A vibration suppression method based on high-precision closed-loop synchronous rotating coordinate transformation

Abstract

This invention relates to a vibration suppression method based on high-precision closed-loop synchronous rotating coordinate transformation. First, a dynamic model of the deflection of a magnetically levitated rotor affected by mass imbalance is established. Then, a synchronous vibration controller based on a high-precision closed-loop synchronous rotating coordinate transformation method is used to track the synchronous frequency disturbance component, and a high-precision closed-loop synchronous frequency signal detection method is employed to improve the detection accuracy of the synchronous frequency vibration signal. Finally, the synchronous frequency vibration signal is eliminated by inverting and compensating the original system, thereby eliminating the synchronous frequency disturbance current and the synchronous frequency vibration torque. This method overcomes the problem of low detection accuracy of synchronous frequency signals in traditional synchronous rotating coordinate transformation methods, effectively improving the suppression effect of synchronous frequency disturbance current, and providing a new control method for unbalanced rotor vibration control. This invention belongs to the field of magnetically levitated rotor control and can be used for unbalanced vibration control of two-degree-of-freedom deflection of magnetically levitated rotors.

Description

Technical Field

[0001] This invention relates to a vibration suppression method based on high-precision closed-loop synchronous rotating coordinate transformation, which is applicable to suppressing the same-frequency disturbance current and same-frequency vibration torque caused by rotor mass imbalance in magnetic levitation rotor systems. Background Technology

[0002] Rotor imbalance is the primary vibration source in magnetic levitation rotor systems. The two main sources of imbalance are rotor mass imbalance and sensor errors. Rotor mass imbalance is caused by uneven material mass distribution and manufacturing errors. Static imbalance caused by the misalignment of the center of mass and geometric center generates a synchronous vibration force; dynamic imbalance caused by the misalignment of the principal axis of inertia and geometric axis generates a synchronous vibration torque. These synchronous vibration forces and torques, when transmitted to the spacecraft platform, severely affect the spacecraft's pointing accuracy and ultra-agile maneuverability.

[0003] To address the aforementioned issues, Peng Cong proposed an unbalanced vibration suppression method based on a second-order notch filter to suppress the same-frequency vibration torque in a magnetically levitated rotor system with a strong gyroscopic effect. This method introduces a limit switch to distinguish between low and high speeds of the rotor and adjusts the phase angle to ensure system stability across the entire speed range. However, this method leads to greater vibration during polarity switching, affecting system stability. Zheng Shiqiang proposed a same-frequency vibration suppression method for active magnetic bearings based on synchronous rotating coordinate transformation. However, this method suffers from severe phase lag and low suppression accuracy in the high-frequency band due to the introduction of a low-pass filter to remove high-frequency noise and its open-loop suppression mechanism. Summary of the Invention

[0004] The technical problem solved by this invention is to propose a vibration suppression method based on high-precision closed-loop synchronous rotating coordinate transformation, addressing the same-frequency disturbance current and same-frequency vibration torque caused by rotor mass imbalance in magnetic levitation rotor systems. This method leverages the dual-input, dual-output, and strongly coupled characteristics of the system's deflection channels, employing only a single HCSRF controller to simultaneously suppress the same-frequency disturbance current and same-frequency vibration torque of both deflection channels. To overcome the low detection accuracy of same-frequency signals in traditional synchronous rotating coordinate transformation methods, a high-precision closed-loop same-frequency signal detection stage is used, improving the detection accuracy of same-frequency vibration signals and enhancing the suppression effect of unbalanced vibration.

[0005] 1. The technical solution of this invention is: to establish a synchronous vibration controller based on a high-precision closed-loop synchronous rotating coordinate transformation method to perform high-precision tracking, and then to invert and compensate it back to the original system to eliminate the synchronous vibration signal, thereby eliminating the synchronous disturbance current and synchronous vibration torque. Specifically, it includes the following steps:

[0006] (1) Establish a dynamic model of the deflection of the magnetically levitated rotor affected by rotor mass imbalance.

