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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-A~r]~(-1)C~r的石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为n≤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。
In this paper, the design problems of the output proportional feedback-series integral compensator (PI compensator) and the output dynamic feedback-series integral compensator (PDI compensator) under the condition of arbitrary configuration of closed-loop system poles are studied in this paper. . In this paper, the determinant of the m × m polynomial matrix of the closed-loop system’s eigenvalue equation is derived by decomposing the matrix [sI-A ~ r] ~ (-1) C ~ r. Based on this, a new design method is established. For the PI and PDI compensators, it is proved that the poles of the closed-circuit system can be arbitrarily configured with n≤min {2p + (m-1) [2p / m], n + m} and ηD≤min (v + vp + 2p + (2p / m), n + m + v} (n and v are the order of the system and the dynamic compensator respectively, m is the output vector dimension, p is the control vector dimension, (2p / m) m integer part, m ≤ p), and the design method than the existing simple and practical.Finally illustrates its application.