Adaptive PID control of robot manipulators with H<inf>∞</inf> tracking performance

Abstract

This paper proposes a novel adaptive robust PID controller to deal with the trajectory tracking of robot manipulators with nonlinear uncertainties and disturbances. Based on the classical PID controller, an adaptive PID controller is designed to deal with the nonlinear uncertainties of the system. The adaptation mechanism which is motivated from the sliding mode control derived for tuning three PID control gains is to minimize the sliding condition in this study, so as to accelerate the convergent speed of sliding mode surface to reduce the tracking error. To guarantee the stability of the control system with nonlinear uncertainties, a supervisory controller is proposed to compensate the error between the adaptive PID controller and the ideal controller which is derived from the nominal plant. It attenuates the uncertainties and the external disturbances in the sense of the Lyapunov function with the specified H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> tracking performance. The designed controller is unrelated to the model errors and has some merits such as good robustness, simple calculation, easy application and so on. And some guidelines of setting control parameters and the effects of them are also proposed. Finally simulations based on a two-joint robot manipulator and comparison with classical PID controller show that the present controller performs well in application.