorcurrentand(possibly)inputandoutputvoltagestocomputethedutyratiointhenextswitchingcyclesothattheerrorbetweenthecurrent andthetargetcontrolvariable(thevalley,thepeak,ortheaveragecurrent)isreducedtozero.Thesamplingofthecurrentoccursatequallyspacedintervalsequaltotheswitching .Withoutlossofgenerality,weassumethatthesample isobtainedbysamplingtheinductorcurrent atthebeginningofthe thswitchingperiod.Inallderivationsinthissection,theboostconverterisusedasanexample.TheresultsandconclusionsareextendedtootherbasicconverterconfigurationsinSectionV. Fig.1.Digitallycontrolledconverteremployinganoutervoltageandaninnercurrentloop. Fig.2.Trailingedgemodulation.A.PredictiveValleyCurrentControlThegoaloftheproposedcontrolmethodistoensurethatthevalleyinductorcurrentfollowsthereference .Therequireddutycycleforthenextswitchingperiodispredictedbasedonthesampledcurrentandpossiblytheinputandtheoutputvoltage.TheresultinginductorcurrentwaveformisshowninFig.3.Sincetheinputandtheoutputvoltageareslowlyvaryingsig-nals,theycanbeconsideredconstantduringaswitchingperiod.Thesampledinductorcurrent attime canbefoundasafunctionoftheprevioussampledvalue andtheap-plieddutyratio ,providedthattheinputvoltage,theoutputvoltage,theinductanceandtheswitchingperiodareknown Weusethenotation .Bycollectingterms,(1)canberewrittenas (2) etal.:PREDICTIVEDIGITALCURRENTPROGRAMMEDCONTROL Fig.3.InductorcurrentwaveformintheboostconverterundervalleycurrentWecanthenextend(2)foranotherswitchingcycletoobtain Thepredictionforthedutycycle cannowbeobtainedbasedonthevaluessampledinthepreviousswitchingperiod.Denotingthesampledcurrentas [ ],andsubstitutingthecon-trolobjective in(3),wehave Equation(4)canbesolvedforthepredicteddutycycle Equation(5)givesthebasiccontrollawforthepredictivecur-rentprogrammedcontrol.StabilitypropertiesofthepredictivevalleycurrentcontrolundertrailingedgemodulationcanbeexaminedwithreferencetothewaveformsofFig.4.Thesolidlineshowsthecurrentwaveforminsteadystate,whilethedashedlineshowsthecur-rentwithaperturbation atthebeginningoftheswitching .Sincetheeffectsofthepredicteddutycycle cannotbeobserveduntilthenextswitchingperiod,thispertur-bationappearsatthebeginningofthe thcycle.Withthenextdutyratio computedaccordingto(5),thevalleycurrentreachesthereference bytheendofthe switchingperiod.Theinitiallyassumedperturbationdisappears.Asaresult,forthepredictivevalleycontrolundertrailingedgemodulation,thecurrentcontrollerisinherentlystableforallop-eratingpoints.B.PredictivePeakCurrentControlPeakcurrentcontrol,whichamongotheradvantagesfeaturesinstantaneouspeakcurrentprotection,isthemostpopularcur-rentprogrammedcontrolmethodinanalogimplementationsfordc–dcapplications.Inthissection,weexaminepropertiesofthepredictivepeakcurrentcontrolundertrailingedgemodulation. Fig.4.Valleycurrentcontrolundertrailingedgemodulation. Fig.5.Peakcurrentcontrolundertrailingedgemodulation.Fig.5showstheinductorcurrentwaveformswherethesolidlinecorrespondstothesteadystateoperation,whilethedashedlineshowsthecurrentwithaperturbation atthebeginningoftheswitchingperiod .Inthiscase,thecontrolobjectiveisthatthepeakcurrentfollowsthereference .AsshowninFig.5,thenextdutyratio iscomputedsothatthepeakcurrentin thcycleequalsthereferencevalue .Ourobjectiveistofindhowtheperturbation propagatesunderthiscontrollaw.Fortheboostconverterincontinuousconductionmode(CCM),thesteady-statedutycycle andthesteady-statepeak aregivenby (6)and (7)where isthesteady-statevalleycurrent.AsshowninFig.5,assumethattheperturbation intheinductorcurrenthasbeendetectedbysamplingtheinductorcurrentintheswitching .Again,thisperturbationwillpropagatetothebegin-ningofthe thswitchingperiod.Takingintoaccountthisperturbation,thenewdutycyclecanbepredictedusingthefollowingrelationship: (8) IEEETRANSACTIONSONPOWERELECTRONICS,VOL.18,NO.1,JANUARY2003Using(6)and(7),thepredicteddutycyclecanbewrittenas Uponapplicationofthisdutycycle,thecurrentattheendofthe thswitchingcyclebecomes Therefore,thecurrentperturbationattheendofthe periodisgivenby Equation(11)showsthatoscillationsoccurundertheoperatingconditionswhenthedutycycleisgreaterthan0.5.Thisisex-actlythesameasinanalogcurrent-programmedcontrol,wheretheinstabilityisusuallysuppressedbyaddingaslope-compen-sationrampsignaltothesensedcurrentsignal[2].C.PredictiveAveCurrentControlInsomeapplications,theaveragecurrentcontrolispreferredcomparedtovalleyorpeakcurrentcontrol.Inparticular,inPFCapplications,theanalogaveragecurrentcontrolresultsinverylowcurrentdistortionwithouttheneedforanyadditionalInpredictiveaveragecurrentcontrol,thenewdutycycleiscomputedsothattheaveragecurrent inthenextswitchingcycleequalsthereference .Theaveragecurrentin thswitchingcyclecanbewrittenintermsofthevalleycurrentandtheapplieddutycycle Basedon(12),andassumingthesteady-stateandperturbedwaveformsasshowninFig.6,thepredicteddutycyclecanbefoundfrom Insteadystate,wehave Subtracting(14)from(13)yields Ifwedefine ,(15)canbesimplifiedas (16) Fig.6.Averagecurrentcontrolundertrailingedgemodulation.Byneglectingthesecondorderterm,weobtain Using(17),wecanfindthepredicteddutycycleintermsoftheperturbationandsteady-statevalues Theinductorcurrentattheendofthe thswitchingcycleisthenfoundas Finally,theperturbedcurrentattheendofthe thperiodisgivenby Weconcludethatundertrailingedgemodulationthepredictiveaveragecurrentcontrolhasthesameinstabilityproblemundertheoperatingconditionswhenthedutycycleisgreaterthan0.5.III.SELECTIONOFTHEODULATIONETHODINORRELATIONITHTHEONTROLInSectionII,wefoundthatundertrailingedgemodulationonlythepredictivevalleycurrentcontrolcanbeachievedwithout“period-doubling”oscillationsforalloperatingcondi-tions.Adistinctionbetweenthevalleycurrentcontrolandtheothertwocontrolobjectives(peakoraveragecurrent)isthatintrailingedgemodulationthetargetedcontrolvariable(thevalleycurrent)canalwaysbesampledatthebeginningoftheswitchingperiod,i.e.,atequallyspacedintervalsequaltotheswitchingperiod .Thisisnotthecaseforpeakoraveragecurrentcontrol.Forexample,undertrailingedgemodulation,thepeakcurrentoccursat ,i.e.,atvariabletimeinstantsduringaswitchingperiod.Asaresult,eventhoughthecon-trollermayachievetheobjectiveofforcingthepeakcurrenttofollowthereference,aperturbationinthecurrentwaveformcangrowintime,causingundesirableoscillations. etal.:PREDICTIVEDIGITALCURRENTPROGRAMMEDCONTROL