数字信号处理 线性系统的时域分析法

1、控制器电炉测量元件r(t)c(t)r(t)01tc(t)01tc(t)01tc(t)01tc(t)01t%100)()()(%hhthp稳态性能-稳态误差ess0) t (ktlim，) t () t ( r要求时当)s(H)s(G1)s(G)s(R)s(C)s(:设nr2qq1jr1k2kkk2jm1ii)s2s()ss()zs(K)s(D)s(Masasasabsbsbsbmnn1n1n1n0m1m1m1m0k2kkki1j;S共轭复根实根0tr1k2kkt2kkkkkkq1jr1k2kktktsj1t )1sin(e1BCt )1cos(eBeA)s (L) t (kkkkkjk2kkk

2、i1j;S共轭复根实根临界稳定个为零其余为负或振荡不稳定个为正稳定全负1c10) t (klimt特征根实部特征根：r(t)0tc(t)0tc(t)0tc(t)0tj0特征根全部位于左半S平面0)(1110nnnnasasasasD02)(21223nnnKssssD21223122)()(nnnnKsssKss0750075006 .34)(123KssssD0)4 .74667500(8 .74336 .31112131Ksss)s(R)s(H)s(G11selim0sss)s(sE) t (elimelim0stss)s(R)s(H)s(G11)s(Ee(t)0tvnjjvmiisTss

3、KsHsG11)1()1()()(c(t)0Rtc(t)0tr(t)c(t)0r(t)tr(t)0te(t)0tc(t)0tG2(s)H(s)/1+ G1(s) G2(s)H(s)essn=limsE（s）=lim- s G2(s)H(s)N(s)/1+ G1(s) G2(s)H(s)令N（s）=1/sessn=- G2(0) H(0)/1+ G1(0) G2(0) H(0)G1(S)G2(S)G1(0) G2(0) H(0)1essn=-1/ G1(0) 减小及消除的essn方法1. G1(0) = K1 essn 2. G1(s)=k1/s essn=lims/k1=0令N（s）=1/se

4、ssn=- G2(0) H(0)/1+ G1(0) G2(0) H(0)例:系统如图所示。图中R(s)=R0(s)/s为阶跃输入信号;M为比例控制器输;N(s)=n0/s为阶跃扰动.试求系统的稳态误差.)s(NKK)1sT(sK)s(C)s(E2122nn100)(limKnssEensssn不稳定稳定T1|eT1dt)t(dh0tTt0t2222)()()(nnnsssRsCsc(t)0Rtc(t)0Rt0t),tsin(e111) t (hdt2ns1)s(s1s2s)s(C2d22n2nn22nc(t)0Rt)1(1,)1(12221nnTT)T1s)(T1s(s)s(C212n0,111)(212121teethTTTTTtTtc(t)0Rt0t),tsin(e111) t (hdt2n221)arccos1sin(2ln1dndntt0)sin(112rdttern0t),tsin(e111) t (hdt2n211)(et