§8-4 脈沖傳遞函數(shù)

1、8-4 脈沖傳遞函數(shù))(21)(21(z)c(z)g(z) (s)r(z)(s)ggc(z) 21 zggsggzrzg(s)(tr)(*trt)(zrc(t)c(z)(*tc定義：輸出脈沖序列的z變換與輸入脈沖序列的z變換之比。一.線性數(shù)字系統(tǒng)的開環(huán)脈沖傳函1.串聯(lián)環(huán)節(jié)間無同步采樣開關(guān)隔離時的脈沖傳函結(jié)論:沒有采樣開關(guān)隔離時兩個線性環(huán)節(jié)串聯(lián),其脈沖傳函為這兩個環(huán)節(jié)的傳函相乘之積的z變換。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

2、) (z)d(z)gc(z) 212112 2.串聯(lián)環(huán)節(jié)有同步采樣開關(guān)時的脈沖傳函結(jié)論:有采樣開關(guān)隔離時兩個線性環(huán)節(jié)串聯(lián)，其脈沖傳函為兩個環(huán)節(jié)分別求z變換后的乘積。 可推廣到可推廣到n n個環(huán)節(jié)。個環(huán)節(jié)。)(*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

3、2g g- -(s)(s)2 2g g(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)零階保持器c(t)(tr)(*tr3.環(huán)節(jié)與零階保持器串聯(lián)時的

4、脈沖傳函 )10t-e-1)(z-(z)10t-e-z(1 10s10s1z (z)2g1g(s)2(s)g1zgg(z) g1(s)g2(s)解: 例例1 1：求下圖所示的兩個串聯(lián)環(huán)節(jié)的脈沖傳函,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.求右圖所示二環(huán)節(jié)串聯(lián)的脈沖傳函求右圖所示二環(huán)節(jié)串聯(lián)的脈沖傳函, , 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-

5、(1 1-tse-1zg(z) sasaas例3.設(shè)與零階保持器串聯(lián)的環(huán)節(jié)的傳函為 ,試求脈沖傳函。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而對上式采樣得式得由上 二.線性數(shù)字控制系統(tǒng)的閉環(huán)傳函h(s)d(s)g(s)r(s)x(

6、s)c(s)(se-)()(1)()(r(z)c(z) (s)*(s)d*gh1)(*)(*)(*(s)*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.試求下圖所示系統(tǒng)的閉環(huán)傳函解：c(s) )e-1)(z-(z21e ) 1(1)z-(1 ) 1(1)1 (zg(z) )(1)

7、(r(z)c(z) 1 -11 -21 -0ezsszsssezgzgst121211 -e 1211 -e)1 -e1)(z-(z-1211 -e )1 -e1)(z-(z-1211 -e1)1 -e1)(z-(z-121-1er(z)c(z)ezzezezezezezsest01) 1(1ssr(s)-t例5.試求取如圖所示線性數(shù)字系統(tǒng)的閉環(huán)傳函解:例6.求如圖所示線性數(shù)字系統(tǒng)的傳遞函數(shù)解：解： )()()(2*sgsusy)()()()()(1sgsfsysrsu)()()()()()()(12*1sgsfsgsusgsrsu則有)()()()(*21*1*sfggsusrgsu)(1)()(*21*1*sfggsrgsu兩邊離散化之后，可得)()(1)()(2*21*1sgsfggsrgsy)(1)()()(*21*2*1*sfggsgsrgsy)(1)()()(2121zfg