Variable Structure Tracking Control-Observer for a Perturbed Inertia Wheel Pendulum via Position Measurements

In this paper we address the robust tracking control problem, against unknown but bounded matched disturbances, for an inertia wheel pendulum. The interested periodic motion of the pendulum will be at the upright position which corresponds to an unstable equilibrium point of the unforced system. A two-relay controller based reference model was developed for generating the reference trajectories where a second order sliding modes controller enforces the unactuated link to follow such prescribed trajectory. The desired amplitude and frequency were tuned by choosing the two-relay control gains properly. A variable structure observer was developed to estimate the velocity of the pendulum and the wheel. Lyapunov stability analysis was made to demonstrate robustness of the closed-loop system. Performance issues of the constructed controller-observer were illustrated in a numerical study.