应用平衡截断的模型降阶

Model reduction using balanced truncation

将高阶系统降为低阶系统研究是控制理论的一个基本方法,平衡截断方法是一维系统降阶的有效方法.受一维降阶方法的启发,研究了二阶线性时不变系统的降阶方法.简单的介绍了一维能控性、能观性、Gramian矩阵和一阶系统的平衡截断方法和基本思想.通过分析二阶系统和一阶系统之间的关系,定义了二阶能控性和能观性Gramian矩阵,将一阶平衡截断的方法应用到了二阶系统.在保持二阶系统结构的前提下构造一个维系统,将著名的平衡截断技巧应用于本文定义的二阶Gramians矩阵,对二阶模型进行降解.同时给出了两种降阶算法并证明这种算法是保持二阶结构的.

To study higher order systems in control theory,it is a usual method that higher order systems are reduced to lower order systems.The balanced truncation technique have well applied to one-order systems.Motivated by the method of one-order system reductions,in this paper we study the reduction method for two-order LMI systems.We briefly introduce the controllability、observability、gramian matrix and the method and idea of the balanced truncation techniques for one-order systems.By analyzing the relationship between the one-order system and two-order system,the objective of this paper is to constructing a reduced system by preserving the second-order structure of the original system.This model reduction method uses a variant of the well-known balanced truncation technique applied to second-order gramians.We also give two reduction computing methods and a proof that the method do preserving the second-order structure.