## 1 Introduction
For a magnetically levitated centrifugal compressor, [PERSON] [18] proposed the use of a conventional trap to eliminate the same-frequency perturbation in the glitch signal and to use an improved adaptive trap method to estimate the frequency of the glitch signal, showing that the system gradually stabilized. [PERSON] [19] designed an adaptive trap for vibration monitoring with an active magnetic levitation bearing condition detection capability that can accurately extract the vibration fundamental wave components, and the convergence of the modified trap is independent of frequency and replication, obtaining higher estimation accuracy and fast monitoring across the whole speed range. [PERSON] [20] employs a two-stage trap to achieve the suppression of same-frequency vibrations by polarity-switching in the low-speed and high-speed zones of the rotor system. [PERSON] [21] analyzed, in depth, the effectiveness of traps on the channel vibration control of rotor systems during high- and low-speed switching zones. [PERSON] [22] proposed the vibration suppression method of the polarity switching tracking filter and the disturbance observer for the unbalanced vibration of the high-speedmotor rotor. [PERSON] [23] proposed a general model of the magnetically suspended flexible rotor under base motion, considering the rotor shrinkage fit and AMB sensor/actuator not being collocated, based on the finite element method and [PERSON]'s equation. Aiming at the vibration control problem of the AMB rigid rotor system, this study investigates a control strategy that integrates the AFC and ANF to achieve vibration control for high-speed AMB motors across the full rotational speed range, ensuring systemic stability and efficiency. The innovation of this study is primarily reflected in the following two aspects: First, to address the radial vibration component produced by unbalanced forces during the high-speed rotor operation, which is synchronous with the rotational speed, the ANF was designed. With the real-time monitoring of the rotor vibration signals and the adaptive adjustment of the center frequency and bandwidth, the ANF effectively suppresses vibrations in the high-speed region, thereby enhancing the system's stability. Second, considering the varying closed-loop stability conditions of the magnetic levitation rigid rotor system when operating near the radial rigid critical speed, a control strategy based on polarity switching combined with the adaptive notch filter was proposed. This strategy, integrated with the AFC, ensures the stable operation of the AMB high-speed rigid rotor system across the full speed range, including the rigid critical speed. This study first processes the rotor vibration information through a fuzzy controller to optimize the control effect. Subsequently, the stability theory is employed to analyze the radial stability of the rotor system after incorporating the automatic balancing control based on the adaptive notch filter. The stability of the rotor system across the full speed range, including the rigid critical speed, is ensured by the polarity-switching strategy. Finally, the effectiveness of the method is verified through simulations and experiments. The structure of this paper is as follows: Section 1 introduces the research background and the problem, Section 2 establishes the dynamic model of the AMB rigid rotor system, Section 3 elaborates on the adaptive notch filter control strategy based on fuzzy control, Section 4 verifies the effectiveness of the control strategy through simulation, Section 5 further validates the practical application effect of the method through experiments, and Section 6 summarizes the full text and proposes future research directions.