Constructive feedback linearization of mechanical systems with friction and underactuation degree one

This paper presents a constructive methodology to control a class of unstable underactuated mechanical systems with underactuation degree one, by means of classical feedback linearization and Lyapunov design. The design is presented proposing a dummy output that allows to redesign it in a constructive way to solve the problem. We prove that the proposed output solves the problem yielding an explicit and compact control law. The stability of the obtained solution does not change taking into account the friction effects even in the unactuated coordinate. The new result is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling and a controller for the Inertia Wheel pendulum with friction.