A Novel Conformable Fractional-Order Terminal Sliding Mode Controller for a Class of Uncertain Nonlinear Systems

Abstract

This paper proposes a conformable fractional-order terminal sliding mode controller for a class of nonlinear systems subject to uncertainties. First, a novel conformable fractional terminal sliding surface is proposed and its finite-time stability to the equilibrium point is proven. Subsequently, a switching function with a time-varying gain is presented. The system’s stability is guaranteed by the fractional-order Lyapunov stability theorem. The reaching and convergence time are analytically calculated. The designed controller has simple calculations. The control scheme improves the convergence speed, chattering phenomena, and control effort in the presence of disturbance and uncertainty. The simulation results show the efficiency of the proposed controller.

Keywords:

• Conformable derivative
• Fractional-order derivative
• Fractional-order sliding mode control
• Lyapunov stability theorem
• Uncertain system
• Terminal sliding mode control

Additional information

Notes on contributors

Sara Haghighatnia

S Haghighatnia received the BSc degree in electrical engineering from Sadjad University of Technology, Mashhad, Iran, 2009, the MSc degree in control engineering from Islamic Azad University, Mashhad, 2012. She obtained PhD in control engineering from Shahrood University of Technology in 2019. Her fields of research are optimization, nonlinear control strategies, variable structure control and fractional control.