On the renovation and analysis of high order sliding mode approaches with application to robotic systems

Abstract

Variable structure control (VSC) approaches have been widely used to study nonlinear or ill-defined systems. While sliding mode methods can enhance the system robustness, a chattering phenomenon degrades system performances. In order to reduce this phenomenon appearing on the control law, several concepts have been proposed, particularly those called high order sliding mode (HOSM) approaches. In this paper, a renovated theorem of HOSM based on high order procedures has been presented, aiming to improve and to simplify the implementation of HOSM controllers. As the stability of dynamical systems is a fundamental requirement for its practical value, an original proposal for developing general forms of the Lyapunov equation matrices has been demonstrated for high orders of sliding modes, which are essential for the HOSM stability analysis-based Lyapunov theory. Simulation results present control comparisons between motion control behaviours of a robotic system controlled by the proposed HOSM approaches.