Nutation and Precession Stability Criterion of Magnetically Suspended Rigid Rotors With Gyroscopic Effects Based on Positive and Negative Frequency Characteristics

For magnetically suspended rigid rotors with significant gyroscopic effects and high rotor speed, it is necessary to stabilize the forward whirling (nutation) and backward whirling (precession) modes. This paper derives the necessary and sufficient conditions for marginal stability of the whirling modes and further presents their absolute stability criterion based on the positive and negative frequency characteristics of the control channel. Then, the relative stability judging method of the nutation and precession modes is further developed, describing analytically the rotor speed margin, gain, and phase margins. The key advantage of the criterion is that it is independent from the rotational speed and it can reveal analytically the relationships between the rotor speed stability margins of the different whirling modes and the controller itself. Simulation and experimental results demonstrate the validity and superiority of the proposed stability criterion.