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1,Chap6TheCompensationofthelinearcontrolsystems,P553,2,Chap6TheCompensationofthelinearcontrolsystems,3,6.1Introduction,6.1.1Whatiscompensationorcorrectionofacontrolsystem?,solution,4,Thisclosed-loopsystemcanbestable.,Wemakethesystemstablebyincreasingacomponent.,6.1Introduction,Thisprocedureiscalledthecompensationorcorrection.,Definitionofthecompensation:,increasingacomponent,whichmakesthesystemsperformancetobeimproved,otherthanonlyvaryingthesystemsparameters,thisprocedureiscalledthecompensationorcorrectionofthesystem.,5,Compensator:Thecompensatorisanadditionalcomponentorcircuitthatisinsertedintoacontrolsystemtocompensateforadeficientperformance.,6.1Introduction,6.1.2Typesofthecompensation,6,(1)Cascade(orseries)compensation(2)Feedbackcompensation(3)Bothseriesandfeedbackcompensation(4)Feed-forwardcompensation,(1)Cascade(orseries)compensation,Features:simplebuttheeffectstoberestricted.,6.1Introduction,7,(2)Feedbackcompensation,Features:complicatedbutnoiselimiting,theeffectsaremorethanthecascadecompensation.,(3)Bothcascadeandfeedbackcompensation,Features:haveadvantagesbothofcascadeandfeedbackcompensation.,6.1Introduction,8,(4)Feed-forwardcompensation,Features:theoreticallywecanmaketheerrorofasystemtobezeroandnoeffectstothetransientperformanceofthesystem.,6.1Introduction,Demonstration:,9,6.1Introduction,Butnoeffecttothecharacteristicequation:1+G10G20=0,Question:actuallythecouldnotbeeasyimplementedespeciallymaybetheG20isvariable.,10,6.1Introduction,Alsonoeffecttothecharacteristicequation:1+G10G20=0,Question:actuallythecouldnotbeeasyimplementedespeciallymaybetheG20isvariable.AndtheF(s)couldnotbeeasymeasured.,11,example,6.1Introduction,ForthesystemshowninFig.6.1.7:,Solution:,Thinking:ifr(t)=n(t)=t,DetermineGCRandGCN,makeesstobezeroasaexercise.,12,6.2Operationanalysisofthebasiccompensators,6.2.1ActiveCompensation,PIDcontrolleractive“compensator”.,Transferfunction:,13,PDcontroller,14,EffectsofPDcontroller:,2)PDcontrollerimprovethesystemsstability(toincreasedampingandreducemaximumovershoot);,3)PDcontrollerreducetherisetimeandsettlingtime;,4)PDcontrollerincreaseBW(BandWidth)andimproveGM(Kg),PM(c),andMr.,1)PDcontrollerdoesnotalterthesystemtype;,6.2Operationanalysisofthebasiccompensators,bringinthenoise!,15,PIcontroller,6.2Operationanalysisofthebasiccompensators,16,EffectsofPIcontroller:,1)Increasethesystemstypeclearthesteady-stateerror;,2)reduceBW(BandWidth)andGM(Kg),PM(c)andMr;,6.2Operationanalysisofthebasiccompensators,beneficialtothenoiselimiting,notbeneficialtothesystemsstability.,17,PIDcontroller,6.2Operationanalysisofthebasiccompensators,Transferfunction:,PIDcontrollerhaveadvantagesbothofPIandPD.,18,CircuitsofPID,19,Forexample:,Diskdrivercontrolsystem,20,solution,Howtoget?Shownin6.3detail.,21,6.2.2Passivecompensationcontrollers,Typesofpassivecompensationcontroller,22,Zeroandpole,6.2.2Passivecompensationcontrollers,23,EffectsaresimilartoPD.,Compensationideal:makemtobec!,24,Circuitofthephase-leadcontroller,25,Zeroandpole,6.2.2Passivecompensationcontrollers,26,EffectsaresimilartoPI.,Compensationideal:Make1/tobeinthelowerfrequency-bandandfarfromc!,27,CircuitofthePhase-lagcontroller,28,6.2.2Passivecompensationcontrollers,29,EffectsaresimilartoPID.,Compensationideal:Firstmakethephase-lagcompensationtosatisfyessandcompensateapartofc.secondmakethephase-leadcompensationtosatisfythetransitionalrequirements.,30,CircuitofthePhaselag-leadcontroller,31,6.2.3Comparingactivecompensationcontrollersandpassivecompensationcontrollers,6.2Operationanalysisofthebasiccompensators,32,6.3CascadecompensationbyRootlocimethod,6.3.1Phase-leadcompensation(P569),Example6.3.1:,TherootlociofthesystemshowninFig.6.3.1,solution,Analysis:unstable.phase-leadcompensation,33,6.3CascadecompensationbyRootlocimethod,34,6.3CascadecompensationbyRootlocimethod,Therearetwoapproachestodeterminezcandpc.,35,6.3CascadecompensationbyRootlocimethod,ForthisexamplewechoosetheMaximummethod:,Intermsofthesineslaw:,36,Rootlocusofthecompenstedsystem,6.3CascadecompensationbyRootlocimethod,TherootlocusofthecompensatedsystemisshowninFig.6.3.4,Fig.6.3.4,Stepsofthecascadephase-leadCompensation:,(1)Determinethedominantrootsbasedontheperformancespecificationsofthesystem:,(2)plottherootlocusofthesystemandanalyzewhatcompensationdeviceshouldbeapplied.,37,6.3CascadecompensationbyRootlocimethod,(3)Determinetheanglectobecompensated:,(4)calculateand:,(6)plottherootlocusofthecompensatedsystemandmakevaliditycheck.,38,Example6.3.2:,Solution:,TherootlocusofthesystemisshowninFig.6.3.5.,6.3.2Phase-lagcompensationusingtherootlocus(P577),39,6.3.2Phase-lagcompensationusingtherootlocus(P577),Fig6.3.6,Thedetailoftheroot-lociisshowninFig6.3.6.,40,Fig6.3.6,6.3.2Phase-lagcompensationusingtherootlocus(P577),41,Validate,6.3.2Phase-lagcompensationusingtherootlocus(P577),Stepsofthecascadephase-lagCompensation:,(1)Determinethedominantrootsbasedontheperformancespecificationsofthesystem:,(2)plottherootlocusofthesystemandanalyzewhatcompensationdeviceshouldbeapplied.,Ifthephase-lagCompensationbeapplied:,42,6.3.2Phase-lagcompensationusingtherootlocus(P577),(5)plottherootlocusofthecompensatedsystemandmakevaliditycheck.,6.3.3Phaselag-leadcompensationbytherootlocusmethod,Basicideal:,43,First:makethephase-leadcompensationtosatisfythetransitionalrequirements.Second:makethephase-lagcompensationtosatisfyessrequirements.,MakecompensationusingPDandPIforexample6.3.1andexample6.3.2,Exercise:,6.3.3Phaselag-leadcompensationbytherootlocusmethod,44,6.4.1Phase-LeadCompensationusingBodediagram,6.4Cascadecompensationbyfrequencyresponsemethod,45,6.4Cascadecompensationbyfrequencyresponsemethod,46,6.4Cascadecompensationbyfrequencyresponsemethod,47,Example:,6.4Cascadecompensationbyfrequencyresponsemethod,solution:,48,6.4Cascadecompensationbyfrequencyresponsemethod,Makevaliditycheckforthisexample.2.MakecompensationusingPDforthisexample.,Exercise:,49,6.4.2Phase-LagCompensationusingBodediagram,Example:,solution:,Fig.6.4.2,50,6.4.2Phase-LagCompensationusingBodediagram,Validate,Fig.6.4.2,51,6.4.2Phase-LagCompensationusingBodediagram,1.Makevaliditycheckforthisexample.2.Makephase-lagcompensationforc=50oandKv=20.,Stepsofthephase-lagcompensation:,Exercise:,52,6.4.4Compensationaccordingtothedesiredfrequencyresponse,Example,solution,First:makethephase-lagcompensationtosatisfyessandcompensateapartofc.Second:makethephase-leadcompensationtosatisfytherequirementscandcetc.,6.4.3Phase-Lag-leadCompensationusingBodediagram,Fig.6.4.3,53,6.4.4Compensationaccordingtothedesiredfrequency
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