In this work the modeling and basic control design process of a rotary flexible spindle hovered by Active Magnetic Bearings (AMB) whose good capabilities for machine-tool industry extensively treated in the literature is presented. The modeling takes into account the three main behavioral characteristics of such magnetically-levitated rotor: the rigid dynamics, the flexible dynamics and the rotating unbalanced motion. Besides, the gyroscopic coupling is also studied proving that in this case, its effects are not significant and can be neglected. Using this model, a stabilizing controller based on symmetry properties is successfully designed for the system and a complete experimental analysis of its performance is carried out. Also, the predictions of the model are compared with the actual measured experimental results on a laboratory set-up based on the MBC500 Rotor Dynamics. Afterwards, a brief study about some nonlinear behavior observed in the system and its effect over the system stability at the critical speed is included.