Lateral vibration control and stabilization of the quasiperiodic oscillations for rotor-active magnetic bearings system

This work aims to improve the vibrational behaviors of the rotor-active magnetic bearings (AMB) system via proposing a new control methodology for such lateral vibrations. Accordingly, the rotor-AMB system model is modified by integrating the conventional proportional-derivative (PD) controller along with the positive position feedback (PPF) controller to the considered system. The control currents in the rotor-AMB system are designed to become a combination of two control signals: One of them is generated via the PD controller, and the other one comes from the PPF controller. Based on the suggested control method, the whole dynamical system model is derived and then analyzed by the multiple time-scale perturbation method. Then, the bifurcation diagrams of both the spinning speed and rotor eccentricity response curves are investigated before and after control. The obtained analytical results showed that the integrating of the PPF controller to the considered system could mitigate the system lateral vibration close to zero. Moreover, the system quasiperiodic motions have been stabilized after control and the sensitivity to the initial conditions has eliminated. Finally, numerical validations for the obtained analytical results are performed that illustrated an excellent agreement with the analytical ones.