Adaptive Second-Order Sliding Mode Control Design for a Class of Nonlinear Systems with Unknown Input

You Zheng,Jianxing Liu,Xinyi Liu,Dandan Fang,L Wu

doi:10.1155/2015/319495

Abstract

An adaptive second-order sliding mode controller is proposed for a class of nonlinear systems with unknown input. The proposed controller continuously drives the sliding variable and its time derivative to zero in the presence of disturbances withunknownboundaries. A Lyapunov approach is used to show finite time stability for the system in the presence of a class of uncertainty. An illustrative simulation example is presented to demonstrate the performance and robustness of the proposed controller.

Highlights

Sliding mode control (SMC) has gained much attention due to its attractive characteristics of finite time convergence and robustness against uncertainties [1,2,3]
Robustness of a control system is essential based on the reason that various uncertainties exist in practical systems
An adaptive-gain approach will be adopted when designing super-twisting control law (STW) control law, which does not require the bounded value of σ

Summary

Introduction

Sliding mode control (SMC) has gained much attention due to its attractive characteristics of finite time convergence and robustness against uncertainties [1,2,3]. Robustness of a control system is essential based on the reason that various uncertainties exist in practical systems. These nonlinear systems are with structured and unstructured uncertainties and external disturbances such as load variation. The discontinuous control function is replaced by “saturation” or continuous “sigmoid” functions in [27, 28] Such approach constrains the sliding system’s trajectories not to the sliding surface but to its vicinity losing the robustness to the disturbances. Based on the Lyapunov theory, the proposed control law continuously drives the sliding variable and its time derivative to zero in the presence of bounded unknown input but without knowing the boundary. The stability and the robustness of the control system are proven, and the tracking performance is ensured

Problem Formulation

Adaptive-Gain STW Controller Design

Simulation Results and Discussions

Conclusions