4__敏感性分析简介.ppt

1 Chapter4FeedbackControlSystemCharacteristics Themaintopicofchapter4istointroducethedefinitionsofopen andclosed loopcontrolsystemandtodiscussthesensitivityofasystemtoaparameterchange 系统的敏感性 系统参数变化对系统性能的影响 2 4 1Open andClosed Loopcontrolsystem Fig4 1Anopen loopsystem Anopen loop direct systemoperateswithoutfeedbackanddirectlygeneratestheoutputinresponsetoaninputsignal 3 Fig4 2Anclosed loopsystem Anclosed loopsystemusesameasurementoftheoutputsignalandacomparisonwiththedesiredoutputtogenerateanerrorsignalthatisappliedtotheactuator 4 反馈控制利用偏差信号来激励系统 Where denotestheerrorsignal wehave Solvingfor Theerrorsignalis Itisclearthat toreducetheerror themagnitudeofmustbegreaterthanoneovertherangeofsunderconsideration 5 4 2Sensitivityofcontrolsystemstoparametervariations Aprocess representedbythetransferfunction whateveritsnature issubjecttoachangingenvironment aging ignoranceoftheexactvaluesoftheprocessparameters andothernaturalfactorsthataffectacontrolprocess Intheopen loopsystem alltheseerrorsandchangesresultinachangingandinaccurateoutput However aclosed loopsystemsensesthechangeintheoutputduetotheprocesschangesandattemptstocorrecttheoutput Soaprimaryadvantageofaclosed loopfeedbackcontrolsystemisitsabilitytoreducethesystem ssensitivity 闭环系统的作用就是减少系统的敏感性 6 Fortheclosed loopcase ifGH s 1forallcomplexfrequenciesofinterest wecanobtain IfH s 1 wehavethedesiredresult thatis theoutputisequaltotheinput Therefore thefirstadvantageofafeedbacksystemisthattheeffectofthevariationoftheparametersoftheprocess G s isreduced 直接消除G s 的变化对控制效果的影响 7 Thesystemsensitivityisdefinedastheratioofthepercentagechangeinthesystemtransferfunctiontothepercentagechangeoftheprocesstransferfunction orparameters forasmallincrementalchange Letthesystemtransferfunctionbe andthereforethesensitivityisdefinedas 系统传函变化百分比 被控过程传函变化的百分比 8 Inthelimit forsmallincrementalchanges Sbecomes Clearly thesensitivityoftheopen loopsystemisequalto1Andthesensitivityoftheclosed loopisreadilyobtained Again thesensitivityofthesystemmaybereducedbelowthatoftheopen loopsystembyincreasingGH s 9 ThesensitivityofthefeedbacksystemtochangesinthefeedbackelementH s is WhenGHislarge thesensitivityapproachesunity andthechangesinH s directlyaffecttheoutputresponse Therefore itisimportanttousefeedbackcomponentsthatwillnotvarywithenvironmentalchangesorthatcanbemaintainedconstant 测量环节抗干扰性强 10 Thesensitivityofthefeedbacksystemtochangesinaparameteris Example4 1Anamplifierusedinmanyapplicationshasagain Ka andthefeedbackelementH s 11 Theclosed looptransferfunctionofthefeedbackamplifieris Thesensitivityoftheclosed loopfeedbackamplifieris IfKaislarge thesensitivityislow Forexample if wehave Orthemagnitudeisone thousandthofthemagnitudeoftheopen loopamplifier 12 Thisexampleillustratesthattheopen loopsystemismuchmoresensitivetoparametervariationthantheclosed loopone Inconclusion systemswithsmallsensitivityarenoteasytobeaffectedbyachangingenvironment Inotherwords smallsensitivityimpliesthesystemhasstrongrobustn