Stability Limits of a PD Controller for a Flywheel Supported on Rigid Rotor and Magnetic Bearings

Active magnetic bearings are used to provide a long -life, low -loss suspension of a high -speed flywheel rotor . This paper des cribes a modeling effort used to understand the stability boundaries of the PD controller used to control the active magnetic bearings on a high speed test rig . Limits of stability are described in terms of allowable stiffness and damping values which resu lt in stable levitation of the non -rotating rig. Small signal stability limits for the system is defined as a non -growth in vibration amplitude of a small disturbance. A simple mass -force model was analyzed. The force resulting from the magnetic bearing wa s linearized to include negative displacement stiffness and a current stiffness. The current stiffness was then use in a PD controller. The phase lag of the control loop was modeled by a simple time delay. The stability limits and the associated vibration frequencies were measured and compared to the theoretical values. The results show a region on stiffness versus damping plot that have the same qualitative tendencies as experimental measurements . The resulting stability model was then extended to a flywh eel system. The rotor dynamics of the flywheel was modeled using a rigid rotor supported on magnetic bearings. The equations of motion were written for the center of mass and a small angle linearization of the rotations about the center of mass. The stabil ity limits and the associated vibration frequencies were found as a function of non dimensional magnetic bearing stiffness and damping and non dimensional parameters of flywheel speed and time delay.