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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]~(-1)B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略极点数件分别为η≤min{max{m+(p-1)[m/p],P+(m-1)[p/m]},n}和η_o≤min{ν+max{νm+m+(p-1)[m/p],νp+p+(m+1)[p/m]},n+ν}(其中n和ν分別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。
In this paper, the problem of closed-circuit poles is arbitrarily configured by using output proportional feedback and dynamic compensator when the linear time-invariant energy-controlled observer system x = Ax + Bu, y = Cx. In this paper, the closed-loop system characteristic polynomial is represented as a determinant of p × p-dimensional matrix by means of the right-only factorization matrix of [sI-A] ~ (-1) B matrix. Based on this expression, A Simple, Practical New Approach to Design Dynamic Compensators. It is proved that the number of closed-pole devices can be arbitrarily configured with output proportional feedback and dynamic compensator as follows: η≤min {max {m + (p-1) [m / p], P + (m-1) [p / m] , n} and η_o≤min {ν + max {νm + m + (p-1) [m / p], νp + p + (m + 1) [p / m]}, n + ν} Respectively, the order of the control object and the dynamic compensator, p = rankB, m = rankC), the article finally illustrates the application of this method.