????x2?系统的状态方程如下：x6??x1?x2x4?x3x5??K1x3?K1X6??Kbx3J2KpU(s)+-令?(s)?y，则y?x1U(s)+解：系统的模拟结构图如下：K1Kp+-1-1 试求图1-27系统的模拟结构图，并建立其状态空间表达式。KpKn1x3??x3?x4?x5?x6J1J1J1J1K1KKx1?1x6?1uKpKpKp-K1KpKps?K1?x6+K1Kps?K1-+K1Kp图1-27系统方块结构图-第一章答案s-+x5++?+-Kn1J1Kns1J1sx4??《现代控制理论参考答案》图1-30双输入--双输出系统模拟结构图x3KbJ2KbJ2s2?x2?(s)??(s)x1?????1??x???x????2???x3????????x4???????x5?????????x6????00000K1Kp000010?写成矢量矩阵形式为：0KbJ2Kp?J11?K10U?x1??x??2??x3?y??100000????x4??x5?????x6????000有电路原理可知：L2x2?R2x2?x3R2上的电压作为输出量的输出方程。R1x1?L1x1?x3?u所以，系统的状态空间表达式及输出方程表达式为解：由图，令i1?x1,i2?x2,uc?x3，输出量y?R2x21-2有电路如图1-28所示。以电压u(t)为输入量，求以电感中的电流和电容上的电压作为状态变量的状态方程，和以电阻x1?x2?Cx3KnJ100?1J00000 R1既得 L1??0???0?0??x1???0???x??Kp??2??0??x?J1??3???0?u?x4??0????0???xK1??5??K1???K1??x6???K????p??Kp??x1??图1-28 电路图x3??x2??11x1?x2CCy?R2x2?i1CR111x1?x3?uL1L1L1R21x2?x3L2L2---------Uc---------L2i2R2。y??0R2?1??0?x?x?2???a2?????x?3??1????4??0?x?R1????L1??x?1。?x???02?。???x3??1???????C?0?x1??0??x2????x3??1?a10?a5R2L21?C?x1??x?y??1010??2??x3????x4??1?s?as?a1(sI?A)??2??10?a5?0?000?a4u1u200sa40?a6???1??a3?解：系统的状态空间表达式如下所示：1-4 两输入u1，u2，两输出y1，y2的系统，其模拟结构图如图1-30所示，试求其状态空间表达式和传递函数阵。?1?s?as?a1?1Wux(s)?(sI?A)B??2??10?a5?01??1?L1??x????1L1????1?x2?0uL2????????x3???0???0?????0??x1??0?x??b?a6???2???11??x3??0?????a3??x4??000sa4b1b2图1-30双输入--双输出系统模拟结构图0?a6???1??a3?++-0?0??u0??b2??1--?0?b?1?0??0---a50?0??0??b2???a1a3a6++a4y2a2??1y1?.....相应的模拟结构图如下：..(2)y?5y?7y?3y?u?3u?2uu1-6 （2）已知系统传递函数W(s)??。?1?10??x1??0??0?x。??x???0?u?x???0012??2????。???x3????3?7?5????x3????1???????x1??y??231??x2????x3??-..--解：令x1?y，x2?y，x3?y，则有?1?s?as?a1Wuy(s)?C(sI?A)?1B??1010??2??10?a5?01-5系统的动态特性由下列微分方程描述列写其相应的状态空间表达式，并画出相应的模拟结构图。1016(s?1)?43?3?3解：W(s)???s(s?2)(s?3)2(s?3)2s?3s?2s6(s?1),试求出系统的约旦标准型的实现，并画出相应的模拟结构图2s(s?2)(s?3)??5x3700sa4?10?a6???1??a3?x2?33x1?1?0?b?1?0??00?0??0??b2?2+++y?1???310?x?x?2??0?30?????3??0?x0?2????00?x4??010?y???4?3?（1）画出其模拟结构图（2）求系统的传递函数解：1-8 求下列矩阵的特征矢量1-7 给定下列状态空间表达式?1??010??x1??0??x?x?2????2?30??x2???1?u?????????3???x????11?3????x3????2??‘x?1?y??001??x2?????x3??0??x1??0?0??x2??1???????u0??x3??1??????0??x4??1??x1???1??x2?33???x3????x4?0??s?1?（2）W(s)?(sI?A)?2s?30?????1?1s?3??sI?A?s(s?3)2?2(s?3)?(s?3)(s?2)(s?1)??s?3?2?s?30??1(sI?A)?1??2(s?3)s(s?3)0?(s?3)(s?2)(s?1)???s?5s?1(s?1)(s?2)????(s?3)?1?s(s?3)???(s?3)(s?2)(s?1)???(2s?1)(s?3)????s?3?2??0?s?30????1Wux(s)?(sI?A)?1B??2(s?3)s(s?3)0??1?(s?3)(s?2)(s?1)???s?5??2?s?1(s?1)(s?2)?????(s?3)?1?Wuy(s)?C(sI?A)?1B??001??s(s?3)??(s?3)(s?2)(s?1)??(2s?1)(s?3)??(2s?1)?(s?2)(s?1)
VIP专享《现代控制理论》第3版（刘豹 - 唐万生）课后习题答案
