带动态前馈和线性状态变量反馈的多变量系统的根轨迹
Root Loci of Multivariable Systems With Dynamic Feedforward and Linear State Variable Feedback
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摘要: 本文研究了采用动态前馈和线性状态变量反馈的真(proper)多变量线性系 统的根轨迹渐近特性,证明了系统的无穷远极点的阶数、渐近线方向和原点在一大 类条件下具有不变性,讨论了实现这一大类条件的可能性和系统在高增益参数下渐 近稳定的充要条件. 本文将Wolovich广义补偿设计技术与多变量根轨迹技术相结合,导出了一 个带多变量要轨迹渐近特性补偿的新的广义补偿设计算法.它不仅使原设计的闭环 传递矩阵Td(s)在g=1时维持不变,而且环节K(s)、H(s)和Q-1(s)等亦不变.Abstract: The root locus asymptotic behaviour of the proper multivariable systems with dynamic feed for ward and linear state variable feedback(d .f.& 1. s. v .f.)is researched. The orders ,asymptotic directions and pivots of the root loci to these systems are shown to be invariant under a large class of cases. Realizability of this class of cases is discussed. The necessary and sufficient conditions for asymptotic stability of the system under high gain g are discussed. The combination of wolovich's general compensation technique via d. f& l. s. v .f, and multivariable root locus technique is Suggested and discussed. A synthesis algorithm of the new general compensation technique with the compensation for root locus asymptotic behaviour is deduced. It maintains not only the originally designed closed-loop transfer matrix when g=1,, but also the originally designed blocks K(s),H(s)and Q-l(s).
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