Abstract: For a class of uncertain linear discrete systems,a preview compensation and observer based design method of repetitive controller was proposed.To improve the tracking performance,the preview information was introduced to the controller and the design problem of the repetitive controller was transformed into a stability problem of a class of two-dimensional linear discrete systems.Using linear matrix inequality (LMI),the method of solving parameters for preview repetitive controller was obtained.On this basis,the observer-based preview repetitive control was further investigated by considering the unobservable state of the system.The validity of the proposed method was verified by a numerical simulation of linear motor tracking control.

Key words: linear matrix inequality, two-dimensional model, repetitive control, discrete system, repetitive control, observer, preview compensation

摘要： 针对一类不确定线性离散系统,提出一种基于预见补偿和观测器的重复控制器设计方法。首先,为提高跟踪精度,将预见信息引入控制器,并将重复控制器的设计问题转化为一类二维线性离散系统的稳定性问题。然后,通过线性矩阵不等式(LMI)方法,获得预见重复控制器的参数求解方法。在此基础上,考虑到系统状态不可观测,进一步考虑线性离散系统基于预见补偿和观测器的重复控制器设计问题。最后,通过直线电机跟踪控制数值仿真验证了所提方法的有效性。

关键词: 线性矩阵不等式, 二维模型, 预见控制, 离散系统, 重复控制, 观测器, 预见补偿