A novel design of robust relay-discontinuous sliding mode controller for robot manipulators with parameter perturbations

This paper represents a new approach for the design of variable structure control of robot manipulator systems with parameter perturbations. A new sliding mode control law is introduced with the idea of constructing a discontinuous relay controller. The approach is based on establishing the sufficient conditions for the existence of a sliding mode in the robot arm system. The techniques of matrix norm inequalities are used to cope with robustness issues. Moreover, some effective parameter-independent conditions are developed in a concise manner for the globally asymptotic stability of the multivariable system using linear matrix inequalities (LMI) and principle of Rayleigh´s min/max matrix eigenvalue inequality. The stability conditions are derived by using the Lyapunov full quadratic form which is introduced to the robust robot control for the first time. By the newly derived sliding and stability conditions, a new variable structure control law is designed for the stabilization of the robot motion with parameter perturbations. The parameter perturbations of the robot motion are evaluated by the Frobenius norm. Simulation results have shown that the control performance of the robot system is satisfactory.