解：A的特征方程 解得： p22??2p12,p32?解得： p21?p31??p11 10??0?（3）A?302??????12?7?6??解之得：?1??1,?2??2,?3??3解得： p23??3p13,p33?3p13 令p11?1 ???p12??1???（或令p12?1，得P2?p22???2?）???1???p32?????2??p11???1?????（或令p11??1，得P1??p21???1?）??p31????1??10??p11??0?p11??当?1??1时，302??p21????p21???????????12?7?6????p31???p31??10??p13??0?p13??当?1??3时，302??p23???3?p23???????????12?7?6????p33???p33??1p12 令p12?2 2得 10??p12??0?p12??当?1??2时，302??p22???2?p22? ??????????12?7?6????p32???p32??0????1?I?A???3??2???3?6?2?11??6?0????127??6??令p13?1 得 得 ?p11??1?P1??p21????1???????p31?????1??1-9将下列状态空间表达式化成约旦标准型（并联分解）?p12??2?P2??p22????4???????p32????1???p13??1?P3??p23????3???????p33????3??解：A的特征方程 ?1??41?2??x1??31??x?x?2???102??x2???27?u?????????3???x???1?13????x3????53??（2）?x1??y1??120????y???011??x2???x??2???3?2????4?1?I?A???1??2??(??1)(??3)2?0???1??3???1??1,2?3,?3?1?41?2??p11??p11?当?1?3时，??102?????p21???3??p21???1?13????p31????p31??解之得 p21?p31?p11 令p11?1 得 ?41?2??p11??p11??1当?2?3时，???102??p21??3?p21??????????1???1?13????p31????p31????1??解之得 p12?p22?1,p22?p32 令p12?1 ?41?2??p13??p当?3?1时，?13??102??p23???1?13??????p23???????p33???p33??解之得 p13?0,p23?2p33 令p33?1 ?110??0?12?T???102? T?1???101??11?2?????01?1?????0?12??31??8?1?T?1B???11?2??27????52?01?1???????????53?????34???p11??1?P1???p21??p????1???31????1???p12??1?得 P2???p22?????0?????p32???0???p13??0?得 P3???p23??p????2???33????1??约旦标准型?1?W1(s)??s?1?0?（2）并联联结?1?W1(s)??s?1?0??求系统的闭环传递函数解：?1?W(s)?W2(s)W1(s)??s?31??s?1?1?W(s)?W1(s)?W1(s)??s?1?0?1-10 已知两系统的传递函数分别为W1(s)和W2(s)试求两子系统串联联结和并联连接时，系统的传递函数阵，并讨论所得结果解：（1）串联联结1-11 （第3版教材）已知如图1-22所示的系统，其中子系统1、2的传递函数阵分别为?1?W1(s)W21(s)??s?1?0??1?(s?1)(s?3)??1?2??(s?1)1?s?2? s?1??s?2??110?120????314??CT????102???203?011???101??????310??8?1?~???030?~xx???52?u???????001????34???314?~y???x203??1?s? 1??s?2?1??1s??10???s?1??1??01??0??s?2???1??1s?4??s?1??0??0???s2?5s?7(s?2)(s?3)(s?4)??1?(s?1)(s?2)??1??1s?2???s?3s?1??1??s?2??s?1?1?W2(s)??s?31??s?1?10?W2(s)????01?1?s?2?s?1??s?2?1?s?1??s?2?1?s?4??0??1?s?4??0????1?s?1W1(s)???2??I?W1(s)W2(s)??1?求系统的闭环传递函数解：?1?W1(s)W1(s)??s?1?2?1?s? 1??s?2???1?s?1I?W1(s)W(s)?I???0?1??1?s?3??s?1s?1?s?2?1sW(s)??I?W1(s)W2(s)?W1(s)??s?2??s?3?0??ss?1???s?31??1s?1????s?1?(s?2)(s?1)s???s?2s(s?3)??????1??1s?3??00?s?1?s?3??????1?1??1?s??10???s?1s???1??1?01????2?s?2?s?2??1?1??1?s?2???s??10???s?1s?I?W1(s)W1(s)??s?1???1??s?301??2?2???s?2?s?2???1??s?3s?2s??I?W1(s)W1(s)??1?2s(s?1)?s?2?s?5s?2???2?s?1??1-11（第2版教材） 已知如图1-22所示的系统，其中子系统1、2的传递函数阵分别为1??1?s?3??s?2s(s?1)?s?2?1sW(s)??I?W1(s)W1(s)?W1(s)?2???s?5s?2??2s?2??ss?1???s?32s?31??????s(s?1)?(s?2)2ss(s?2)s(s?2)?2??22(s?2)21s?5s?2????????s?1ss?1?s?2??s?3s?1?s?2??s?3?0??(s?1)2(3s?8)?22(s?2)(s?5s?2)??32s?6s?6s??(s?2)(s2?5s?2)??10?W2(s)????01?1??s?1s?2s?????s?2??0?s?1??s?1?s(s?3)??s?2??s?3??1?s?1??s?2???s?1??s2?5s?2?s?2??2s?5s?2??1??s?2s??10???s?1??1??01???0?s?2??1?s?s?3??s?2??1?s?1??s?2??W(z)?解法2： 解法1：（1）b????1??1?x1(k?1)?x2(k)y(k)??11?x(k)?1?11?（2） A=???41?y(k)?3x1(k)?2x2(k)1-12 已知差分方程为?1?求T,使得TB??? ?1?所以，状态空间表达式为?1?1?CT??32?????3?1?01??x2(k?1)??2x1(k)?3x2(k)?u2z?311??z2?3z?2z?1z?2得T?11??1?1???40??11??0T?1AT???????????01???2?3??01???5?1???40??1?z(k?1)???z(k)??1?u(k)?5?1????y(k)??3?1?z(k)??10??1?x(k?1)??x(k)???1?u(k)0?2????1??0?0?x(k?1)??x(k)???1?u(k)?2?3????y(k)??32?x(k)y(k?2)?3y(k?1)?2y(k)?2u(k?1)?3u(k)2-4 用三种方法计算以下矩阵指数函数eAt。?11???? 所以 01???1?1?T??? 01??试将其用离散状态空间表达式表示，并使驱动函数u的系数b(即控制列阵)为第二章习题答案
【VIP专享】《现代控制理论》第3版(刘豹_唐万生)课后习题答案
