《现代控制理论参考答案》
第一章答案
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。
U(s)+-K1Kps?K1+-Kps?K1s+-1J1sKbJ2s2?(s)Kns图1-27系统方块结构图
解:系统的模拟结构图如下:
Kp+U(s)-K1Kp+-K1Kp?x6+-K1x5++?+-1J1?x4x3KbJ2?x2??(s)x1Kn?图1-30双输入--双输出系统模拟结构图
系统的状态方程如下:
x1?x2x2????Kbx3J2KpKpKn1x3??x3?x4?x5?x6J1J1J1J1 x4?x3x5??K1x3?K1X6x6?????K1KKx1?1x6?1uKpKpKp令?(s)?y,则y?x1
——
所以,系统的状态空间表达式及输出方程表达式为
?????1??x???x????2???x3????????x4???????x5?????????x6????00000K1Kp10Kb0J2Kp0?J10100?K1000?KnJ1000001J0000???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??x??2??x3?y??100000????x4??x5?????x6??
1-2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R2上的电压作为输出量的输出方程。
R1L1L2i1CUi2---------Uc---------R2图1-28 电路图
解:由图,令i1?x1,i2?x2,uc?x3,输出量y?R2x2
R1x1?L1x1?x3?u有电路原理可知:L2x2?R2x2?x3??x1??x2??x3?????R111x1?x3?uL1L1L1R21x2?x3L2L2
既得
x1?x2?Cx3?11x1?x2CCy?R2x2写成矢量矩阵形式为:
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?。0?1??x????R11L?1????L111???x????x。2???0?R2??1?L?L2L2??x??1?0?2??u?x。????3????1??C?10????x3????0??C? ????x??1?y??0R20?x?2???x3??
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。u1b1+??y1---a1a2a5a61u2b+-2?++?--ay23a4图1-30双输入--双输出系统模拟结构图
解:系统的状态空间表达式如下所示:
??x?1??0100?0??x??????x2??a2?a10?a0????1????06xb?x??3??100??2?x???110??u?x???4??0?a5?a4?a??3??x???03?4??0b?2??
?x1???1010??x?y2??x?3??x?4???s?100?(sI?A)??a2s?a10a?6???10s?1?? ?0a5a4a?3?欢迎下载 ——
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《现代控制理论》第3版课后习题答案
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