Finite Time Adaptive Smooth Non Linear Sliding Mode Control for Second  Order Dynamic Systems

Abstract

In this paper, a feedback control law that employs an adaptive smooth nonlinear approximation of the Super-Twisting ( STW ) algorithm is presented in order to generate a smooth control law capable of regulating in finite time a second-order system that is affected by unknown disturbances and uncertainties. A nonlinear sliding surface is created in order to set the desired dynamics of the response, so that the control law is proposed to establish global properties of stability for unperturbed and perturbed systems. More specifically, the method entails determining parameters that eliminate chattering in noise-free models by means of a simple cut-off frequency design parameter approach. Therefore, the approach is characterized by its simplicity and robustness. A second order mechanical system is used to demonstrate the effectiveness of the proposed approach.