[0007] In a magnetically levitated rotor system using a Lorentz force magnetic bearing to control deflection, the electromagnetic torque controlling the rotor's radial single-degree-of-freedom deflection is:

[0008]

[0009] In the formula, N is the number of turns of the coil, and I x and I y Here, B represents the coil current magnitudes for the radial X and Y channels, respectively, and B represents the magnetic field magnitude of the LFMB air gap. r The radius of the LFMB stator frame is... The central angle corresponding to the coil;

[0010] Furthermore, according to the gyroscope equations, the deflection dynamics equation of the rotor is:

[0011]

[0012] In the formula, J x J y and J z Let Ω be the moment of inertia of each axis of the rotor, α and β be the deflection angles of the rotor about the x-axis and y-axis, respectively, and Ω be the rotor speed. The rotor deflection control model is derived from equations (1) and (2):

[0013]

[0014] The essence of rotor mass dynamic imbalance is the misalignment between the inertial axis and the geometric axis. There exists an angle where the sensor detects the deflection angle symmetrically about the geometric axis. However, since the rotor is rotating around the rotation axis, the deflection angle detected by the sensor fluctuates in sync. Therefore, the rotor deflection angle detected by the sensor at this time is:

[0015]

[0016] In the formula, α and β are the rotor deflection angles under ideal conditions, respectively. r and β r These represent the actual deflection angles of the rotor when there is a mass imbalance, ε d and θ d These represent the eccentricity between the inertial axis and the geometric axis, and the initial phase, respectively.

[0017] Fluctuations in the deflection angle, after passing through the controller and power amplifier, generate harmonic currents of the same frequency, which, after passing through the torque coefficient, produce a vibrational torque of the same frequency. The harmonic currents of the same frequency can be expressed as:

[0018]

[0019] In the formula, χ x and χ yThe harmonic current coefficient represents the frequency of the rotor, which is related to the rotor speed and increases with increasing speed. Substituting equation (4) into equation (2) yields:

[0020]

[0021] make This refers to the vibrational torque generated by the rotor's dynamic imbalance, which has the same frequency as the rotational speed.

[0022] (2) Establish a synchronous vibration controller based on a high-precision closed-loop synchronous rotating coordinate transformation method.

[0023] According to the principle of rotor mass imbalance, the rotor's center of mass and geometric center do not coincide. When the rotor rotates at a high speed Ω, the frequency of the unbalanced vibration is equal to the rotor speed. Therefore, the signal output by the displacement sensor contains a component with the same frequency as the speed Ω. Let the dual-channel orthogonal AC signal output by the displacement sensor be S. x and S y The DC signal after passing through the synchronous rotating coordinate transformation system is set as R. x and R y ;

[0024] Let S x -O m -S y To fix the sensor coordinate system, R x -O m -R y For a rotating coordinate system with the same frequency, O m For the rotor's center of mass, O c Let O be the geometric center of the rotor. c The coordinates in the fixed sensor coordinate system are: (s) x ,s y The coordinates of (r) in the same frequency rotating coordinate system are (r) x ,r y When the rotor rotates at a high speed Ω, according to the principle of synchronous rotation coordinate transformation, the relationship of synchronous rotation coordinate transformation can be expressed as:

[0025]

[0026] In equation (7), θ is the phase compensation factor, used to ensure the stability of the system across the entire speed range. The signal R after synchronous rotating coordinate transformation... x and R yTheoretically, the signal is a DC signal, containing both the signal with the same frequency as the rotational speed and high-frequency noise. Therefore, it is necessary to filter out the high-frequency noise and detect the signal with the same frequency as the rotational speed. While a first-order low-pass filter is simple in structure and has low computational complexity, it suffers from low detection accuracy and phase lag in the high-frequency band, severely affecting the compensation effect of the DC signal obtained after inverse SRF transformation. Therefore, a high-precision closed-loop same-frequency signal detection method is designed. Part of the DC signal after SRF transformation directly enters the output of the high-precision closed-loop detection, while the other part is connected in series with a PI controller and a low-pass filter, providing negative feedback from the output to the input, thus forming a closed-loop same-frequency signal detection. Let G1 represent the PI controller and G2 represent the low-pass filter, which can be represented as:

[0027]

[0028] Therefore, the closed-loop transfer function of the high-precision closed-loop synchronous signal detection (HCSD) stage is:

[0029]

