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

This paper studies sliding-mode control of a class of multibody underactuated systems with discontinuous friction on the unactuated configuration variable taking into account parametric uncertainties. Global motion for this class system including sticking, stick-slip, and slip regimes are analysed, and their corresponding equilibria are identified. The control objective is to avoid the sticking and the stick-slip regimes while tracking a desired velocity in the slip regime. Three sliding-mode controllers which are robust to parametric uncertainties are proposed, and their stabilities are proved 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.