Design fractional-order terminal sliding mode controller for a class of fractional-order matched uncertain systems

In this study, a new fractional-order terminal sliding mode controller (FOTSMC) is designed for stabilization of a class of fractional-order nonlinear systems in the presence of matched uncertainties and external disturbances. Fractional-order terminal sliding mode control which is combination of terminal sliding mode control with the fractional calculus is a fast and robust control method for uncertain dynamical systems. The matched uncertainties mean the uncertainties and disturbances which appear in the same channel that the control signal there is. According to design procedure of sliding mode control (SMC), first, a proper fractional -order terminal switching surface is presented. Then, through using the Lyapunov stability theory and SMC theory, a robust fractional-order control law is designed to guarantee the existence of the sliding motion in finite time. The proposed fractional-order fast terminal sliding mode controller ensures fast, finite time and robust stability of the fractional-order nonlinear dynamical systems, counteracts the disturbances and uncertainties as well as alleviates the chattering problem. Finally, the effectiveness of the presented control strategy is depicted via simulation results of practical examples.

Keywords:

Terminal sliding mode control , Fractional calculus , Finite time stability , Lyapunov stability theory , Fractional-order matched uncertain systems