搜索
5-1DesigningStableControlLoopsByDanMitchellandBobMammanoABSTRACTTheobjectiveofthistopicistoprovidethedesignerwithapracticalreviewofloopcompensationtechniquesappliedtoswitchingpowersupplyfeedbackcontrol.Atop-downsystemapproachistakenstartingwithbasicfeedbackcontrolconceptsandleadingtostep-by-stepdesignprocedures,initiallyappliedtoasimplebuckregulatorandthenexpandedtoothertopologiesandcontrolalgorithms.SampledesignsaredemonstratedwithMathcadsimulationstoillustrategainandphasemarginsandtheirimpactonperformanceanalysis.I.INTRODUCTIONInsuringstabilityofaproposedpowersupplysolutionisoftenoneofthemorechallengingaspectsofthedesignprocess.Nothingismoredisconcertingthantohaveyourlovinglycraftedbreadboardbreakintowildoscillationsjustasitisbeingdemonstratedtothebossorcustomer,butinsuringagainstthisunfortunateeventtakessomeanalysiswhichmanydesignersviewasformidable.Pathstakenbydesignengineersoftenemphasizeeithercut-and-tryempiricaltestinginthelaboratoryorcomputersimulationslookingfornumericalsolutionsbasedoncomplexmathematicalmodels.Whilebothoftheseapproacheshaveaplaceincircuitdesign,abasicunderstandingoffeedbacktheorywillusuallyallowthedefinitionofanacceptablecompensationnetworkwithaminimumofcomputationaleffort.II.STABILITYDEFINEDFig.1givesaquickillustrationofatleastonedefinitionofstability.Initssimplestterms,asystemisstableif,whensubjectedtoaperturbationfromsomesource,itsresponsetothatperturbationeventuallydiesout.Notethatinanypracticalsystem,instabilitycannotresultinacompletelyunboundedresponseasthesystemwilleitherreachasaturationlevel–orfail.Oscillationinaswitchingregulatorcan,atmost,varythedutycyclebetweenzeroand100%andwhilethatmaynotpreventfailure,itwillultimatelimittheresponseofanunstablesystem.PerturbationPerturbationStableSystemUnstableSystemttResponseResponseFig.1.Definitionofstability.AnotherwayofvisualizingstabilityisshowninFig.2.Whilethisgraphicallyillustratestheconceptofsystemstability,italsopointsoutthatwemustmakeafurtherdistinctionbetweenlarge-signalandsmall-signalstability.Whilesmall-signalstabilityisanimportantandnecessarycriterion,asystemcouldsatisfythisrequirementandyetstillbecomeunstablewithalarge-signalperturbation.Itisimportantthatdesignersrememberthatallthegainandphasecalculationswemightperformareonlytoinsuresmall-signalstability.Thesecalculationsarebasedupon–andonlyapplicableto-linearsystems,andaswitchingregulatoris–bydefinition–anon-linearsystem.Wesolvethisconundrumbyperformingouranalysisusingsmall-signalperturbationsaroundalarge-signaloperatingpoint,adistinctionwhichwillbefurtherclarifiedinourdesignprocedurediscussion.5-2UnconditionallyStableUnstableSmall-SignalStableLarge-SignalUnstableFig.2.Large-signalvs.small-signalstability.III.FEEDBACKCONTROLPRINCIPLESThebasicregulatorisshowninFig.3whereanuncontrolledsourceofvoltage(orcurrent,orpower)isappliedtotheinputofoursystemwiththeexpectationthatthevoltage(orcurrent,orpower)attheoutputwillbeverywellcontrolled.Thebasisofourcontrolissomeformofreference,andanydeviationbetweentheoutputandthereferencebecomesanerror.Inafeedback-controlledsystem,negativefeedbackisusedtoreducethiserrortoanacceptablevalue–asclosetozeroaswewanttospendtheefforttoachieve.Typically,however,wealsowanttoreducetheerrorquickly,butinherentwithfeedbackcontrolisthetradeoffbetweensystemresponseandsystemstability.Themoreresponsivethefeedbacknetworkis,thegreaterbecomestheriskofinstability.OutputFeedforwardFeedbackSystemInputReferenceFig.3.Thebasicregulator.Atthispointweshouldalsomentionthatthereisanothermethodofcontrol–feedforward.Withfeedforwardcontrol,acontrolsignalisdevelopeddirectlyinresponsetoaninputvariationorperturbation.Feedforwardislessaccuratethanfeedbacksinceoutputsensingisnotinvolved,however,thereisnodelaywaitingforanoutputerrorsignaltobedeveloped,andfeedforwardcontrolcannotcauseinstability.Itshouldbeclearthatfeedforwardcontrolwilltypicallynotbeadequateastheonlycontrolmethodforavoltageregulator,butitisoftenusedtogetherwithfeedbacktoimprovearegulator’sresponsetodynamicinputvariations.ThebasisforfeedbackcontrolisillustratedwiththeflowdiagramofFig.4wherethegoalisfortheoutputtofollowthereferencepredictablyandfortheeffectsofexternalperturbations,suchasinputvoltagevariations,tobereducedtotolerablelevelsattheoutput.GHuy+_NegativeFeedbackReferenceOutputInputsGH1GuyGuGH)1y(GHyGuy+==+−=Fig.4.Flowgraphoffeedbackcontrol.Withoutfeedback,thereference-to-outputtransferfunctiony/uisequaltoG,andwecanexpresstheoutputasGuy=Withtheadditionoffeedback(actuallythesubtractionofthefeedbacksignal)yHGGuy−=andthereference-to-outputtransferfunctionbecomesGH1Guy+=Ifweassumethat1GH,thentheoveralltransferfunctionsimplifiestoH1uy=5-3NotonlyisthisresultnowindependentofG,itisalsoindependentofalltheparametersofthesystemwhichmightimpactG(supplyvoltage,temperature,componenttolerances,etc.)andisdeterminedinsteadsolelybythefeedbacknetworkH(and,ofcourse,bythereference).NotethattheaccuracyofH(usuallyresistortolerances)andinthesummingcircuit(erroramplifieroffsetvoltage)willstillcontributetoanoutputerror.Inpracti