[0030] Finally, the DC signal, after passing through the high-precision closed-loop same-frequency signal detection stage, is converted back into an AC signal using the inverse SRF transformation matrix:

[0031]

[0032] The transformation relationship between equations (7) and (10) can be obtained by Laplace transform:

[0033]

[0034] The signal R after synchronous rotational coordinate transformation x and R y After the high-precision closed-loop same-frequency signal detection process, it can be expressed as:

[0035]

[0036] From equations (11) and (12), it can be seen that the open-loop transfer function of the same-frequency vibration controller based on the high-precision closed-loop synchronous rotating coordinate transformation method can be expressed as:

[0037]

[0038] Therefore, its closed-loop transfer function can be expressed as:

[0039]

[0040] In the formula, k is the closed-loop gain of the high-precision closed-loop same-frequency vibration signal suppression method, and:

[0041]

[0042] From equation (14), the frequency characteristic of the closed-loop transfer function of the same-frequency vibration controller based on the high-precision closed-loop synchronous rotating coordinate transformation method (HCSRF) is:

[0043]

[0044] From equation (16), we know that when w→Ω, we have N HCSRF (jw)→0. Furthermore, the notch depth is related to the gain k of the High-Precision Closed-Loop Synchronous Rotating Coordinate Transformation (HCSRF) method, and the scaling factor k in the High-Precision Closed-Loop Same-Frequency Signal Detection (HCSD) stage. i It is related to the time constant τ of LPF.

[0045] (3) Suppressing co-frequency disturbance current and co-frequency vibration torque

[0046] Based on the principle of rotor mass imbalance, the current in the LFMB consists of two parts: one part controls the stable levitation and deflection of the rotor, and the other part is a disturbance current with the same frequency as the rotor. That is, the rotor deflection control current can be expressed as:

[0047]

[0048] In equation (17), I x and I y i represents the rotor deflection control current. x and i y I represents the current used to control the stable levitation and deflection of the rotor. xs and I ys This represents the disturbance current that has the same frequency as the rotor.

[0049] With the introduction of an HCSRF controller into the original deflection control system, the output currents of the x-channel and y-channel power amplifiers are expressed as follows:

[0050]

[0051] in,

[0052]

[0053] In the formula, s x and s y For an ideal sensor displacement signal, d x and d y S is the same-frequency vibration signal introduced due to rotor mass imbalance. x and S y This represents the actual displacement signal from the displacement sensor. From equations (16)-(19), we can obtain:

[0054]

[0055] As analyzed in the previous section, when w→Ω, N HCSRF (jw)→0, then I xs →0,I ys →0. That is, the harmonic current of the same frequency in the deflection control current is completely suppressed. As can be seen from equation (20), at this time, I x →i x I y →i y This effectively suppresses the same-frequency disturbance current in the deflection control current;

[0056] From equation (1), the expression for the torque of vibration at the same frequency is:

[0057]

[0058] From equation (21), it can be seen that when the same frequency disturbance current is suppressed, i.e., I xs →0,I ys When →0, there is T αs →0,T βs →0, meaning that when the same-frequency disturbance current is effectively suppressed, the same-frequency vibration torque is also completely suppressed;

[0059] The principle of this invention is as follows: First, the displacement signals of the two deflection channels with orthogonal characteristics are converted into DC signals through a same-frequency conversion matrix; then, a high-precision closed-loop same-frequency signal detection stage is used to eliminate high-frequency noise in the DC signal; then, through the same-frequency conversion inverse matrix, a vibration signal containing only the same frequency as the rotational speed is obtained; finally, the inverse compensation is applied to the original system to eliminate the same-frequency vibration signal, thereby eliminating the same-frequency disturbance current and the same-frequency vibration torque.

