带有常数干扰的正则线性系统的镇定

Stabilization of the regular linear system with constant disturbance

本文考虑带有常数干扰的抽象正则线性系统的状态反馈镇定问题.本文控制设计采用线性系统的动态补偿方法,将传统的PID控制推广到无穷维正则线性系统.通过引入积分作用,控制器可以有效地补偿常数干扰.论文给出了具体的状态反馈法则,并证明了对应闭环系统的指数稳定性.理论结果被应用于带有常数干扰的不稳定热方程,给出了控制器及其闭环系统的指数稳定性,数值仿真验证了本文理论结果的有效性.

In this paper,we are concerned with the stabilization problem of the regular linear system with the constant disturbance.The method of dynamic compensation for the linear system is used to the controller design.The conventional PID control is extended to the infinite-dimensional regular linear systems.By introducing the integral action,the controller can compensate for the constant disturbance effectively.The concrete state feedback law is proposed and the exponential stability of the corresponding closed-loop system is proved in this paper.The theoretical results are applied to the unstable heat equation with constant disturbance.Both the controller and its exponential stability of the corresponding heat closedloop system are given.The numerical simulation is given to show the effectiveness of the obtained theoretical results.