Vibrational Stabilization of the Kapitza Pendulum Using Model Predictive Control with Constrained Base Displacement

It is well known that, for some systems, stabilization can be achieved by open-loop control in the form of high-frequency vibrations. Vibrational control is attractive since it requires no sensors. On the other hand, however, vibrational control requires careful selection of the frequency and amplitude of the input. The present paper is aimed at understanding the robustness of vibrational control and the required control effort by applying nonlinear model predictive control to the classical Kapitza pendulum. A numerical investigation shows that closed-loop control using nonlinear model predictive control is significantly more efficient than open-loop vibrational control with respect to signal power.