滑模控制系统中的芝诺行为研究  

Research on Zeno Behavior in Sliding-mode Control Systems

作　　者：王忠明 于灏 WANG Zhongming;YU Hao(The Education Examination Authority of Jilin Province,Changchun,Jilin 130033,China;School of Automation,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]吉林省教育考试院,吉林长春130033 [2]北京理工大学自动化学院,北京100081

出　　处：《控制与信息技术》2024年第3期45-52,共8页CONTROL AND INFORMATION TECHNOLOGY

基　　金：国家自然科学基金优秀青年科学基金项目(海外)。

摘　　要：滑模控制器作为典型的变结构非连续控制器,因具有鲁棒性强、结构简单等优点被广泛应用,但其切换特性也会引入抖振、切换时延等不良现象。文章从混杂动力学及芝诺行为的角度出发,对滑模控制系统中的抖振现象提出新的解释与分析。首先,通过对能够以任意频率瞬时完成控制信号切换的理想滑模控制系统进行分析,得到了其存在芝诺行为的充分条件;接着,考虑了两类现实滑模控制器的开关器件约束,即具有正切换间隔下界及具有迟滞现象;并在理想滑模控制器芝诺行为的理论分析结果基础上,讨论了上述两类现实滑模控制系统中抖振现象与理想滑模控制器芝诺行为间的关系;最终,证明了理想滑模控制器的不可实现性与现实滑模控制器中抖振现象的不可避免性。Sliding-mode controllers,typically featuring variable structures and a discontinuous mode,have been widely applied due to their robustness and straightforward structures.However,their switching characteristics also introduce adverse effects such as chattering and switching delays.This paper focuses on explaining and analyzing chattering in sliding-mode control systems from novel perspectives surrounding hybrid dynamics and Zeno behavior.An initial analysis on an ideal sliding-mode control system capable of switching control signals instantaneously at any frequency,revealed the sufficient conditions for Zeno behavior occurrences.Subsequent investigations incorporated constraints of switching devices in two types of sliding-mode controllers in real applications:those with a lower bound on positive switching intervals and those exhibiting hysteresis.Building upon the theoretical results related to the Zeno behavior in the ideal sliding-mode controller,this study examined the correlation between chattering in these two types of sliding-mode control systems and the Zeno behavior of the ideal sliding-mode controller.The study results finally demonstrated the impracticality of ideal sliding-mode controllers and the inevitability of chattering in sliding-mode controllers in practical applications.

关 键 词：滑模控制 混杂动力学系统 芝诺行为 抖振现象 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]