线性周期系统特征指数的配置

Characteristic Exponent Assignment for Linear Periodic System

线性周期系统的稳定性完全由它的特征指数决定,该文研究如何配置线性周期系统的特征指数.为了配置特征指数,首先需要用旋转变换将原系统化简成块能控标准形.在块能控标准形的基础上文中提出一种设计周期状态反馈的方法,可以任意配置线性周期系统的特征指数.文章还给出了一个线性周期系统特征指数可以任意配置的充分条件.此设计方法曾应用于磁控小卫星的控制器设计,仿真结果表明,采用该文提出的设计方法控制线性周期系统是非常有效的.

The stability of the linear periodic system is determined by it's characteristic exponent. This paper studies how to assign characteristic exponent for linear periodic system. In order to do this, the original system has to be converted to the block controllable form by rotating transform first. Then based on the block controllable form, a method to design a periodic state feedback control law is presented, which can arbitrarily relocate the system's characteristic exponents. A sufficient condition that characteristic exponent can be assigned arbitrarily for linear periodic system is also attained. The method is applied to controller design of small satellite using magnet-torquer. The simulation result demonstrates the validity of this method to control the linear periodic system.