Partial-energy-shaping control for orbital stabilization of high frequency oscillations of the Furuta pendulum

We consider the problem of creating oscillations of the Furata pendulum around the open-loop unstable equilibrium. Following a proposed technique, we start with shaping the energy of the unactuated link. An dissipativity-based controller is designed to create oscillations, neglecting possibility of unbounded motion of the directly actuated link. After that, an auxiliary linear feedback action is added to the control law, stabilizing a desired level of the reshaped energy. Parameters of the controller are tuned to approximately keep the originally created oscillations but ensuring bounded motion of both links. The analysis is valid only for oscillations of sufficiently high frequency and is based on higher order averaging technique. Performance of the designed controller is verified using numerical simulations and experiments.