Generating oscillations in inertia wheel pendulum via two-relay controller

The problem of generating oscillations of the inertia wheel pendulum is considered. We combine exact feedback linearization with two-relay controller, tuned using frequency-domain tools, such as computing the locus of a perturbed relay system. Explicit expressions for the parameters of the controller in terms of the desired frequency and amplitude are derived. Sufficient conditions for orbital asymptotic stability of the closed-loop system are obtained with the help of the Poincaré map. Performance is validated via experiments. The approach can be easily applied for a minimum phase system, provided the behavior of the states of the zero dynamics is of no concern.