在频率域上具有稳定性约束的线性系统的模型简化

Simplification of Linear System Model with stability Constraits in Frequency Domain

摘要: 本文作者曾经提供在最小二乘方的误差意义下有关高阶传递函数简化成低阶传递函数的一种频率域上的简化方法．曾经也通过具有纯滞后的一阶惯性环节（或二阶振荡环节），并借助Pade近似式首先将具有纯滞后的传递函数简化；同时就以得到具有Pade近似的一阶惯性环节（或二阶振荡环节）的低阶传递函数，而在最小二乘方的误差意义下作为有关高阶传递函数的近似式．不过，上述的简化低阶传递函数所描述的系统有可能是不稳定的．本文针对这个问题，提出在最小二乘方的误差的要求下还考虑稳定性约束条件．这样一来，将频率域上模型简化问题转化成具有不等式约束的最优化问题．因此，就可借助罚函数法解决线性系统模型在频率域上简化问题，同时简化模型所描述的系统仍是稳定的．

Abstract: In one of previous papers by tbe same author was proposed a simplified system describedwith lower order transfer functions, and yet the system obtained might happen to be not so stable.In this paper and for the purpose of tackling this problem, a new frequency simplification techniquewith stability into consideration is presented to simplify a transfer function of high dimension intoone of lower dimension by means of least squares so as to achieve a stable system.