1、8-4 脉冲传递函数)(21)(21(z)C(z)G(z)(s)R(z)(s)GGC(z)21 zGGsGGZRZG(s)(tr)(*trT)(zrc(t)c(z)(*tC定义：输出脉冲序列的Z变换与输入脉冲序列的z变换之比。一.线性数字系统的开环脉冲传函1.串联环节间无同步采样开关隔离时的脉冲传函结论:没有采样开关隔离时两个线性环节串联,其脉冲传函为这两个环节的传函相乘之积的z变换。0)()()()(nnznTgzRzCzG)(zRG1(s)G2(s)(*tCc(t)(trT)(*tr)(zC(z)(z)GGR(z)C(z)G(z)(z)R(z)(z)GGC(z)(z)R(z)GD(z)(z
2、)D(z)GC(z)212112 2.串联环节有同步采样开关时的脉冲传函结论:有采样开关隔离时两个线性环节串联，其脉冲传函为两个环节分别求z变换后的乘积。可推广到可推广到n n个环节。个环节。)(*tdG2(s)G1(s)Tc(t)(tr)(*tr)(*tcd(t)(zDT)(zC (s)(s)2 2G GZZ1 1-z z-111 1-(s)z(s)z2 2G GZZ-(s)(s)2 2G GZZ TsTs(s)e(s)e2 2G G-(s)(s)2 2G GZZ(s)(s)2 2G G(s)(s)1 1G GZZG(z)G(z)TsTs(s)e(s)e2 2G G-(s)(s)2 2G G
3、(s)(s)2 2G G )TsTse e -(1(1(s)(s)2 2G G(s)(s)1 1G G(s)(s)2 2(s)G(s)G1 1G G s s(s)(s)2 2G G(s)(s)2 2G G TsTse e-1 1(s)(s)1 1G G令令 s s(s)(s)2 2G G)TsTse e(1(1(s)(s)2 2G Gs sTsTs-e-e1 1(s)(s)2 2(s)G(s)G1 1G G s sTsTs-e-e1 1(s)(s)1 1G G G2(s)零阶保持器c(t)(tr)(*tr3.环节与零阶保持器串联时的脉冲传函)10T-e-1)(z-(z)10T-e-z(1 10
4、s10s1Z (z)2G1G(s)2(s)G1ZGG(z)G1(s)G2(s)解:例例1 1：求下图所示的两个串联环节的脉冲传函,其中10s10(s)2G,s1(s)1G)10)(1(210 1-zz1010z 10s101Z(z)2(z)G1GG(z)TezzzTezZsG1(s)G2(s)例例2.2.求右图所示二环节串联的脉冲传函求右图所示二环节串联的脉冲传函,G G1 1(s)(s)、G G2 2(s)(s)同上。同上。解:)aT-e-a(zaT-e-1 1sa1)Z1-z-(1 a)s(s1)Z1-z-(1 1-Tse-1ZG(z)sasaas例3.设与零阶保持器串联的环节的传函为 ,
5、试求脉冲传函。解：ssG1)(R(s)G1(s)H(s)G2(s)c(s)(*SC)(*srY(s)-H(z)2G1G1)z(2G1GR(z)(z)(z)(z)2G1GC(z)H(z)2G1G11R(z)(z)(s)*H)2G1(G-(s)*(s)*(s)*(s)H(s)2(s)G1G-R(s)(s)3 H(s)C(s)Y(s)Y(s)-R(s)(s)(s)*(s)2(s)G1GC(s)CrrrRrrrrr而对上式采样得式得由上 二.线性数字控制系统的闭环传函H(s)D(s)G(s)R(s)X(s)C(s)(se-)()(1)()(R(z)C(z)(s)*(s)D*GH1)(*)(*)(*(s
6、)*C (s)*(s)E*(s)D*G(s)*C )(*)(*1(s)*R(s)*E (s)*(s)E*(s)D*GH-(s)*R(s)*E (s)*(s)E*H(s)G(s)D-R(s)E(s)H(s)C(s)-R(s)E(s)(s)*(S)E*D(s)*X (s)*D(s)EX(s)(s)*G(s)XC(s)zDzGHzGzDsRsDsGsDsGH 例4.试求下图所示系统的闭环传函解：C(s)e-1)(z-(z21e)1(1)z-(1 )1(1)1(ZG(z)(1)(R(z)C(z)1-11-21-0ezssZsssezGzGsT121211-e 1211-e)1-e1)(z-(z-121
7、1-e )1-e1)(z-(z-1211-e1)1-e1)(z-(z-121-1eR(z)C(z)ezzezezezezezSeST01)1(1SSR(s)-T例5.试求取如图所示线性数字系统的闭环传函解:例6.求如图所示线性数字系统的传递函数解：解：)()()(2*sGsUsY)()()()()(1sGsFsYsRsU)()()()()()()(12*1sGsFsGsUsGsRsU则有)()()()(*21*1*sFGGsUsRGsU)(1)()(*21*1*sFGGsRGsU两边离散化之后，可得)()(1)()(2*21*1sGsFGGsRGsY)(1)()()(*21*2*1*sFGGsGsRGsY)(1)()()(2121zFGGzGzRGzY于是 所以，闭环系统输出的z变换为P2709-6.a）)()(1()1()(1010zRezzezzCTTb）)()(1()(1)(10210zRezzzzRezzzzzCTTc）ssRZezzzCT)()(10
