Adaptive Nonsingular Fast Terminal Sliding Mode Tracking Control for Second-order Nonlinear Systems with External Disturbances

This paper proposes an adaptive nonsingular fast terminal sliding mode (NFTSM) tracking controller for second-order nonlinear systems with external disturbances. Firstly, a novel NFTSM mainfold is constructed to directly address the singularity issue from the perspective of sliding mode surface design and enhance the convergence speed of the tracking error. Then, in order to achieve more accurate dynamic response on the uncertain nonlinear system, a robust adaptive control strategy is introduced into the sliding mode control strategy to estimate the unknown external disturbance. The system states can converge to an arbitrarily small set around the origin within a finite time. Finally, a simulation example is included to further testify the validity of the proposed control approach.

I. Introduction

In the previous few decades, the controller design for complex nonlinear systems has attracted a great attention [1]–[3]. In most cases, practical nonlinear system models are subject to various uncertainties or external disturbances [4]. Nonlinear systems make it difficult for traditional control techniques, such as PID control [5] and feedback control [6], to meet the high-precision requirements of industrial applications [7]. With the development of modern control theory, a lot of excellent results have been reported to realize the uncertain nonlinear systems stabilization, such as fuzzy control [8], optimal control [9], adaptive control [10], learning-based methods [11] and sliding mode control (SMC) [12].