Fig.7.Leadingedgemodulation.Akeypointineliminatingthestabilityproblemistoenablesamplingofthetargetedvariableofinterest(valley,peakorav-eragecurrent)atequallyspacedintervalsequaltotheswitchingperiod.Inthissection,weshowhowthiscanbeaccomplishedbyselectingthemodulationmethodincorrelationwiththetar-getedcontrolobjective.A.PredictivePeakCurrentControlUsingLeadingEdgeTheleadingedgemodulationisillustratedbythewaveformsofFig.7.Thepulsating,switchcontrolsignalisgeneratedbycomparingthecontrolvariablewithaleadingsaw-toothsignal.Atthebeginningofaswitchingperiod,thetransistorswitchisturnedoff,andthenturnedonat .Theswitchremainsonuntiltheendoftheperiod.Thepeakcurrentoccursatthebe-ginningofeachswitchingperiod,andcanthereforebesampledatequallyspacedintervalsequalto .FollowingthesamestepsasinSectionII-A,onefindsthatthepredictivepeakcurrentcon-trolunderleadingedgemodulationfollowsthelaw[givenby(5)]asthevalleycurrentcontrolundertrailingedgemod-ulation.ThewaveformsofFig.8illustratethepointthataper-turbationdisappearswithinaswitchingperiodandthereforethepredictivepeakcurrentcontrolunderleadingedgemodulationisinherentlystable.B.PredictiveAveCurrentControlUsingDualEdge(Triangle)ModulationThedualedge,ortrianglemodulation,isfoundtobesuitableforachievingpredictiveaveragecurrentcontrolwithoutoscil-lationproblems.Thismodulationcanbedefinedastrailing,il-lustratedbythewaveformsofFig.9,orasleading,asshowninFig.10.Inthecaseofthetrailingtrianglemodulation,thetransistorswitchisonatthebeginningofaswitchingcycle,itisturnedoffat andthenturnedonagainat .Inthecaseoftheleadingtrianglemodulation,thetransistorswitchisoffatthebeginningofaswitchingcycle.Bothtrianglemod-ulationmethodsaresuitableforthepredictiveaveragecurrent Fig.8.Peakcurrentcontrolunderleadingedgemodulation. Fig.9.Trailingtrianglemodulation.control.Weagainfindthatthesamecontrollawgivenby(5)appliesinthiscase.TheinductorcurrentwaveformillustratingoperationofthepredictiveaveragecurrentcontrolundertrailingtrianglemodulationisshowninFig.11.Thispredictiveaveragecurrentcontroldoesnothaveoscillationproblems.C.SummaryofPredictiveCurrentControlandModulationTableIsummarizesthecorrelationbetweendifferentmodu-lationmethodsandthecontrolledvariablesofinterest.Itcanbeobservedthatforeachvariableofinterest(valley,peakorav-eragecurrent)thereisachoiceoftheappropriatemodulationmethodtoachievepredictivedigitalcontrolwithoutoscillationproblems.Furthermore,thepredictivecontrollaw[givenby(5)]appliesto:1)valleycurrentcontrolundertrailingedgemodulation;2)peakcurrentcontrolunderleadingedgemodulation;3)averagecurrentcontrolundertrianglemodulation. IEEETRANSACTIONSONPOWERELECTRONICS,VOL.18,NO.1,JANUARY2003 Fig.10.Leadingtrianglemodulation. Fig.11.Averagecurrentcontrolundertrianglemodulation.TABLEIORRELATIONODULATIONONTROL.