Dynamics and adaptive backstepping control of rotor-hybrid foil-magnetic bearings system

The hybrid foil-magnetic bearing (HFMB) is a contactless-type bearing composed of a foil bearing (FB) in the inner side and an active magnetic bearing (AMB) in the outer side. It has the advantages of low drag torque, high DN value (bearing inner diameter times rotating speed), and high supporting efficiency. However, significant subsynchronous vibration will degrade the stability of the rotor-HFMBs system, which is an obstacle to the industrial implementation of HFMBs. To control the rotor vibration, this paper presents a dynamic model of the rotor-HFMBs system with unknown parameters and the design of an adaptive backstepping controller (ABC) for it. The stability of the closed-loop system is established. Simulation results of the rotor-HFMBs system controlled by ABC are compared with the proportional-integral-derivative controller (PID), illustrating that the ABC is capable of eliminating rotor vibration, and it is more effective than the PID.