Tracking control for inverted orbital stabilization of inertia wheel pendulum—Trajectory generation, stability analysis, and experiments

A second order sliding mode control is developed to solve the tracking control problem for an inertia wheel pendulum. The desired trajectory is centered at the upright position where the open-loop system becomes a non-minimum-phase system. We have recently proved that a two relay controller produces oscillations at the scalar output of an underactuated system where the desired amplitude and frequency are reached by choosing its gains. In this paper we go much further and develop a reference model, based on two-relay controller, to generate a set of desired trajectories for the inertia wheel pendulumallowing us to design a robust tracking controller. Performance issues of the constructed controller are illustrated in an experimental study.