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Because of their many advantages non-contact magnetic bearings have been developed over the last 20 years for space-borne applications. In spite of these advantages these bearings have often proved difficult to design when installed in compliant structures due to the complex interaction of the structural resonances on the one hand and the static and dynamic constraints of the bearings actuators and their power amplifiers on the other. In this paper a mathematical model of the magnetic bearing rotor system for a flywheel energy storage system is developed, which takes these factors into account. Using this model it is shown by formulating an optimization problem that the vibrations due to rotor imbalance can be minimized by appropriate choices of the magnetic bearing stiffness and damping coefficients within the range allowed by the system constraints.