Robust global second-order sliding mode control with adaptive parameter-tuning law for perturbed dynamical systems

Abstract

This paper offers an adaptive global second-order sliding surface for perturbed dynamical systems with matched and unmatched external disturbances. Based on the composite nonlinear feedback theory, a nonlinear function Ψ( x1) is employed in the switching surface to adjust the damping ratio of the controlled system. Initially, using a constant gain matrix, a small value of the damping ratio is achieved presenting a fast performance. As the system state converges to the origin, the damping ratio of the closed-loop system is increased that yields fast settling time and a low overshoot. A novel smooth and chattering-free controller is proposed to fulfill the removal of the reaching mode and the existence of the sliding behavior around the surface from the beginning. The adaptive gain tuning controller reduces the required information for the upper bound of disturbances. Moreover, the selection of the constant parameters μ1 and τ1 for the control law is turned into a cost function and solved by a particle swarm optimization method. Several criteria are derived to assure the robust stability of the uncertain dynamical system. Some simulations are offered to demonstrate the effectiveness of the planned technique.