基于内平衡变换和Riccati方程的模型降阶及应用

Based on Internal Balance Transform and Riccati Equation Model Reduction and Application

对于一个高阶的控制系统,为了实现对其适时控制,需要一个降阶模型与之对应,对此低阶模型设计控制器以达到对原系统控制的目的。首先,在内平衡变换的基础上,确定降阶模型的阶数;其次,通过解一个Riccati方程得到一个变换矩阵,进而得到降阶以后的模型;然后,介绍了两种经典的模型降阶方法,以作为与此方法的比较。最后,对两个实例进行了仿真计算。计算表明,此方法是有效和可行的。

It is always difficult that a higher rank model system is controlled. Hence,a reducing model is often needed to equal to the original system in order to control timely. So, a controller is designed for this lower rank model so as to reach the same goal with the original system. Firstly, the internal balance transform is used to the original system and the rank of the reduced model is determined.Secondly ,finding the linear transform through solving a Riccati equation ,the final reduced model is obtained by aggregation method. Thirdly, two classical model reduction methods are introduced so that comparing with the method of this paper.Finally,the simulation is made for the two practical examples. It is shown that the calculating result is satisfied, the method is reasonable and effective.