Optimal second order sliding mode control for linear uncertain systems

•A robust optimal control strategy for linear uncertain systems is proposed.•The proposed controller is an optimal second order sliding mode controller.•The optimal controller is designed using linear quadratic regulator technique.•Second order sliding mode is realized by employing a combination of integral and terminal sliding surfaces.•Chattering phenomenon in the control input is reduced.

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.