New variable structure PD-controllers design for robot manipulators with parameter perturbations

In this article two types of new variable structure PD 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 PD-controller is built upon the conventional equivalent control approach when full robot dynamics model is well known. In this case, equivalent control cancelled the robot dynamics almost completely, and switching part of the controller is used only for establishing the sliding mode and for providing global asymptotical stability of the robot system. However, the tracking PD-controller does not use an equivalent control term and requires no 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, as this approach is different from existing ones, 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 better than that of existing systems.