A novel robust adaptive second-order sliding mode tracking control technique for uncertain dynamical systems with matched and unmatched disturbances

This paper investigates a robust adaptive second-order sliding mode control method for tracking problem of a class of uncertain linear systems with matched and unmatched disturbances. The fundamental idea of the suggested control method is that the discontinuous sign function is used for the time-derivative of the control signal and hence the smooth control input achieved after an integration process is continuous and removes the chattering problem. Using a PID sliding surface, the finite-time convergence of output tracking errors is obtained. The adaptive gain-tuning control law removes the necessity of gaining information about the upper bounds of the external disturbances. The control system is in the sliding mode and then, tracking errors converge to the origin in a finite time under the presence of the external disturbances. Simulation results on an uncertain numerical system and a turntable servo-system are presented to indicate the effectiveness and feasibility of the proposed scheme.