Open loop robust vibrational stabilization of a two wire system inside the snap-through instability region

Snap-through instabilities occur in the dynamics of several classes of electromechanical systems which are of interest in connection with a number of actuator technologies. We describe two types of electromechanical devices (electrostatic and electromagnetic) for which snap-through instabilities occur, and we propose and analyze a novel open-loop oscillatory control design for stabilizing the operation of a prototype electromagnetic system (which we call the two-wire system) inside the snap-through instability region. We argue that this design has several advantages over competing feedback designs in terms of implementation cost and robustness. Our approach involves averaging theory and the design of an averaged potential function around whose critical points the dynamics of the controlled system is organized. A globally stabilizing control law is designed by parametrically shaping the averaged potential. Practical features of the control law are discussed, and the performance of the controlled system is shown to be robust with respect to a class of disturbances