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1、PART2Unit2AstabilityandthetimeresponseThestabilityofacontinuousordiscrete-timesystemisdeterminedbyitsresponsetoinputordisturbanee.Intuitively,astablesystemisonethatremainsatrest(orinequi1ibrium)unlessexcitedbyanexternalsourceandrcturnstorestifallexcitationsareremoved.Theoutputwi
2、llpassthroughatransientphaseandsettiedowntoasteady-stateresponsethatwillbeofthesameformas,orboundedby,theinput.Ifweapplythesameinputtoanunstablesystem,theoutputwillneversettledowntoasteady-statephase;itwi11increaseinanunboundedmanner,usuallyexponcntidilyorwithoscillationofincrca
3、singamplitude.连续或离散系统的稳定性由其对输入或者干扰的响应决定。直观地说,如果一个系统是稳定的,则其停留在稳态(或者平衡点),除非是受到外部激励,且当外部激励去除后,输击又回到稳态点。输出经过瞬态阶段后将回到与输入有相同形式的稳态或者是在输入的附近。如果我们将同样的输入作用于不稳定的系统,其输出将不会回到稳态,而是以无界的方式增长,通常其幅值是指数增长或者振荡增长。Stabilitycanbepreciselydefinedintermsoftheimpulseresponse儿⑴ofacontinuoussystem,Kronrcke
4、rdellaresponse儿伙)ofadiscrctc-timcsystem,asfollows:Acontinuous(discrcte-time)systemisstableifitsimpulseresponse儿(/)(Kroneckerresponse儿伙))approacheszeroastimeapproachesinfinity.系统的稳定性可以用连续系统的脉冲响应儿⑴或者离散系统的Kronrcker△响应儿伙)来定义:一个连续(离散)系统是稳定的,如果其脉冲响应儿⑴(KronrckerA响应儿伙))当时间趋于无穷大吋趋于零。Anac
5、ceptablesystemmustatminimumsatisfythethrccbasiccritcriaofstability,accuracy,andasatisfactorytransientresponse.Thesethreectiteriaareimpliedinthestatementthatanacceptablesystemmusthaveasatisfactorytimeresponsetospecifiedinputsanddisturbances.SoalthoughweworkintheLaplaceandfrequenc
6、ydomainsforconvenience,wemustbeabletorelatethesetwodomains,atleastqualitativcly,tothetimedomain.一个可接受的系统必须至少满足:稳定性、精度和满意的瞬态响应这三个指标。在陈述:“一个可接受的系统对指定输入和扰动必须有满意的时域响应”已经包含了这三个指标的含义。因此尽管我们为了方便工作在拉氏域或者频率域,我们必须与时间域(至少是定性的)相联系。WiththetransferfunctionintheformofEq.(2-2AT),theorderofthesy
7、stemindefinedastheorderofthecharacteristicfunctionD(s),thehighestpowerofsappearinginD(s)establishestheorderofthesystern.在传递函数所在的方程(2-2A-1)中,系统的阶次定义为特征函数D(s)的阶次,因此D(s)的最高次幕决定了系统的阶次。Thefirsttermistheforcedsolution,duetotheinput,andthesecondthetransientsolution,duetothesystempole.F
8、ig.2~2A~2showsthistransicntaswellasc(t)・Thetran