Controller Gain Selection for an Electromagnetic Suspension under Random Excitation

This paper considers the modeling and control of an electromagnetic suspension for vibration isolation. Here, the nonlinear dynamic equations for a single degree of freedom suspension are derived using a lumped-parameter model of the system that includes factors for flux leakage, fringing and finite permeability of the materials. To study the vibration isolation characteristics a set of linearized dynamic equations are used. The feedback signals considered are the airgap size, the absolute velocity of the isolated load and the current in the circuit. A stability boundary plot that illustrates the domain of controller gains that will stabilize the system is given. Also presented are design procedures that can be used to determine the controller gains that (i) minimize the mean square absolute displacement response of the suspension or (ii) minimize a measure of the system power dissipation. In both cases the suspension system is assumed to be excited by random white noise disturbances.