Vibration characteristics and cross-feedback control of magnetically suspended blower based on complex-factor model

•A novel analysis method based on the complex-factor model is proposed to analyze the vibration characteristics of the MSB due to the unbalance terms, and the precise vibration models are established.•The cross-feedback control model using the complex-exponential function method is proposed to effectively control the low-frequency precession and the high-frequency nutation of the MSB.•In comparison to the commonly used complex-factor cross-feedback model, the proposed complex-exponential function cross-feedback model could further reduce the precession amplitude by 38.88%, and mitigate the nutation by 60.42%. The research of vibration characteristics and active control methods of the magnetically suspended blower (MSB) are conducted for mitigation of the vibration amplitudes and the dynamic displacements of rotor shaft of the MSB at high speed. Firstly, the dynamic models with four degrees of freedom (DOFs) of the rotor shaft in the MSB are established. Secondly, the vibration characteristics of rotor shaft considering the rotor unbalance and misalignment are analyzed using the complex-factor model. Furthermore, the complex-factor and complex-exponential function cross-feedback models are respectively used to suppress the vibration amplitudes and the dynamic displacements of rotor shaft. Both numerical simulation and experimental tests of the cross-feedback model are conducted to verify the models. It is shown that a wide cutoff frequency of low-pass filter (LPF) could mitigate the precession, and a wide cutoff frequency of high-pass filter (HPF) could suppress the nutation. The proposed complex-exponential function cross-feedback model could be used to reduce the precession amplitude of the rotor shaft by 38.88%, and mitigate its nutation by 60.42%.