Time-Varying Second-Order Sliding Mode Control for Systems Subject to External Disturbance

Jie Wu,Xiaodi Li,Haitao Zhu

doi:10.1109/access.2020.3029255

Abstract

In this article, the design problem of a class of novel second-order sliding mode controller for systems subject to external disturbance is investigated, where the sliding variable is affected by a time-varying regulation. On the one hand, for the unmatched disturbance bounded by positive functions, a second-order sliding mode controller is proposed to prove the finite-time stability of aforementioned system through the backstepping-like method and virtual control strategy. On the other hand, for the non-vanishing bounded disturbance, a non-singular terminal sliding mode surface containing disturbance observations is designed via a finite-time disturbance observation method and the finite-time stability of the system controlled output is realized. The claimed performances of the proposed methods are validated by two simulation examples.

Highlights

Over the past decades, finite-time control method has received much research attention owing to its advantages in fast transient and high-precision performances [1]–[3]
Lots of interesting results on finitetime stability (FTS) have been raised from theoretical and practical points of view. [4] proposed Lyapunov theorem on FTS of continuous autonomous systems, which provided a basic tool for analysis of FTS of nonlinear control systems
In this article, we will investigate the time-varying second-order sliding mode (SOSM) controller design for systems subject to external disturbance, and strive to achieve the FTS of system under two situations of disturbance: disturbance bounded by positive functions and non-vanishing bounded disturbance

Summary

INTRODUCTION

Finite-time control method has received much research attention owing to its advantages in fast transient and high-precision performances [1]–[3]. Compared with sliding mode based on linear hyperplanes, TSM have some superior properties, such as fast, efficient, and finite-time convergence This controller is useful for high precision control as it speeds up the rate of convergence near an equilibrium point. For the singularity of TSM controller, [19] presented a global non-singular terminal sliding mode (NTSM) controller for a class of nonlinear dynamical systems with parameter uncertainty and external disturbance. In this article, we will investigate the time-varying SOSM controller design for systems subject to external disturbance, and strive to achieve the FTS of system under two situations of disturbance: disturbance bounded by positive functions and non-vanishing bounded disturbance. The symbol Ci denotes the set of all differentiable functions whose first ith time derivatives are continuous

PRELIMINARIES

Design

EXAMPLES

CONCLUSION