## 7 Conclusions  
This study addresses the issue of unbalanced vibration control in high-speed rigid rotor systems with active magnetic bearings (AMBs) by proposing an adaptive fuzzy control strategy based on a switching notch filter. The following conclusions are drawn based on theoretical analysis, simulation verification, and experimental research:  
The proposed control strategy, which combines AFC-ANF, demonstrates significant vibration-suppression effects across the entire speed range. Simulation results indicate that, compared to the traditional PID control, the AFC reduces the system's levitation stabilization time from 0.17 s to 0.06 s. The system employs negative polarity control for the notch filter near the rigid body critical speed frequency and positive polarity control above this frequency. When the AMB high-speed motor operates below the critical speed, the negative polarity control reduces the rotor vibration from 0.5 \(\times\) 10\({}^{-6}\) m to 0.27 \(\times\) 10\({}^{-6}\) m, a 46% reduction When operating above the critical speed, the positive polarity control reduces the rotor vibration displacement from 1.96 \(\times\) 10 m to 0.66 \(\times\) 10\({}^{-6}\) m, a 66% reduction, effectively suppressing the unbalanced rotor vibration. During the constant acceleration, the rotor vibration displacement is reduced from 1.5 \(\times\) 10\({}^{-6}\) m to 0.9 \(\times\) 10\({}^{-6}\) m within a short period, a 40% reduction, quickly achieving rotor imbalance control. The experimental data further validate the effectiveness of this strategy, with stable levitation achieved within 3.3 ms after applying the bias voltage. At 45,000 rpm, the rotor vibration error voltage indicates the excellent dynamic response observed during the acceleration, steady-state operation, and deceleration phases. Therefore, the proposed AFC-ANF combined control strategy demonstrates significant advantages in vibration suppression and systemic stability, providing a new solution for the high-performance control of AMB rigid rotor systems. Compared to the existing literature, the innovation of this study lies in the integration of fuzzy control with an adaptive notch filter, enabling the precise control of the AMB rigid rotor system across the entire speed range. However, this study has some limitations. For instance, the real-time computational complexity of the control strategy is relatively high, which may impose higher demands on hardware performance. Additionally, the impact of external disturbances (such as sensor noise) in the experimental environment on control effectiveness requires further investigation. Future studies could explore more efficient algorithm optimization methods to reduce the computational burden and extend this strategy to more complex multi-rotor or flexible rotor systems. In summary, the proposed adaptive fuzzy control strategy based on a switching notch filter is not only theoretically innovative but also demonstrates superior performance in practical applications through simulations and experiments. This study provides a new solution for vibration control in AMB rigid rotor systems and lays a solid foundation for future studies in related fields. Figure 16: A 3D plot of rotor radial vibration. (**a**) Rotor vibration of AMB-A. (**b**) Rotor vibration of AMB-B. **Author Contributions:** Conceptualization, L.G. ; methodology, W.L. and Y.L. ; software, J.C.; validation, Z.H. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the Natural Science Foundation of China (52407059) and the State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University grant No. GKZD010089). It was also supported by the Key Research and Development Process of Shaanxi (2024 GX-YBXM-457), as well as the Shaanxi Postdoctoral Science Foundation (No. 2024 BSHSDZZZ226). **Data Availability Statement:** Data are unavailable due to privacy or ethical restrictions.