华中科技大学自动控制原理课件Module 19

PhaseLeadCompensation(3hours),MODULE19,Module19-20采用bode图的方法，设计控制器（校正器），使得系统性能满足要求,Generally,asingleperformancerequirementmaybemetbyselectingaparticularvalueofK.,Example19.1Thebodediagramofaminimum-phasesystemisshowninfollowingfigure.DesignKtomakethesystemtobestable.,-60db/decpassthrough0dblineclosed-loopsystemisunstable.,IncreaseK-20db/decpassthrough0dblineclosed-loopsystemisstable.,Multiple-designconstrain：ItisnotpossibletosatisfybothsystemperformancerequirementswithasinglevalueofgainK,Example19.2(P396),ess0.32%fortheunitrampinput.PO%20%.,Solution:,LettingK=316,fromfig.4.17,0.45,PM45,WhenK=316PM0,K=316,ItisnotpossibletosatisfybothsystemperformancerequirementswithasinglevalueofgainK!,K=316,bodediagrams:,WhenPM=45K=6.3,19.1Compensation(校正)andCompensator（校正器）,(P398)TheshapeoftheBodediagramhastobealteredtoallowittoachievebothperformancerequirements.ThisalterationoftheBodediagramisknownassystemcompensation.,为了满足闭环系统多个性能的要求，需要修改开环bode图的形状，这种bode图的改变称之为校正。,(1)Compensation（校正）,(2)Compensator（校正器）,Acompensatorisanadditionalcomponentorcircuitthatisinsertedintoacontrolsystem.,Cascadecompensation,Feedbackcompensation:,加入compensator开环传函为Gc(s)G(s)H(s)Bodediagram形状改变performance改变,20lg|GcGH(j)|=20lg|Gc(j)|+20lg|GH(j)|,Connaturalcharacteristicdeterminedbyplantandsensor,Compensatorcharacteristicdeterminedbydesigner,Desiredcharacteristicdeterminedbyrequirement,GcGH(j)=Gc(j)+GH(j),Changetheshapeofthebodediagram,KeepK=316,modifythephaseangleplot,Method1:,Method2:,KeepK=316,modifythemagnitudeplot,Example19.2,Proportioncompensator;PhaseLeadCompensator;PhaseLagCompensator;PhaseLead-LagCompensator;ProportionalplusIntegralCompensator(PI);ProportionalplusDifferentialCompensator(PD);ProportionalplusIntegralplusDifferentialCompensator(PID);,(3)BasiccompensatorGc(s),(6)DesigncompensatorGc(s),了解GC(s)的作用根据闭环系统性能要求,选择恰当的校正器确定校正器的具体参数,19.2PhaseLeadCompensation(相位超前校正),CircuitTransferfunctionThecharacteristicsDeterminetheparameter,(1)Phaseleadelement(circuit),(2)Transferfunction,通常,希望校正环节的增益为1再串联的放大器,PhaseLead：,(3)Bodediagrams,20db/dec,超前相角,在频率1与2的几何中心线出现最大的超前相角max,过大高频噪声大；限制15max60,(4)TheeffectofthePhaseleadcompensator（超前校正器的作用）,IncreasePMbyaddingphaselead,Example19.2(P396),ess0.32%fortheunitrampinput.PO20.,Solution:,ess=1/K312.5,PO0.45,PM=45,LettingK=316,Letting=0.45,K=316,addingPhaseleadCompensatorm=45,but,PM45,Example19.2(P396),ess0.32%fortheunitrampinput.PO20%.,K=316,幅值为-10lg处定为新的穿越频率c,超前校正器的设计思路：将m放在新的穿越频率c处；,由于m对应的幅值为10lg；,PM=45,Gc(s)provideapositivephaseincreasingPM,Gc(s)provideapositiveslopetoensure-20de/decpassthrough0dbline,校正后addingGc(s)：低频:不变稳态性能不变；中频：PMPO；cTs;稳定性、瞬态性能变；高频：高频噪声衰减能力下降；,Phaseleadcompensationprocess(校正步骤确定，T参数）,Step1:Calculatethemaxofthecompensator；,max=(PMdPM)110%考虑10的裕量,Step2:Calculatetheparameter;,Step3CalculateanotherparameterT,验算：,UncompensatedSystem:,Compensatedsystem:,PMPOcnTs,Stepresponse:,19.3CommentontheApplicabilityandResultsofPhaseLeadCompensation(对超前校正应用和效果的评价）,(1)Lowfrequencyisunchanged稳态性能不变(2)Middle-frequencyslopeischanged(变为-20db/dec)Theovershootisdecreased.(PMPO）Gaincrossoverfrequencycincrease,ortheopen-loopandclosed-loopbandwidthsareincreased.(带宽增大）Fasterresponse,butHigh-frequencynoiseisincreased.(3)IfweneedPM,weneeddoublephaseleadcompensatororotherapproach.,Example19.3(P417),Thesteadystateerrorduetoaunitrampinputoflessthan25%.Aclosed-loopdampingrationofabout0.7.,Solution:,ess=1/Kv25%Kv=K4,=0.7PM70,LettingK=4,max=57,1=1.62,校验：Computer-generatedBodediagram,Theunitstepresponse,%=10%0.7,还需将m再提高些,Transferfunctionofphaseleadcompensator.characteristicsofphaseleadcompensator.howtousethephaseleadcompensator.,conclusion,AttheendofthisModulestudentsshouldbeabletokn