Electromagnetic vibration absorbers (EMA’s) act in analogy to timed bandstop filters by attenuating vibration modes of mechanical structures over a narrow bandwidth of frequencies. This paper presents the basic dynamic equations and a model of the nonlinear magnetic actuator force that includes the effects of magnetic flux leakage for the EMA. The model also includes the effects of gravity and the reluctance of the magnet iron. A method for linearizing the magnetic force about any desired operating point is presented. Equations are presented that give the optimal PID controller gains at any desired operating point in the air gap. Experimental actuator force measurements are also presented that are used to estimate flux leakage correction factors. Finally, PID controllers are synthesized and applied to an EMA test bed. Impulse response and harmonic response data verify the optimality of the controller gains, and show up to 19 dB attenuation of the main structure vibration when the EMA is tuned using the optimal control gains.