Estimate of the region of attraction of a Kapitza pendulum subject to an harmonic excitation and analysis of the pendulum behavior for a non harmonic excitation

In this work, we present a stability analysis of the inverted pendulum subjected to a vertical excitation in the suspension point. First we apply a harmonic excitation term and physically determine the attraction region when considering a damping term, this can be seen as the estimation of the degree of robustness of the pendulum subjected to an open loop vibrational control. Next that we apply physically two independent excitations to obtain a non harmonic excitation, which is almost always a quasi periodic function. Physically the second excitation function will be add to the pendulum using a vibrating table, due to this the stability region grows, and presents the beating phenomena that not appears for harmonic excitation.