PI和PDI补偿器设计

Design of PI and PDI Compensators

中文摘要

      本文研究了多变量线性时不变系统输出比例反馈—串联积分补偿器（简称PI补偿器）和输出动态反馈—串联积分补偿器（简称PDI补偿器）在闭路系统极点任意配置条件下的设计问题。文中通过矩阵[sI－AT]-1CT的右既约分解导出了闭路系统特征方程的m×m多项式矩阵行列式表示式，据此建立了新的设计方法。对于PI和PDI补偿器证明了闭路系统极点可任意配置数分别是η≤min{2p+(m－1)[2p/m], n+m}和ηD≤min{v+vp+2p+(m－1)[2p/m], n+m+v}(n和v分别为系统和动态补偿器阶数，m为输出向量维数，p为控制向量维数，[2p/m]表示2p/m的整数部分m≤p)。并且该设计方法比已有的简单、实用。最后举例说明了它的应用。

英文摘要

      This paper deals with the problem of arbitrary assigning closed-loop poles linear multivariable time-invariant systems by using output proportional feedback-serial integral compensator(PI compensator) and output dynamic feedback-serial integral compensator(PDI compensator) respectively, Determinant expressions of m×m polynomial matrix for characteristic equation are developed by right reduced factorizations of matrix [sI－AT]-1CT. Based on the expressions, a new design method both simpler and more practical than hitherto is given. It is shown that the number η≤min{2p+(m－1)[2p/m], n+m} and ηD≤min{v+vp+2p+(m－1)[2p/m], n+m+v} of closed loop poles are arbitrarily assignable by using PI and PDI compensator respectively(where n and v are the orders of the system and the dynamic compensator respectively p and m are the dimension of control and output vectors and [2p/m] means the integer part of 2p/m, m≤p).Applications are shown in the examples.