Control of a class of multibody underactuated mechanical systems with discontinuous friction using sliding-mode

Abstract

This paper studies sliding-mode control of a class of multibody underactuated systems with discontinuous friction presenting on the unactuated configuration variable with consideration of parametric uncertainties. Global motion for this class system including sticking, stick-slip, and slip regimes are analyzed, and their corresponding equilibria are identified. Our control objective is to avoid the sticking and stick-slip regimes while track a desired velocity in the slip regime. The proposed sliding-mode controllers are robust to parametric uncertainties, and their stabilities are proved by using the Lyapunov direct method. Two examples, a mass-spring-damping system and a drill-string system, are used to demonstrate the validity of the proposed controllers.