周期离散时间系统的预见控制器设计  

Design of preview controller for periodic discrete-time systems

作　　者：李丽 任祯琴[2] 于晓 LI Li;REN Zhen-qin;YU Xiao(School of Information Management and Statistics,HubeiUniversity of Economics,Wuhan 430205,China;School of Information Technology,Luoyang Normal University,Luoyang 471934,China;School of Science,Shandong Jianzhu University,Jinan 25010l,China;Hubei Data and Analysis Center,Hubei University of Economics,Wuhan 430205,China)

机构地区：[1]湖北经济学院信息管理与统计学院,武汉430205 [2]洛阳师范学院信息技术学院,河南洛阳471934 [3]山东建筑大学理学院,济南250101 [4]湖北经济学院湖北数据与分析中心,武汉430205

出　　处：《控制与决策》2022年第10期2585-2592,共8页Control and Decision

基　　金：国家自然科学基金项目(61903130);山东省自然科学基金项目(ZR2020QA036);湖北省教育厅科研重点项目(D20192202);湖北经济学院科研培育项目(PYZD202005,PYYB202007)。

摘　　要：对于一类线性周期离散时间系统,提出一种新的周期预见控制器的设计方法.首先,利用二维模型方法及系数矩阵的周期性特点,将系统状态与其稳态值之差代替通常的状态差分,成功地构造出原系统的二维(2D)扩大误差系统;然后,针对导出的扩大误差系统,结合Lyapunov稳定性理论和LMI方法,给出闭环系统渐近稳定的条件及预见控制器的设计方法;最后,通过数值仿真说明该方法的有效性.This paper presents a new periodic preview controller design method for a class of linear periodic discrete-time systems. Firstly, the difference between the system state and its steady-state value is substituted for the normal state difference, and the two-dimensional augmented error system of the original system is constructed successfully using a two-dimensional(2D)-based approach and the periodicity of system matrices. Then, for the augmented error system,based on the Lyapunov stability theory and the LMI method, sufficient conditions for the close-loop system to be stable and the design of a periodic controller with preview actions are proposed. Finally, numerical simulation example is given to illustrate the effectiveness of the proposed method.

关 键 词：扩大误差系统 周期系统 二维系统 预见跟踪控制 输出反馈 线性矩阵不等式 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]