L02v3 Analysis on time domain

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1、AnalysisonTimeDomainInternalUseOnly2.1Introductionn时域分析方法的优点：n直接研究系统的时间响应或时域特性n直观、物理概念清楚，n变换法的基础,便于理解、便于比较n计算机技术使经典方法重新得到广泛应用。n方法：n经典法n高阶系统复杂n卷积法n线性时不变InternalUseOnlyn冲激响应之和22.2RepresentationofLTISystemsandSolutionnSystemModelsnrealisticsystemsàapproximatelinearsystem.nLTIàcon

2、stant-coefficientdifferentialequation.nConstructionofacircuitmodelandKirchhoff’slaws(基尔霍夫定律)1tdKVLV(t)=Ri(t)V(t)==i(tt)dV(t)Lit()RRCòCLLC-¥dt11dtKCLi(t)=V(t)i(t)==CV(t)i(t)Vd()ttRRCCLLòRdtL-¥InternalUseOnly3nTwoformsdescribingasystemnInputut--outputdescription:highorderdiffere

3、ntialequationnStatevariabledescription:aseriescoupledoffirst-orderdifferentialequationsnAnalysisprocessofsystemnModel(physicalàmathequation)nSolvingequationintime-domainnClassicmethodnConvoInluttionernalUseOnly4RLCcircuit:ashockabsorber:anelectricalsystemamechanicalsystemInter

4、nalUseOnly不同性质的系统，可能具有相同或类似的数学描述。52.3ClassicSolutionofLTISystemslinearconstant-coefficientdifferentialequationnn-1dr(t)dr(t)drt()C+C+×××++CCrt()0nn11-1nn-dtdtdtmm-1de(t)de(t)det()=E+E+×××++EEet()0mm11-1mm-dtdtdtr(t)=+r(t)rt()h:homogeneoussolution通解hpp:particularsolution特解↓char

5、acteristiceq.nn-1Ca+Caa+×××+CC+=0011nn-特征方程InternalUseOnlycharacteristicroot特征根:a1,a2,…,an6(1)homogeneoussolution齐次解nn-1dr(t)dr(t)drt()C+C+×××+C+=Crt()00nn11-1nn-dtdtdthomogeneousEq.齐次方程nSingleroot：nr()t=Aeaa12tt+Ae+×××+=AeaanittåAeh12nii=1nRepeatedroot：arootaiisrepeatedktimes

6、kk-12k--aaiittæöki()A1t+A21Itnte+×r××na+Akl-Ut+=sAkieeOnç÷ålyAteèøi=17(2)Particularsolution特解p.46InternalUseOnly8p.52#2-4求微分方程的特解已知方程且e(t)=t2，求特解2dr(t)dr()td+2+3r(t)=+e(t)et()2dtdtdt将e(t)=t2代入方程右端，得到t2+2t，故设rp(t)=B1t2+B2t+B3223Bt+(4B+3B)t+(2B+2B+3B)2=+tt1121231210B=,BB=,=-1233

7、9271In2te2rna10lUseOnlyr()t=tt+-p93927(3)Thecompletesolutionnatr=r+r=+åAeirt()hpipi=1nIftheinpute(t)appliestothesystematt=0,thecompletesolutionisvalidonlyfor0+

8、alconditionr(k)(0+)In(kt=e0r,na1,…l,Un-1)seOnly10Determinecoe