Robust position and tracking variable structure PD-controllers design methods for robot manipulators with parameter perturbations

In this paper two types of new variable structure PD-like controllers with and without full dynamics knowledge are designed for position and tracking stabilization of robot manipulator systems with parameter perturbations. The main contribution of this work is the design of the tracking PD-controller for robot manipulators without using full dynamics knowledge. The position controller is built upon the well-known equivalent control method. The tracking controller does not require any exact information about the robot manipulator dynamics and employs only the measurable joint variables and bounds of some robot perturbed parameters. The sufficient conditions for the existence of a sliding mode and the rate of convergence are investigated. Moreover, the global asymptotical stability conditions are also derived with a Lyapunov full quadratic form used for the first time. Linear matrix inequalities are often addressed. Reduced design conditions are also derived. Both analytical and numerical comparisons with the Qu and Dorsey control laws and stability results are also emphasized. Simulations are carried out with a two-link direct drive robot arm model. The simulation results have shown that the control performance of the designed system is satisfactory.