[0060] Compared with existing solutions, the main advantages of this invention are: the synchronous rotation coordinate transformation-based method for suppressing co-frequency vibration is simple in structure, easy to implement, and has few adjustable parameters. At the same time, it adopts a high-precision closed-loop co-frequency signal detection stage to replace the open-loop detection stage in the traditional synchronous rotation coordinate transformation method, which overcomes the problems of severe phase lag and low detection accuracy in the high-frequency band caused by the low-pass filter, and improves the suppression effect of co-frequency vibration signal. Attached Figure Description

[0061] Figure 1 Detailed implementation plan diagram;

[0062] Figure 2 Schematic diagram illustrating the principle of mass imbalance in a magnetically levitated rotor;

[0063] Figure 3 Schematic diagram of a high-precision closed-loop synchronous rotating coordinate transformation method;

[0064] Figure 4 Schematic diagram of a high-precision closed-loop synchronous vibration signal detection system;

[0065] Figure 5 Block diagram of deflection control of magnetic levitation rotor using high-precision closed-loop synchronous rotating coordinate transformation method;

[0066] Figure 6 Experimental results of current magnitude in the α channel before and after using the HCSRF method;

[0067] Figure 7 Experimental results of current magnitude in the β channel before and after using the HCSRF method; Detailed Implementation Plan

[0068] A high-precision closed-loop synchronous rotating coordinate transformation method is used to establish a synchronous vibration controller for high-precision tracking. Then, the controller is inverted and compensated back to the original system to eliminate the synchronous vibration signal, thereby eliminating the synchronous disturbance current and synchronous vibration torque. The specific implementation steps are as follows:

[0069] (1) Establishing a dynamic model of the deflection of a magnetically levitated rotor affected by rotor mass imbalance. In a magnetically levitated rotor system using a Lorentz force magnetic bearing to control deflection, the electromagnetic torque controlling the rotor's radial single-degree-of-freedom deflection is:

[0070]

[0071] In the formula, N is the number of turns of the coil, and I x and I y Here, B represents the coil current magnitudes for the radial X and Y channels, respectively, and B represents the magnetic field magnitude of the LFMB air gap. r The radius of the LFMB stator frame is... The central angle corresponding to the coil;

[0072] Furthermore, according to the gyroscope equations, the deflection dynamics equation of the rotor is:

[0073]

[0074] In the formula, J x J y and J z Let Ω be the moment of inertia of each axis of the rotor, α and β be the deflection angles of the rotor about the x-axis and y-axis, respectively, and Ω be the rotor speed. The rotor deflection control model is derived from equations (1) and (2):

[0075]

[0076] like Figure 2As shown, the essence of rotor mass dynamic imbalance is the misalignment between the inertial axis and the geometric axis. There exists an angle where the sensor detects the deflection angle symmetrically about the geometric axis. However, since the rotor rotates around the rotation axis, the deflection angle detected by the sensor fluctuates in sync. Therefore, the rotor deflection angle detected by the sensor at this time is:

[0077]

[0078] In the formula, α and β are the rotor deflection angles under ideal conditions, respectively. r and β r These represent the actual deflection angles of the rotor when there is a mass imbalance, ε d and θ d These represent the eccentricity between the inertial axis and the geometric axis, and the initial phase, respectively.

[0079] Fluctuations in the deflection angle, after passing through the controller and power amplifier, generate harmonic currents of the same frequency, which, after passing through the torque coefficient, produce a vibrational torque of the same frequency. The harmonic currents of the same frequency can be expressed as:

[0080]

[0081] In the formula, χ x and χ y The harmonic current coefficient represents the frequency of the rotor, which is related to the rotor speed and increases with increasing speed. Substituting equation (4) into equation (2) yields:

[0082]

[0083] make This refers to the vibrational torque generated by the rotor's dynamic imbalance, which has the same frequency as the rotational speed.

[0084] (2) Establish a synchronous vibration controller based on a high-precision closed-loop synchronous rotating coordinate transformation method.

[0085] According to the principle of rotor mass imbalance, the rotor's center of mass and geometric center do not coincide. When the rotor rotates at a high speed Ω, the frequency of the unbalanced vibration is equal to the rotor speed. Therefore, the signal output by the displacement sensor contains a component with the same frequency as the speed Ω. Let the dual-channel orthogonal AC signal output by the displacement sensor be S. x and S y The DC signal after passing through the synchronous rotating coordinate transformation system is set as R. x and R y ;

[0086] Figure 3 This is a schematic diagram of a high-precision closed-loop synchronous rotating coordinate transformation method. Let S... x -O m -S y To fix the sensor coordinate system, R x-O m -R y For a rotating coordinate system with the same frequency, O m For the rotor's center of mass, O c Let O be the geometric center of the rotor. c The coordinates in the fixed sensor coordinate system are: (s) x ,s y The coordinates of (r) in the same frequency rotating coordinate system are (r) x ,r y When the rotor rotates at a high speed Ω, according to the principle of synchronous rotation coordinate transformation, the relationship of synchronous rotation coordinate transformation can be expressed as:

