一类变时滞参数不确定系统的预见重复控制  

Preview Repetitive Control for a Class of Parameter Uncertain Systems with Time-varying Delay

作　　者：李丽[1] 孟晓华 卢延荣 LI LI;XIAOHUA MENG;YANRONG LU(School of Statistics and Mathematics,Hubei University of Economics,Wuhan 430205,China;College of Electrical and Information Engineering,Lanzhou University of Technology,Lan Zhou 730050,China)

机构地区：[1]湖北经济学院统计与数学学院,武汉430205 [2]兰州理工大学电气工程与信息工程学院,兰州730050

出　　处：《应用数学学报》2024年第4期618-642,共25页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(61903130);湖北省自然科学基金(2024AFB885);山东省自然科学基金资助项目(ZR2020QA036)资助。

摘　　要：预见控制能够利用已知的未来目标值信息或干扰信息来改善控制系统性能,重复控制将人类的学习机制引入控制系统,它们都在众多实际工程领域得到很好的应用.当目标值信号为周期信号且可预见时,针对一类变时滞参数不确定系统,本文考虑变时滞系统的预见重复控制问题.首先,引入重复控制器、采用预见控制理论中误差系统的方法及离散二维模型,建立包含未来目标值信号信息的二维扩大误差系统,将原系统的预见重复控制器设计问题转化二维扩大误差系统的输出反馈控制问题;然后,针对二维扩大误差系统,考虑输出反馈时,改造输出方程、融合可预见信号的未来信息和重复控制器.利用Lyapunov稳定性理论和线性矩阵不等式技巧给出系统渐近稳定的条件及预见重复控制器的设计方法.最后两个仿真实验验证了该方法的有效性.Preview control can improve control system performance by utilizing future desired ox external disturbance information,repetitive control introduces human learning mechanism into the control system.Therefore,more and more applications are seen in various real engineering fields,attracting a wide spread attention of researchers.For a class of uncertain system with time-varying delay,the problem of preview repetitive control(PRC)is proposed under the assumption that the reference signals are previewed and periodic.First,the repetitive controller is introduced and the error system in the preview control theory is adopted,and an two-dimensional(2D)augmented error system is constructed.This leads to the problem of preview repetitive controller's design being transformed into a output feedback control problem of the augmented error system.Then,for the 2D augmented error system,the output equation is modified to fuse the previewed future information and the repetitive controller while considering output feedback.Based on Lyapunov method and LMI technique,the conditions of asymptotic stability of the closed-loop system and the design method of the preview repetitive controller are given.Finally,the effectiveness of the proposed method is illustrated by two simulation experiments.

关 键 词：二维扩大误差系统 预见重复控制 重复控制 预见控制 变时滞系统 输出反馈 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]