北航自控原理课件5(英文版)

Chapter5Theperformanceoffeedbackcontrolsystems重点掌握：1、一、二阶系统时域性能指标的定义和计算。2、系统稳态误差的计算。1.Typicaltestsignalsforthetimeresponseofcontrolsystems.2.Theunit-stepresponseandtime-domainspecifications.3.Timeresponseoffirst-orderandsecond-ordersystems.4.Improvementperformanceofsecondsystems.5.Thesteady-stateerroroffeedbackcontrolsystem.Maincontents1.Unitimpulsefunction)(t00t0t1)(dtt0t)(t1)}({tLTypicaltestsignalsforthetimeresponseofcontrolsystems.2.Unitstepfunction)(tr)(1t10t0t0)(trt10stL1)}(1{3.Unitrampfunction)(1)(tttrt00t0t21)}(1{sttL)(trt04.Unitparabolicfunction)(121)(2tttr221t00t0tt0)(tr321)}(121{sttLTheunit-stepresponseandtime-domainspecificationsUnit-stepresponse:Theresponseofacontrolsystemwhentheinputisaunit-stepfunction.Time-domainspecifications1.超调量（Percentovershoot）：指响应超出稳态值的最大偏离量与稳态值之比。%%%100maxssssyyy6.稳态误差(steady-stateerror），期望值与稳态值之差，)(lim0ssEesss2.上升时间（risetime）：指单位阶跃响应曲线，从稳态值得10%上升到90%所需要的时间（也有指丛零上升到稳态之所需要的时间）。rt3.调节时间（settlingtime）：在单位阶跃响应曲线的稳态值附近，取（或）作为误差带，响应曲线达到并不在超出该误差带的最小时间。st%5%24.延迟时间(delaytime)td：指响应曲线第一次达到其终值一半所需的时间。5.峰值时间(Peaktime)tp：指响应超过其终值到达第一个峰值所需的时间。Timeresponseofafirst-ordersystem11)(TssTAssumethetransferfunctionofafirst-ordersystemisTheunitstepresponseforthissystem]111[)(1sTsLtctTe11whenTt4Tt632.0)(tc982.0)(tc95.0)(tcTt3ResponseduetounitstepsignalTimeresponseofasecond-ordersystem)2(2sssnn)(sR)(sC2222)(nnnsssTTheunitstepresponseforthissystem]12[)(2221sssLtcnnn)sin(11)(tetcntnnnjs22,11)10(211cosj2222)()(1)(dnndnnsssssC21ndwhere)sin1(cos1)(2ttetcddtnwhen1022,11nnjsunderdampednNaturalundampedfrequencyDampingratiodDampedfrequency21npt%100%21/enrt60.016.2nst5.3nst5.4nst4ns2,1criticallydamped12)(11)(nnnssssCtnnettc)1(1)(nst75.40%0njs2,1undamped)cos(1)(ttcn1122,1nnsoverdamped022,11nnjsnegativelydamped1s2ststsessesstc2111111)(122113stsThesystemisunstable.707.0Improvementperformanceofasecondsystem(1).Velocityfeedbackcontrolofoutput21222122222nnnnnnnsssKssRsCswherentK121nnss22R(s)E(s)k1sC(s)--(2).Theproportion-differentialcontroloferrorsignalnnss22R(s)E(s)1TdsC(s)-22222221121nndndndnndsssTsTsssTsRsCswherenddT21Effectsofthirdpoleandazeroonthesecond-ordersystemresponse)1)(2()(222rssssTnnr1nnr101Theresponseofathird-ordersystemcanbeapproximatedbythesecond-ordersystem.2222))(/()(nnnssasasTTheresponseforthesecond-ordertransferfunctionwithazeroforvaluesoftheratioA=0.5,B=1,C=2andD=5whenna/45.0Thesteady-stateerroroffeedbackcontrolsystem)(sG)(sH)(sB)(sR)(sC)(sEaDefinitionoferror)()()(sBsRsEa)()()(sCsRsEThesteady-stateerrorisdefinedasssEteestss0limlim)()(1)()(sHsGsRsEasetsDssNKsTsTsTssssKsHsGkkkivlklj00222211121whereKOpenloopgain0Type1system12ThenumberofintegrationsiscalledtypenumberofsystemType0systemType2systemsRsKNsDssDsssEesasss000100limlim)(lim10sRKssvvsSteady-stateerrorduetoinputsignal(1).SteadyStateErrorintheStepinputsrsR01,00,10KressKssrsrKssevvsvvsss00010limlim(2).SteadyStateErrorintheslopinput20sVsR2,01,0,0KVessKssVsVKssevvsvvsss1002010limlim(3).SteadyStateErrorintheacceleratorinput30sasR3,02,1,0KaessKssasaKssevvsvvsss2003010limlimErrorconstant)()(1)()(sHsGsRsE)()(1)(lim0sHsGsRsessswhenssR1)()(lim110sHsGesssDefinedpositionerrorconstantKpas)()(lim0sHsGKsPwhen21ssR)()(lim10sHssGesssDefinedvelocityerrorconstantKvas)()(lim0sHssGKsvwhen31ssR)()(lim120sHsGsesssDefinedaccelerationerrorconstantKaas)()(lim20sHsGsKsa系统型别静态误差系数0rtr阶跃输入tvtr0斜坡输入220tatr加速度输入vpKvKaK000000000123KKK0pssKre10Kvess0assKae0Kr10Kv0Ka0Steady-stateerrorduetodisturbancesignalinputK1s1)(sR)(sN)(sC)(1)(1sNKssEWhen,thenssN1)(11KessIfchangeto1K)(1sG)(lim1)(1lim1010sGsGsessssIf,atleasthasoneintegration.0sse)(1sGConclusionThesteady-stateerrorduetodisturbancesignalinputisdecidedbythefrontblockofdisturbancesignalinputpoint.Example124s42s)(sC)(sB)(sRFindthesteady-stateduetoaunitstepinput.Theerrorisdefinedasand.)()()(tctrte)()()(tbtrteExample2)15(1sss8.01)(sC)(sB)(sR5Findthesteady-stateduetotheinput.Theerrorisdefinedas.)()()(tctrte21)(2tttr