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A magnetically levitated vehicle (MAGLEV) is simplified by a single mass system on a rigid guideway. The equations of motion of the electromechanical components are derived with LAGRANGE-function in state space notation. Because of the instability of the electromagnetic levitation system the vehicle must be actively controlled. The controller is de-signed by Linear Quadratic Control. An observer (KALMAN-Filter) is used to estimate the states which can not be measured or are influenced by noise. For the simulation of the controlled system the toolbox MATLAB is used. Simulation results for the time histories of the magnet gap and the accele-ration are given for a gap initial condition.