状态反馈极点配置的直接方法
A Direct Method for Pole Assignment Using State Feedback
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摘要: 本文研究了线性时不变系统x=Ax+Bu,y=Cx,引进状态反馈u=-Kx任意配置 闭路极点问题.文中通过矩阵[sI-A]-1B的右既约分解矩阵,导出了闭路系统特征方程的 p×p维多项式矩阵行列式表示式(p=rankB).利用这一表示式直接配置闭路极点,计算反 馈矩阵K.文中同时给出了计算矩阵[sI-A]-1B右既约分解矩阵的一种新算法.最后举例 说明了它们的应用,并进一步讨论了K矩阵的灵活算法.Abstract: In this paper the problem of the pole assignment in a linear time-invariant system x=Ax+Bu, y=Cx, using the state feedback law u=Kx is studied. In the paper a determinant experession of the p×p polynomial matrix for the characteristic polynomial of the closed-loop system is derived by means of the relative right reduced factorization matrices of the matrix [sI-A]-1B(p=rakB). Based on the expression the poles are assigned directly and the matrix K is computed. In addition a new algorithm for computing the relative right reduced factorization matrices of the matrix [sI-A]-1B is presented. Finally, a numerical example is given to illustrate their applications, and by means of the example flexible computation of the matrix K is further shown.
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