In the feed drive systems or the spindle systems of machine tools that consist of many mechanical components, a torsional vibration is often generated because of its elastic elements in torque transmission-Generally, the accuracy of motion control system is strongly influenced by the dynamic behavior of coupled transmission components Especially, a torsional vibration caused by the elasticity of mechanical elements might deteriorate the quick movement of system and lead to shorten the life time of the mechanical transmission elements. So, it is necessary to analyze the electromechanical system mathematically to optimize the dynamic characteristics of the feed m1d spindle system. In this paper, based on the DC motor model, a model of electro-drive system with motor has been developed and an optimal criterion for tuning the gain of speed controller is discussed. The frequency bandwidth of the system and the damping ratio in time domain are optimal design specifications for the gain adjustment speed controller. The gains of PI speed controller are then derived from the bandwidth and damping ratio, and those relationships have been classified.