Controller Gain Selection for an Electromagnetic Suspension Under Random Excitation

This paper considers the modeling and control of a single axis electromagnetic suspension for vibration isolation. Here, the nonlinear dynamic equations for the 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 air gap size, the absolute velocity of the isolated load and the current in the coil. Stability boundary plots that illustrate the domain of controller gains that will stabilize the system are presented. It is shown that feedback stabilization can be achieved without current feedback. The paper also considers the design of state feedback controllers that (i) minimize the mean square absolute displacement response of the suspension and (ii) minimize a measure of the system energy dissipation. In both cases the suspension system is assumed to be excited by random white noise disturbances. It is shown that near optimum disturbance attenuation and energy dissipation can be achieved without current feedback. Procedures for selecting these suboptimum controller gains are suggested. The paper compares the suboptimum controller gains with the state feedback gains obtained using Linear Quadratic optimal control theory. It is shown that the disturbance attenuation characteristics of the electromagnetic suspension can be made to be superior to that of a passive isolation system. Experimental results are also presented.