Finite-time Second order sliding mode control for master-slave manipulator with time delays

In this paper a finite-time second order sliding mode control for the teleoperation system in presence of uncertainties, disturbances and time delay is exposed. First, the second order fast nonsingular terminal sliding mode surface is designed to guarantee a finite time convergence and to eliminate the singularity problem. Then, a robust control law is developed to achieve high precision tracking and strong robustness against parametric uncertainties, disturbances, and time delay. The proposed idee consist to use the discontinuous function in the time derivative of the control input. Then, the proposed control, obtained by integration, is applied to the system in order to eliminate the chattering phenomenon and reduces the amplitude of the control effort. The stability of the system is demonstrated using the Lyapunov theory.