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本文介绍一种利用线性控制系统状态方程进行频率特性计算的方法。通常频率特性计算是利用传递函数G(jω)),再代以S=jω。然而,对一个复杂的系统解出传递函数的显式表达式常常是很困难的,有时不得不作许多简化。本文提出一个新的途径:频率特性的数值计算不需传递函数的显式表达式,而是用一组方程表达了输出量和输入量之间的数量关系,这组方程是由状态方程演化而来。这种方法通用性好,适用任何种类,任何阶次的线性控制系统,没有因简化所带来的误差,计算人员直接参与的工作量甚少。
This paper presents a method of calculating the frequency characteristics using the state equation of a linear control system. The frequency characteristic is usually calculated using the transfer function G (jω)) and substituting S = jω. However, it is often difficult to solve the explicit expression of the transfer function for a complex system, sometimes with many simplifications. In this paper, a new approach is proposed: the numerical calculation of frequency characteristics does not require the explicit expression of transfer function, but expresses the quantitative relationship between output and input by a set of equations which are evolved from the state equation Come. This method has good generality and can be applied to any type of linear control system of any order without the error caused by simplification. Therefore, there is very little direct work on the part of calculators.