Nonlinear Active Cancellation of the Parametric Resonance in a Magnetically Levitated Body

An active control strategy for the stabilization of parametric resonance in a magnetically levitated body is proposed. The characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated with the motion of a pendulum-type vibration absorber driven by an appropriate control torque. As a distinguished feature, the proposed control method does not rely on the effective autoparametric energy transfer between the main system and the absorber. Because the main system is not linearly coupled with the absorber, the drawback inherent in the increase of the system degrees of freedom (i.e., the increase of the linear vibrational mode for the main system due to the attachment of the absorber) is overcome. The effective frequency and amplitude of the pure-tone control input—the torque driving the vibration absorber—are designed so that the nonlinear action of the pendulum on the main system counteracts the effect of the resonant parametric excitation. The effectiveness of the theoretically proposed control method is experimentally validated using an apparatus that comprises a phase-lock loop system.