用串联PID,PID-D调节器任意配置闭路极点的多项式矩阵法
Ynomial Matrix Method for Assignment of Closed Loop Poles Using Series PID and PID-D Regulators
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摘要: 本文研究了在线性常参数多变量系统x=Ax+Bu,y=Cx中,引进串联PID和PID-D 调节器,以任意配置闭路极点的问题.文中导出了闭路系统特征方程的m×m维多项式矩阵 行列式表示式,据此建立了设计PID和PID-D调节器的简单方法,给出了可任意配置的闭路 极点数,并给出了计算[sI-At]-1Ct矩阵右既约分解矩阵的新算法.Abstract: In this paper, the problem of pole assignment in linear multivariable time invariant systems x=Ax+Bu,y=Cx using series PID and PID-D regulators is considered. First, a determinant expression of m×m polynomial matrix for the closed loop characteristic equation is developed by means of right reduced factorization of [sI-Ar]-1 Ct (m=rankC). Based on the expression, a simple method for designing PID and PID-D regulators is constructed. The number of assignable poles is given. Second, a new algorithm for right reduced factorization of [sI-Ar]-1Ct is also presented.
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