In this thesis, we examine the Linear DC Motor in a configuration such that it provides the forces necessary to damp vibrations in a large flexible structure. The design is broken down into three steps where in each step, a feedback loop is placed around the actuator and/or the structure. The first loop is a motor compensation loop which effectively decouples the motor model from the structure model by removing the effect of the velocity of the structure on the motor's performance. The second loop stabilizes the relative position response of the combined actuator/structure model. This loop also shapes the magnitude response of the system, thus determining the bandwidth of the actuator. Two designs are developed: a narrow bandwidth design and a wide bandwidth design. The third loop is the vibration suppression design loop and can be designed a number of ways. In this thesis, we develop two decentralized designs and a centralized design. The final system is simulated to check design results. The various nonlinearities of the proof mass actuator are considered and their effect on results noted. These nonlinearites, the stroke and current limits, determine the effectiveness of each vibration suppression design. The linear model is checked for robustness to parameter uncertainty. Results for the various designs are tabulated and discussed. / M.S.