Smooth second-order sliding mode controller for multivariable mechanical systems

Abstract

Abstract This paper proposes a smooth second-order sliding mode controller for a class of multi-input multi-output mechanical systems with uncertain parameters and external disturbances. Since the control law is smooth, the chattering effect that can occur with non-smooth controllers is reduced. Lyapunov-based theorems are used to prove global and finite-time convergence of the sliding mode controller. Numerical simulations are presented to illustrate the performance of the proposed controller by applying it first to a variable-length pendulum and then to a two-link robotic manipulator. For the robotic manipulator, a detailed comparison is given of the finite-time convergence and chattering properties of the proposed controller, a super-twisting controller and a super-twisting like controller. Article Highlights A new smooth second-order sliding mode controller is proposed for multivariable systems with uncertain parameters and external disturbances. Global finite-time convergence of the controller is proved using Lyapunov theory. Numerical simulations are used to show the performance of the controller on the variable-length pendulum and two-link robotic manipulator.

Keywords

• Finite-time convergence
• Second-order sliding mode control
• Smooth sliding mode control
• Multi-input multi-output system