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Summary of Research on Unbalanced Vibration Control of Magnetic Levitation Rotors (2)

Release time:

2023-01-13

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According to the different suppression components, there are two methods for controlling the small electromagnetic force of bearings: 1) co frequency force suppression, which only suppresses the vibration force caused by rotor imbalance; 2) Harmonic force suppression not only suppresses the vibration force caused by rotor imbalance, but also suppresses the harmonic vibration force caused by sensor harmonic noise.

2.1 Small control of bearing electromagnetic force

2.1.1 Same frequency vibration suppression

There are two ways to suppress the same frequency vibration, one is to directly remove the same frequency or harmonic components, and the other is to actively change the control quantity after identifying the imbalance.

There are mainly ways to directly remove the same frequency or harmonic components, such as generalized notch filters and Least Mean Square (LMS) algorithms. The generalized notch filter has received extensive research due to its simple structure. In 1996, reference [9] proposed a generalized multivariable notch filter with a structure shown in Figure 4 to suppress unbalanced vibration. It inserted a sensitivity adjustment matrix T into the general notch filter to adjust the position of the system poles, thereby ensuring the stability of the system. Reference [10] proposed a common frequency current suppression method based on phase-shifting universal notch feedback control, which can effectively suppress the same frequency current generated by the controller, power amplifier system and induced electromotive force. In order to compensate for both current stiffness and displacement stiffness, reference [11] proposed a method of combining sliding mode observer and notch filter to suppress unbalanced vibration, without distinguishing between current stiffness and displacement stiffness, and without considering the low-pass characteristics of the power amplifier. Reference [12] proposes an automatic balance control method based on displacement notch and feedforward compensation for the mass imbalance of active and passive magnetic levitation rotors and the same frequency vibration force caused by the center offset of passive magnetic bearings.

In the 1980s, adaptive filtering algorithms flourished and were initially widely used in noise cancellation. The LMS algorithm has been widely applied due to its simple principle, strong adaptability, anti-interference ability, and good convergence, and was applied in the field of unbalanced vibration control of magnetic levitation rotors in the 1990s. The LMS algorithm is actually a discrete adaptive notch filter, and its principle is shown in Figure 5. Reference [14] proposed a real-time variable frequency switching control strategy based on LMS algorithm in 2009, which reduced periodic unbalanced excitation force; Then, in order to give consideration to stability and Rate of convergence, a variable step size LMS algorithm was proposed and achieved good results in different constant speed tests. The combination of H ∞ algorithm and adaptive step size LMS algorithm to achieve real-time small inertial force compensation improved the robust stability and anti-interference performance of the entire system. In addition, reference [17] proposes an adaptive feedforward compensation based on the LMS algorithm, which offsets the influence of the low-pass characteristics of the power amplifier. The principle of the method is shown in Figure 6.

In 2015, reference [18] applied the method of synchronous rotating frame (SRF) transformation in motor drive control to magnetic bearing systems. The control principle is shown in Figure 7, which is equivalent to a new type of notch filter. By working in series with the controller, it has good performance when the rotor rotates at low speed