摘要:
本文研究了线性时不变能控能观系统x=Ax+Bu,y=Cx应用输出比例反馈和动态
补偿器任意配置闭路极点问题.文中借助于[sI-A]-1B矩阵的右既约分解矩阵,将闭路系统
特征多项式表示成p×p维矩阵行列式表示式,基于这一表示式建立了计算反馈矩阵和设计
动态补偿器的简单、实用的新方法.证明了应用输出比例反馈和动态补偿器可任意配置闭路
极点数分别为η≤min{max {m+(p-1) [m/p], p+(m-1) [p/m],n}和η0≤min {v+max {vm+m+(p-1)[m/p],vp+p+(m-1)[p/m]},n+v} (其中n和v分别为控制对
象和动态补偿器的阶数,p=rankB,m=rankC),文章最后举例说明了这种方法的应用.
Abstract:
In this paper, using the output proportional feedback and dynamic compensator, the problem
of arbitrary pole assignment in a linear time-invariant controllable and observable system
x=Ax+Bu,y=Cx is studied. By means of the right reduced factorization matrices
of the matrix [sl-A]-1B, the characteristic polynomial of the closed loop system is expressed
as determinant expressions of p×p matrix. Based on the expressions, a simple, more practical
new method for computing the output feedback matrix and designing the dynamic compensator is
constructed. It is proved the number of
η≤min{max {m+(p-1) [m/p], p+(m-1) [p/m]},n},andv}
η0min{v+max {vm+m+(p-1)[m/p],vp+p+(m-1)[p/m]},n+v}
are arbitrarily assignable poles of output proportional feedback and the dynamic compensator
respectively (where n and v are order of plant and the dynamic compensator respectively,p=
rank B,m=rank C,[m/p] means the integer part of m/p).
finally,applications of the method are shown by examples.
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