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# Ch9-ä½œä¸šè§£ç­”-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。 ( ) y t 1 ( ) e t 2 ( ) e t 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： 1 2 ( ) 2 ( ) 3 ( ) y t t t 整理成矩阵表示形式如下： 1 1 1 2 2 2 ( ) ( ) 3 0 8 7 ( ) [ ] [ ][ ] [ ][ ] ( ) ( ) 2 1 4 1 ( ) t e t t t e t t 1 2 ( ) ( ) [2 3][ ] ( ) t y t t 即有： 3 0 [ ] 2 1 A 8 7 [ ] 4 1 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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1 1 3 0 ( ) [ ] 2 1 1 0 3 [ ] 1 1 1 1 3 1 s sI A s s s s s 所以： 1
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