“PSCILLATIONSCCURFORTHENDICATEDANGEOFATIOSENOTESSCILLATIONFORTHEANGEOFATIO IV.ROBUSTNESSANDONSIDERATIONSItcanbeseenfromthecontrollawin(5)thatthepredic-tivecontroldependsontheassumptionsthattheinductance,theswitchingperiodandtheoutputvoltageareknown.Inpractice,theswitchingperiod isusuallydeterminedbytheDSPormicroprocessorsystem’sclockanditsvariationscanbeconsideredrelativelyinsignificant.However,thevalueoftheinductancemayhavesignificantinitialtolerancesandmayfurtherbeaffectedbychangesintemperature,operatingconditionsoraging.Theoutputvoltagevaluecanbeobtainedbysampling,whichisusuallydoneforthepurposeofclosingavoltagefeedbackloop.However,theoutputvoltageappearsinthedenominator,whichcomplicatescomputationofthepredicteddutycycle,especiallyinfixed-pointDSP/micropro-cessorsystemssuitableforpowercontrolapplications.Inthissection,wediscusshowtolerancesintheinductance(orpe-riod),andtheapproachofapproximatingtheoutputvoltageusingaconstantvalueaffectthecontrolperformance.Supposethattheconverterisoperatinginsteadystateandthatthecontrolledcurrenthasperturbation atthebeginningoftheswitchingperiod .Takingintoaccountthedifference betweentherealinductancevalueandtheassumedvalue,theerror betweenthepredicteddutycycleandthesteady-statevaluecanbefoundfrom(5) Thiserrorinthepredicteddutycyclecausestheerror ofthecurrentvalueattheendofthe thswitchingperiod Asshownby(22),theerrordecreasesandthecontrolperfor-manceisnotsignificantlyaffectedbytheinductancetolerancesaslongas ,whichisnotdifficulttomeet.Asimilarresultisobtainedfortolerancesintheswitchingperiod.Insteadofusingthereal-timesampledoutputvoltagevalue,weconsiderapproximatingtheoutputvoltagewiththeconstantreferencevalue toavoidthedivisionandtosimplifythecon-trollaw.Supposethatthereisanerror betweentheactualoutputvoltageandthereference.From(5),theresultingerror inthedutycycleisgivenby Asaresult,thecontrolledcurrentwillhaveanerror attheendofthenextswitchingperiod Equation(24)hastwoportions.Thefirsttermofthecurrenterrorisduetothecurrentperturbation,andwillgetsmallerprovidedthattheoutputvoltageerrorsatisfies .Thesecondtermisintroducedbythevoltageerrorandwillhaveaneffectofsettlingtheinductorcurrentinanewsteadystatewithanoffset awayfromthereference.Theoffseterror beobtainedfrom(24)bysetting Forapowerconverterwithwell-regulatedoutputvoltage, isverysmallandinmostcasestheoffseterrorcanbeignored.Weconcludethatitisreasonabletousethe(constant)outputvoltagereferenceinsteadofthesampledoutputvoltagetosimplifythecomputationinthepredictivecurrentcontroller. etal.:PREDICTIVEDIGITALCURRENTPROGRAMMEDCONTROLV.EXTENSIONSOFTHEIGITALROGRAMMEDONTROLTOONVERTERSBasicprinciplesofpredictiveprogrammedcontrolcanbeeasilyextendedtootherbasicconverters,i.e.,thebuckconverterandthebuck–boostconverter.Fig.12showsthegenericCCMinductorcurrentwaveformforswitchingconvertersunderthetrailingedgemodulation.Inthesubintervalwhenthetransistorison,theinductorcurrentincreaseswithaslope ,andthendecreaseswithaslope duringthesubintervalwhenthetransistorisoff.Forthebasicnonisolatedconverters,theslopesaregiveninTableII.Thepredictivecontrollawcanbeexpressedasafunctionoftheslopes , ,theswitchingperiod,andthedutyratiointhepreviouscycleas Byusingtheexpressionsfor and fromTableII,weob-tainthepredictivecontrollawforthebuckconverter andforthebuck–boostconverter Thestabilityconditionsimilarto(11)and(20)canbewrittenmoregenerallyas Thecondition(29)isvalidforallbasicconverters.Insteady-state,theinductorvolt-secondbalanceimplies (30)or Equations(30)and(31)showthatthestabilityconditionundercertainmodulationmethodisthesameforallbasicnonisolatedconvertersincontinuousconductionmode.Moreover,thecor-relationbetweenthemodulationmethodandthecurrentcontrolobjective,andtherobustnessconditions,whichwerediscussedinSectionsIIIandIVfortheboostconverter,applytoallbasicnonisolatedconverters.VI.EXPERIMENTALESULTSTodemonstrateperformanceofthepredictivecurrentcon-trol,a100Wsingle-phaseexperimentalPFCboostconverter(asshowninFig.1)wasdesignedandtestedforavionicsapplica-tions,whichhavemoredemandingspecifications,includingthelineinputfrequencyof400to800Hz,andlowtotalharmonicdistortion(THD)oflessthan10%[17],[18].Thepredictivecur-rentcontrolandtheoutputvoltageregulationarerealizedusing Fig.12.Genericinductorcurrentwaveformundervalleycurrentcontrol.TABLEIILOPEOFTHENDUCTORAVEFORMINONVERTERS theAnalogDevicesADMC-401DSPsystem[19],whichhasbuilt-indigitalPWM,A/Dconverters,anda16-bitfixed-pointcomputationalunit.Theinputinductanceis1mH,theoutputcapacitanceis47 F,andtheoutputdcvoltageisregulatedat190V.Thetwo-loopsystemasshowninFig.1wasimplemented.Theinputcurrentandtheinputvoltagearesampledattheswitchingfrequency(100KHzor200KHz)toensurethehighperformanceofthecurrentloopbasedonthepredictiveaveragecurrentcontrolundertrianglemodulation.TheoutputvoltageloopusesaslowPIregulatorthatprovidesavoltage-loopbandwidthofaboutonethirdofthelineinputfrequency[20].Theoutputvoltageissampledatafrequencyof4KHz,whichissufficienttoimplementfunctionsoftheslowoutputvoltageloopwhileatthesametimebeingrelativelyeasytorealizeusingfixed-pointarithmetic.Figs.13and14showtherectifiedinputvoltage(115Vrms)andtheinputcurrentwaveformsattheswitchingfrequencyof200KHzand100KHz,respectively.Thiscomparisonshowsthattheperformanceofthecurrentcontrolloopdoesn’trelyheavilyonveryhighswitchingfrequency.THDoflessthan2.5%isachievedunderallconditions,evenwhentheinputlinefrequencyis800Hzwithaswitchingfrequencyof100KHz.VII.CThispaperdescribespredictivedigitalcurrentprogrammedcontrolmethods.Ineachswitchingcycle,basedonthesampledvalueofthecurrent,thedutyratiointhepreviouscycle,and(possibly)thesamplesoftheinputand/ortheoutputvoltage,theswitchdutyratiointhenextswitchingcycleiscomputedto IEEETRANSACTIONSONPOWERELECTRONICS,VOL.18,NO.1,JANUARY2003 Fig.13.Rectifiedinputvoltage(top,100V/div),andtheinputcurrent(bottom,1A/div)at200KHzswitchingfrequency,800Hzlinefrequency,THDis2.2%. Fig.14.Rectifiedinputvoltage(top,100V/div),andtheinputcurrent(bottom,1A/div)at100KHzswitchingfrequency,800Hzlinefrequency,THDis2.4%.nulltheerrorbetweentheactualcurrentandthereference.Theimplementationrequiresonlyonecurrentsampleperperiodandhasrelativelymodestprocessingrequirements.Thepredictivedigitalcurrentprogrammedcontrollawisderivedforallbasicconverterconfigurationsandforthreedifferentcontrolvariablesofinterests:valley,peakoraveragecurrent.Itisfoundthatforeachvariableofinterest(valley,peakoraveragecurrent)thereisachoiceoftheappropriatemodulationmethodtoachievepredictivedigitalcurrentcontrolwithout“period-doubling”oscillationproblems.Itisalsoshownthatthepredictivecontrollawisthesameforthecontroltechniquewheretheoscillationproblemiseliminated:1)valleycurrentcontrolundertrailingedgemodulation;2)peakcurrentcontrolunderleadingedgemodulation;3)averagecurrentcontrolunderdual-edge(triangle)mod-Theproposeddigitalcontroltechniquescanbeusedinarangeofpowerconversionapplications,includingdc–dcconvertersandrectifierswithpowerfactorcorrection(PFC).Aprototypeofa100WPFCboostrectifierswitchingat100KHzor200KHzhasbeenconstructedusingaDSPsystemtoimplementthepre-dictiveaveragecurrentcontrolandaPIvoltageloopcontrol.VerylowTHD( 2.5%)oftheinputcurrentandhighperfor-mancethatmeetsrigorousavionicsrequirements(400–800Hzlinefrequency)havebeenexperimentallydemonstrated.[1]C.Deisch,“Simpleswitchingcontrolmethodchangespowerconverterintoacurrentsource,”inProc.IEEEPESC’78Conf.,1978,pp.300–306.[2]S.S.Hsu,A.Brown,L.Rensink,andR.D.Middlebrook,“Modelingandanalysisofswitchingdc-to-dcconvertersinconstant-frequencycurrentprogrammedmode,”inProc.IEEEPESC’79Conf.,1979,pp.284–301.[3]F.C.LeeandR.A.Carter,“Investigationsofstabilityanddynamicper-formancesofswitchingregulatorsemployingcurrent-injectedcontrol,”Proc.IEEEPESC’82Conf.,1982,pp.3–16.[4]R.RedlandN.O.Sokal,“Current-modecontrol,fivedifferenttypes,usedwiththethreebasicclassesofpowerconverters:Small-signalacandlarge-signaldccharacterization,stabilityrequirements,andimple-mentationofpracticalcircuits,”inProc.IEEEPESC’85Conf.,1985,pp.771–785.[5]R.RedlandB.Erisman,“Reducingdistortioninpeak-current-controlledboostpowerfactorcorrectors,”inProc.IEEEAPEC’94Conf.,1994,pp.[6]D.Maksimovic,“Designoftheclamped-currenthigh-power-factorboostrectifier,”inProc.IEEEAPEC’94Conf.,1994,pp.584–590.[7]J.LaiandD.Chen,“Designconsiderationforpowerfactorcorrectionboostconverteroperatingattheboundaryofcontinuousconductionmodeanddiscontinuousconductionmode,”inProc.IEEEAPEC’93Conf.,1993,pp.267–273.[8]J.Chen,R.Erickson,andD.Maksimovic,“Averagedswitchmodelingofboundaryconductionmodedc-to-dcconverters,”inProc.IEEEIECON’01Conf.,2001,pp.844–849.[9]L.Dixon,“Averagecurrentmodecontrolofswitchingpowersupplies,”Proc.UnitrodePowerSupplyDesignSem.,1990.[10]A.H.Mitwalli,S.B.Leeb,G.C.Verghese,andV.J.Thottuvelil,“Anadaptivedigitalcontrollerforaunitypowerfactorconverter,”Trans.PowerElectron.,vol.11,pp.374–382,Mar.1996.[11]S.Buso,P.Mattavelli,L.Rossetto,andG.Spiazzi,“Simpledigitalcon-verterimprovingdynamicperformanceofpowerfactorpreregulators,”IEEETrans.PowerElectron.,vol.13,pp.814–823,Sept.1998.[12]A.Prodic,J.Chen,D.Maksimovic,andR.W.Erickson,“Digitallycon-trolledlow-harmonicrectifierhavingfastdynamicresponses,”inProc.IEEEAPEC’02Conf.,2002,pp.476–482.[13]R.Wu,S.B.Dewan,andG.R.Slemon,“AnalysisofaPWMactodcvoltagesourceconverterunderthepredictedcurrentcontrolwithafixedswitchingfrequency,”IEEETrans.Ind.Applicat.,vol.27,no.4,pp.756–764,July/Aug.1991.[14]T.Kawabata,T.Miyashita,andY.Yamamoto,“DeadbeatcontrolofthreephasePWMinverter,”IEEETrans.PowerElectron.,vol.5,pp.21–28,Jan.1990.[15]S.BibianandH.Jin,“Highperformancepredictivedead-beatdigitalcontrollerfordcpowersupplies,”inProc.IEEEAPEC’01Conf.,2001,pp.67–73. ,“Digitalcontrolwithimprovedperformancesforboostpowerfactorcorrectioncircuits,”inProc.IEEEAPEC’01Conf.,2001,pp.