[0087]

[0088] In equation (7), θ is the phase compensation factor, used to ensure the stability of the system across the entire speed range. The signal R after synchronous rotating coordinate transformation... x and R y Theoretically, the signal is a DC signal, containing both the signal with the same frequency as the rotational speed and high-frequency noise. Therefore, it is necessary to filter out the high-frequency noise and detect the signal with the same frequency as the rotational speed. While a first-order low-pass filter is simple in structure and has low computational complexity, it suffers from low detection accuracy and phase lag in the high-frequency range, severely affecting the compensation effect of the DC signal obtained after inverse SRF transformation. Therefore, a high-precision closed-loop method for detecting the same-frequency signal is designed, such as... Figure 4 As shown. Part of the DC signal after SRF conversion directly enters the output of the high-precision closed-loop detection, while the other part is connected in series with a PI controller and a low-pass filter, providing negative feedback from the output to the input, thus forming a closed-loop same-frequency signal detection. Let G1 represent the PI controller and G2 represent the low-pass filter, which can be represented as:

[0089]

[0090] Therefore, the closed-loop transfer function of the high-precision closed-loop synchronous signal detection (HCSD) stage is:

[0091]

[0092] Finally, the DC signal, after passing through the high-precision closed-loop same-frequency signal detection stage, is converted back into an AC signal using the inverse SRF transformation matrix:

[0093]

[0094] The transformation relationship between equations (7) and (10) can be obtained by Laplace transform:

[0095]

[0096] The signal R after synchronous rotational coordinate transformation x and R y After the high-precision closed-loop same-frequency signal detection process, it can be expressed as:

[0097]

[0098] From equations (11) and (12), it can be seen that the open-loop transfer function of the same-frequency vibration controller based on the high-precision closed-loop synchronous rotating coordinate transformation method can be expressed as:

[0099]

[0100] Therefore, its closed-loop transfer function can be expressed as:

[0101]

[0102] In the formula, k is the closed-loop gain of the high-precision closed-loop same-frequency vibration signal suppression method, and:

[0103]

[0104] From equation (14), the frequency characteristic of the closed-loop transfer function of the same-frequency vibration controller based on the high-precision closed-loop synchronous rotating coordinate transformation method (HCSRF) is:

[0105]

[0106] From equation (16), we know that when w→Ω, we have N HCSRF (jw)→0. Furthermore, the notch depth is related to the gain k of the High-Precision Closed-Loop Synchronous Rotating Coordinate Transformation (HCSRF) method, and the scaling factor k in the High-Precision Closed-Loop Same-Frequency Signal Detection (HCSD) stage. i It is related to the time constant τ of LPF.

[0107] (3) Suppressing co-frequency disturbance current and co-frequency vibration torque

[0108] Based on the principle of rotor mass imbalance, the current in the LFMB consists of two parts: one part controls the stable levitation and deflection of the rotor, and the other part is a disturbance current with the same frequency as the rotor. That is, the rotor deflection control current can be expressed as:

[0109]

[0110] In equation (17), I x and I y i represents the rotor deflection control current. x and i y I represents the current used to control the stable levitation and deflection of the rotor. xs and I ysThis represents the disturbance current that has the same frequency as the rotor.

[0111] like Figure 5 As shown, with the introduction of an HCSRF controller into the original deflection control system, the output currents of the x-channel and y-channel power amplifiers are expressed as follows:

[0112]

[0113] in,

[0114]

[0115] In the formula, s x and s y For an ideal sensor displacement signal, d x and d y S is the same-frequency vibration signal introduced due to rotor mass imbalance. x and S y This represents the actual displacement signal from the displacement sensor. From equations (16)-(19), we can obtain:

[0116]

[0117] As analyzed in the previous section, when w→Ω, N HCSRF (jw)→0, then I xs →0,I ys →0. That is, the harmonic current of the same frequency in the deflection control current is completely suppressed. As can be seen from equation (20), at this time, I x →i x I y →i y This effectively suppresses the same-frequency disturbance current in the deflection control current;

