Robust Stabilization of a Class of Underactuated Mechanical Systems of 2 DOF via Continuous Higher-Order Sliding-Modes

In this chapter we design robust controllers for a Class of underactuated mechanical systems of two DOF, using a continuous Higher Order Sliding-Mode strategy. Two kinds of controller designs are presented: One generates a fifth-order sliding-mode and achieves Local Finite-Time Stability (LFTS). The other one is a robust controller that provides Global Asymptotic Stability (GAS). These controllers compensate matched Lipschitz disturbances and/or uncertainties, cope with an uncertain control coefficient and generate a continuous control signal, possibly reducing the chattering effect. We provide evidence of the performance of the controllers using 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.