Ch9-作业解答-2010

Ch9-作业解答-2010

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Ch 12 习题参考解答 12-4 给定系统流图如题图 12-4 所示, 1 . 列写状态方程和输出方程。 2 . 设采样间隔 T=0.1s ,建立该系统的离散化模型。 3 . 求离散系统的传输函数阵,并判断该离散系统是否 BIBO 稳定。 () yt 1 et 2 1 1 8 1 4 7 2 2 3 -3 -1 1 p 1 p 1 2 1 2 1 题图 12-4 解: 1 . 选定状态变量为两个积分器的输出,分别记为 1 t 2 t 。见题图 12-4 。由流 图可得状态方程: 1 1 1 2 2 1 2 1 2 ( ) 3 ( ) 8 ( ) 7 ( ) ( ) 2 ( ) ( ) 4 ( ) ( ) t t e t e t t t t e t e t    输出方程: 12 ( ) 2 ( ) 3 ( ) y t t t  整理成矩阵表示形式如下: 11 1 22 2 ( ) ( ) 3 0 8 7 [ ] [ ][ ] [ ][ ] ( ) ( ) 2 1 4 1 t e t t t e t t 1 2 ( ) [2 3][ ] t t 即有: 30 [] 21 A 87 41 B [2 3] C [0 0] D 2 . 离散化: 先用拉式变换法求 At e
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11 30 ( ) [ ] 21 1 0 3 [ ] 1 1 1 1 3 1 s sI A s s s s s    所以: 1 1 1 3 3 1 0 3 {( ) } {[ ]} 1 1 1 1 3 1 0 [ ] At t t t t s e sI A s s s e e e e
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Ch9-作业解答-2010

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