Design and Tuning of Robust Proportional-Derivative Sliding-Mode Control (PD-SMC) in Stabilization of 2-DOF Robot Manipulator

A proportional-derivative sliding-mode control (PD-SMC) scheme is addressed for tracking problem of a two-degree of freedom robot manipulator. The sliding-mode control (SMC) may be a robust method in presence of parameters change and system uncertainties. In a typical control problem, the proportional-derivative (PD) control law provides a fast response while the stability of the closed loop system is increased. Hence a two degree of freedom robot manuplator is considered. Then the asymptotic stability of closed loop system with the PD-SMC policy would be shown by using of the well-known Lyapunov stability theory. As a result of this paper, the asymptotic stability criteria would be checked in term of some simple matrix inequalities. Having satisfaction of such matrix inequalities in the tracking problem of the robot manipulator, the tracking error and its derivative would be converged to zero. In order to compare the results with the other control approaches, the controller parameters are firstly tuned in an optimization way via the genetic algorithm (GA) method. Then some numerical examples are provided to show the effectiveness and robustness of the PD-SMC in comparing with the existing methods.