Research on Zeno Behavior in Sliding-mode Control Systems

Abstract

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.

Keywords

• sliding-mode control
• hybrid dynamical systems
• zeno behavior
• chattering