線型定常システムの過渡応答の数値解析

概要

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In this paper, methods of evaluating transient responses of linear time-invariant systems using the state space equations are presented. These methods, completely free from eigenvalue problems, are first given by Liou and reformed by several authors. But they are mainly limitted to homogeneous forms X'=AX. First, when computing matrix exponential e^<AT> by the power series expansion, we show the number of terms necessary for the required accuracy. Next, in the case of heterogeneous equations X'=AX-F, where F is a forced input, we show (1)the method is extended by evaluating forced responce matrices, Which are evaluated in a similiar way with e^<AT>, (2)when F are special form functions, these are important for transient responses, X'=AX-F can be transformed to the form X'=BX. Last, from comparisons with the 4-th order Runge-Kutta method, the advantages of our methods are given. These methods are simple, accurate and effective; some examples are shown.
一般社団法人情報処理学会の論文
1973-01-15