信号与系统ppt第二章系统数学模型的建立.pdf

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1、Ch2Time-DomainAnalysisofLTISystemcontents：1differential(difference)equation—time-domainresponse求微分(差分）方程的解——求时域响应homogeneoussolution+particularsolutiontotalsolutionclassicsolution齐次解+特解全解zero-inputresponse+zero-stateresponse零输入响应+零状态响应2Unitimpulseresponseh(t),

2、unitsampleresponseh(n)单位冲激响应h(t)，单位样值响应h(n)3Convolutionsum/integralofexcitationandimpulseresponse,application激励与冲激响应的卷积积分(卷积和)及其应用§2.2系统数学模型的建立•元件约束条件•网络拓扑约束•KVL•KCL2d11ddCvt()vt()vt()It()2SdtRdtLdt§2-1Time-domainanalysisofcontinuoussystem§2-1-1differential

3、equationofsystemandclassicsolutionForanyLTIsystem,thegeneralformulaofnth-orderlinearconstant-coefficientdifferentialequationis（LCCDE）：nn1mm1drdrdrdededeaaarbbbbenn1n110mmm1m110dtdtdtdtdtdtusingclassicsolution:totalsolution=homogeneoussolution+

4、particularsolutionr(t)r(t)r(t)nphomogeneoussolutionr(t)isthesolutionofhomogeneousequationsnnn1drdrdrgeneralsolutionis：cetaaar0nn1n110dtdtdtsecularequationis：nn1aaa0n110特征方程：nlatentrootsofthisn-ordernaturalfrequencyequationis：,,(i1,2

5、n)12nprototypeofsolutions：n1isdistinctrealroot：itIrn(t)ciei121isk-repeatedroot：issimplerootjcoefficientci,cjknr(t)ce1ttkicejtniji1jk1particularsolution:accordingtoexcitation,checktabletoobtainr(t)ptotalsolutionr(t)r(t)r(t)npExample1：Findhom

6、ogeneoussolution:"'r(t)5r(t)6r(t)e(t)SL：secularequationis：2560Obtainsecularroot:2,312homogeneoussolutionis：r(t)ce2tce3tn12Example3:Findhomogeneoussolution:"'SL：r(t)4r(t)4r(t)e(t)24402doubleroot1,22t2tr(t)ctecen12与几种典型激励函数相应的特解

7、激励函数et()响应函数rt()的特解常数EBppp1tBt0Bt1BtBpp1tteBesin(t)Bcos(t)Bsin(t)12cos(t)ptpp1tecos(t)Bt0Bt1Btpp1Bcos(t)ptpp1tesin(t)Dt0Dt1Dtpp1Dsin(t)特殊情况：特解与齐次解重复t①若输入ft()e，为微分方程对应的特征方程的单根t2tBteBte0则特解的形式为0，若为二重根，则特解的形式为"''Example4:e

8、quationisr(t)3r(t)2r(t)e(t)2e(t)Ifexcitationis：2,finditsparticularsolutionr(t).e(t)tpChecktable2-3-,theformatofparticularsolutionis:2r(t)AtAtAf210"''rf(t),rf(t),rf(t)e(t),e