Time-Varying Barrier Lyapunov Functions Based Adaptive Backstepping Control for Active Magnetic Bearings with State Constraints

In this manuscript, the rotor displacement control problem of active magnetic bearings system is considered and resolved. Especially, this paper considers the constraint of rotor displacement to avoid the damage and safety accidents of AMB systems due to excessive rotor displacement deviation. Time-varying barrier Lyapunov function is introduced and utilized to make the rotor displacement in a specific range. According to different operating characteristics and requirements at different times, the limitation of the rotor displacement also changes. Additionally, adaptive backstepping technique is presented to design the rotor displacement controller with time-varying state constraints, the stability analysis is provided as well. Finally, simulation examples have verified the effectiveness of the proposed control scheme.