[17]I.Moir,“More-electricaircraft-systemconsiderations,”inProc.IEEColloq.Elect.Mach.,Syst.,MoreElect.,Aircraft,1999,pp.10/1–10/9.[18]P.Athalye,D.Maksimovic,andR.Erickson,“High-performancefront-endconverterforavionicsapplications,”inProc.PowerConv.Intell.MotionConf.,Sept.2001.[19]AnalogDevicesInc.,“ADMC-401single-chip,DSP-basedhighperfor-mancemotorcontroller,rev.B,”,2000.[20]R.Erickson,M.Madigan,andS.Singer,“Designofasimplehighpowerfactorrectifierbasedontheflybackconverter,”inProc.IEEEAPEC’90Conf.,1990,pp.792–801. JingquanChen(S’01–M’02)receivedtheB.S.degreeinelectricalengineeringfromTsinghuaUniversity,Beijing,China,in1995,theM.S.degreeinpowerelectronicsfromChineseAcademyofSciences,Beijing,China,in1998,andthePh.D.degreeinelectricalengineeringfromtheUniversityofColoradoatBoulderin2002.HeiscurrentlyaSeniorMemberoftheResearchStaffatPhilipsResearch,BriarcliffManor,NY.Hisresearchinterestsincludesynthesis,modeling,anddigitalcontrolofswitchingpowerconverters,powerfactorcorrectiontechniques,andlightingelectronics. etal.:PREDICTIVEDIGITALCURRENTPROGRAMMEDCONTROL AleksandarProdic(S’00)wasborninNoviSad,Yugoslavia,onJuly19,1970.HereceivedtheDipl.Ing.degreeinelectricalengineeringfromtheUniversityofNoviSadin1994andtheM.S.degreefromtheUniversityofColoradoinBoulderin2000whereheiscurrentlypursuingPh.D.degreeinelectricalengineering.SinceSeptember1999,hehasbeenaResearchAssistantintheColoradoPowerElectronicsCenter(CoPEC),UniversityofColoradoatBoulder.Hisresearchinterestsareindigitalcontrolofswitchingpowerconverters,includingmodeling,design,simulation,andmixed-signalVLSIand/orDSPimplementation. RobertW.Erickson(F’00)receivedtheB.S.,M.S.,andPh.D.degreesinelectricalengineeringfromtheCaliforniaInstituteofTechnology,Pasadena,in1978,1980,and1982,respectively.Since1982,hehasbeenamemberofthefacultyofelectricalandcomputerengineeringattheUniversityofColorado,Boulder,whereheiscurrentlyProfessorandChairman.TheColoradoPowerElectronicsCenterishelpingtheindustryinlow-harmonicrectifiers,dc–dcconvertersforbattery-poweredsystems,andmagneticsmodelingformultiple-outputconverters.HeistheauthorofthetextbookofPowerElectronics(2ndedition).Heistheauthorofapproximately60journalandconferencepapersintheareaofpowerelectronics.Dr.EricksonreceivedtheIEEEPowerElectronicsSocietyTransactionsPrizePaperAwardin1996. DraganMaksimovic(M’89)receivedtheB.S.andM.S.degreesinelectricalengineeringfromtheUniversityofBelgrade,Yugoslavia,andthePh.D.degreefromtheCaliforniaInstituteofTechnology,Pasadena,in1984,1986,and1989,respectively.From1989to1992,hewaswiththeUniversityofBelgrade,Yugoslavia.Since1992hehasbeenwiththeDepartmentofElectricalandComputerEngineering,UniversityofColorado,Boulder,whereheiscurrentlyanAssociateProfessorandCo-DirectoroftheColoradoPowerElectronicsCenter(CoPEC).Hiscurrentresearchinterestsincludesimulationandcontroltechniques,mixed-signalintegrated-circuitdesignforpowermanagementapplications,andpowerelectronicsforlow-power,portablesystems.Dr.MaksimovicreceivedNSFCAREERAward,in1997,andaPowerElec-tronicsSocietyTransactionsPrizePaperAward.