Robust global stabilization of a class of underactuated mechanical systems of two degrees of freedom

In this article, the global stabilization of a class of underactuated mechanical systems of two degrees of freedom (DoF) is addressed, despite the presence of Lipschitz disturbances and/or uncertainties and uncertain control coefficient in the model. Using two second-order continuous sliding modes algorithms, the control task is performed, reaching finite-time convergence in one part of the dynamics and generating a continuous control signal. The efficacy of the proposed controllers is illustrated via simulations for the reaction wheel pendulum (RWP) and the translational oscillator with rotational actuator (TORA) systems, and by means of experiments on the RWP system, comparing the presented algorithms with a linearizing controller.