Stabilization of a Class of 2-DOF Underactuated Mechanical Systems Via Lyapunov's Direct Approach

Abstract

We study a class of 2-DOF underactuated mechanical systems(UAMS) where the objective is to obtain a design framework for stabilization. We propose a stabilization procedure via Lyapunov's direct approach to a class of UAMS employing partial feedback linearization and a change of coordinates. Asymptotic stability of unstable equilibrium point has been achieved in a large region of attraction and we make use of La Salle's theorem to prove it. Designed controller scheme has been successfully illustrated through simulations on two different UAMS namely the pendulum on a cart and the inertia wheel pendulum.