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1、ControlLoopCookbookLloydH.DixonINTRODUCTION:KEA(S)ErroramplifierwithcompensationSwitchingpowersuppliesuseclosed-loopKMODPulsewidthmodulatorfeedbacktoachievedesignobjectivesforlineandloadregulationanddynamicresponse.KpWRPowerswitchingtopologyFortunately,theclo
2、sed-loopsystemsusedinKLC(S)Outputpowerfilterswitchingpowersuppliesareusuallynotverycom-plicated,permittingtheuseofsimpleanalyticalKFBFeedbacktechniquestoachieveloopstabilization.Asimpli-AlthoughthepulsewidthmodulatorandpowerfiedversionoftheNyquiststabilitycri
3、teriacanbeswitchingcircuitarereallynotlinearelements,theirusedbecauseunitygaincrossoveroccursonlystate-spaceaveragedlinearequivalentscanonceinthegainvs.frequencycharacteristic.Bodebeusedatfrequenciesbelowtheswitchingplotsprovideasimpleandpowerfulmethodofdis-f
4、requency,fS.playingandcalculatingtheloopgainparametersOpen-Ioopandclosed-loopgain:(seeAppendixB).ThispaperbeginswithaquickTheopen-loopgain,T,isdefinedasthetotalreviewofbasiccontrollooptheory.gainaroundtheentirefeedbackloop(whethertheLinearControlLoopTheoryloo
5、pisactuallyopen,forpurposeofmeasurement,AsshowninFigure1,apowersupplyfeedbackorclosed,innormaloperation).loopcanbedescribedintermsofsmall-signallin-T(s)=KEA.KMOD.KpWR.KLC.KFB(1)earequivalentgainblocks.The(s)appendedtocertaingainblocksindicatesthatthegainvarie
6、sasClosed-loopgain,G,definestheoutputvs.afunctionoffrequency.controlinputrelationship,withtheloopclosed:VINO~KpWR~KLCi.0OUTPUTKMOD~"-'g~NTROLREFERENCEI~FigureFeedbackLoopG5-1ControlLoopCookbookT"Gain"elementsasshowninFigure1neednotG(s)=~(2)KFB"=i=""Thavethesa
7、meunitsfortheiroutputandinput(suchasVoltsNolt).IfFig.1isacurrentmodecon-Atlowfrequencies,open-loopgainTisnor-trolloop,"Output"isacurrentsource,andKFBismallyverymuchgreaterthan1,sothatclosed-loopmostlikelyacurrentsenseresistor.KFB"gain"isgainGapproachestheidea
8、l1/KFB.Athigherfre-thenexpressedinVolts/Amp,andclosedloopgainquencies,Tdiminishes,mostlybecauseoftheG(s)isactuallyatransconductance(AmpsNolt).low-passfiltercharacteristicKLC(S)-Thefrequen
