带非同位干扰执行动态有限维系统的输出追踪

Output tracking of finite dimensional system with actuator dynamics subject to non-collocated disturbance

本文考虑了边界带有非同位干扰的波动方程和常微分方程串联系统的性能输出追踪问题.边界带有非同位干扰的波动方程可以看作常微分方程控制系统的执行动态.通过利用轨道规划方法将非同位干扰变换到控制通道,于是克服了非同位干扰带来的困难.与现有Backstepping方法不同,文章利用动态补偿法给出了一个新的状态反馈控制器,使得控制器设计以及所设计的控制器本身更加简单,证明了闭环系统解的一致有界性与性能输出的指数追踪.数值模拟表明,所给的方法是非常有效的.

In this paper,the performance output tracking problem of cascade system about wave equation subject to unmatched disturbance on the boundary and ordinary differential equation is considered.The wave equation with unmatched disturbance on the boundary can be used as the actuator dynamics of ordinary differential equation control system.By using trajectory planning method to transform the non-collocated disturbance to the control channel,the difficulty caused by the non-collocated disturbance is overcome.Different from the existing backstepping method,this paper presents a new state feedback controller by using the dynamic compensation method,which makes the design of the controller and the controller itself are much simpler.As a result,the uniform boundedness of the solution of the closed-loop system and the exponential tracking of the performance output are proved.The numerical simulation shows that the proposed method is very effective.