具有跟踪鲁棒性能的H_∞最优预见控制  

H_∞ optimal preview control with robust tracking performance

作　　者：李丽[1] 廖福成[1] 

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《工程科学学报》2015年第10期1376-1386,共11页Chinese Journal of Engineering

基　　金：国家自然科学基金资助项目(61174209)

摘　　要：研究了一类不确定离散时间系统的鲁棒H∞预见控制问题.其中采用一种新的方法构造扩大误差系统,避免对时变的系数矩阵取差分,从而成功构造简化的扩大误差系统.然后针对所求得的不确定系统的扩大误差系统,通过引入带有预见作用的状态反馈,研究鲁棒H∞保成本控制问题,得到确保鲁棒H∞控制器存在的充分条件及H∞状态反馈控制器的设计方法.该条件可以通过求解一个线性矩阵不等式优化问题而实现.所得控制器回到原系统就得到带有预见作用的最优预见控制器.而且,通过引入积分器,实现闭环系统对目标值信号的鲁棒无静差跟踪.最后的数值算例说明了本文理论的有效性.A robust H∞preview control problem is proposed for a class of uncertain discrete-time systems. A new method is derived to construct an augmented error system,avoiding applying the difference operator to the time-varying matrix,and simplify the augmented error system. Then for the augmented error system of the uncertain system,the problem of guaranteed cost robust H∞control is considered via a state feedback with integral and preview actions. The sufficient condition for the existence of the robust H∞controller and H∞state feedback controller design methods are presented. The condition can be realized by solving a linear matrix inequality optimization problem. By putting the controller obtained into the original system,we can get the preview controller. Moreover,introducing an integrator makes the closed-loop system robustly track the reference signal without steady-state error. The effectiveness of the proposed method is shown by numerical simulation.

关 键 词：离散时间系统 预见控制 鲁棒性 线性矩阵不等式 积分器 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]