Output feedback second-order sliding-mode tracking control for perturbed inertia wheel pendulum

This paper addresses the robust output feedback tracking control problem for an inertia wheel pendulum in the presence of uniformly bounded matched disturbances. The periodic motion of the pendulum will be at the upright position which corresponds to the unstable equilibrium point of the unforced system. A two-relay-controller-based reference model was developed for generating the desired trajectories to be tracked by the unactuated link of the inertia wheel pendulum and then design an output feedback robust tracking controller. The desired amplitude and frequency were tuned by choosing the two-relay control gains properly. A second-order sliding-mode tracking controller interconnected with a second-order sliding-mode observer was capable to track the prescribed reference trajectory rejecting matched external disturbances. Performance issues of the constructed controller-observer were illustrated in a numerical study.