[0118] From equation (1), the expression for the torque of vibration at the same frequency is:

[0119]

[0120] From equation (21), it can be seen that when the same frequency disturbance current is suppressed, i.e., I xs →0,I ys When →0, there is T αs →0,T βs →0, meaning that when the same-frequency disturbance current is effectively suppressed, the same-frequency vibration torque is also completely suppressed;

[0121] To verify the effectiveness of the proposed method, Figure 6 and Figure 7Experimental results before and after applying this method at 5000 rpm are presented. The time-domain waveforms and FFT-analyzed spectra of the deflection α-channel and β-channel control currents before and after applying this method are shown. As can be seen from the figures, the magnitude of the α-channel control current decreased from -31.46 dB to -39.98 dB, a reduction of 62.55%; the magnitude of the β-channel control current decreased from -28.51 dB to -38.64 dB, a reduction of 68.8%. Therefore, the method of this invention can effectively suppress the same-frequency disturbance current in the magnetic levitation rotor system.

[0122] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A vibration suppression method based on high-precision closed-loop synchronous rotation coordinate transformation, characterized by: To address the synchronous vibration signal introduced by rotor mass imbalance in a magnetic levitation rotor system, a synchronous vibration controller based on a high-precision closed-loop synchronous rotating coordinate transformation method is established to track it with high precision. Then, the signal is inverted and compensated back into the original system to eliminate the synchronous vibration signal, thereby eliminating synchronous disturbance current and synchronous vibration torque. The specific steps include: (1) Establish a dynamic model of the deflection of the magnetically levitated rotor affected by rotor mass imbalance. In a magnetically levitated rotor system using a Lorentz force magnetic bearing to control deflection, the electromagnetic torque controlling the rotor's radial single-degree-of-freedom deflection is: (1) wherein N is the number of turns of the coil, and are the magnitude of the coil current in the radial X and Y channels, respectively, and B is the magnitude of the magnetic field in the air gap of the LFMB, is the radius of the LFMB stator skeleton, is the central angle corresponding to the coil. Furthermore, according to the gyroscope equations, the deflection dynamics equation of the rotor is: (2) wherein , and are the moments of inertia of the respective axes of the rotor, and are the deflection angles of the rotor about the x-axis and the y-axis, respectively, is the rotor speed; from equations (1) and (2) a rotor deflection control model is derived: (3) The essence of rotor mass dynamic imbalance is the misalignment between the inertial axis and the geometric axis. There exists an angle at which the sensor detects the deflection angle symmetrically about the geometric axis. However, since the rotor rotates around the rotation axis, the deflection angle detected by the sensor fluctuates in sync. Therefore, the rotor deflection angle detected by the sensor at this time is: (4) wherein and are the ideal rotor deflection angles, and are the actual rotor deflection angles in the presence of mass imbalance, and are the eccentricity and initial phase between the inertia axis and the geometric axis, respectively. The fluctuation in deflection angle, after passing through the controller and power amplifier, generates a harmonic current of the same frequency, which, after passing through the torque coefficient, produces a vibration torque of the same frequency; the harmonic current of the same frequency can be expressed as: (5) In equation (5), and The harmonic current coefficient represents the frequency of the rotor, which is related to the rotor speed and increases with the increase of the speed; substituting equation (4) into equation (2) yields: (6) make This refers to the vibrational torque generated by the rotor's dynamic imbalance, which has the same frequency as the rotational speed. (2) Establish a synchronous vibration controller based on a high-precision closed-loop synchronous rotating coordinate transformation method. According to the principle of rotor mass imbalance, the rotor's center of mass and geometric center do not coincide. When the rotor rotates at a speed of... When rotating at high speed, the frequency of the unbalanced vibration is equal to the rotor speed; therefore, the signal output by the displacement sensor contains information related to the rotational speed. Components of the same frequency; set the dual-channel orthogonal AC signal output by the displacement sensor as... and The DC signal after passing through the synchronous rotating coordinate transformation system is set as and ; set up To fix the sensor coordinate system, For a coordinate system rotating at the same frequency, The rotor's center of mass, Let the geometric center be the rotor's geometric center; The coordinates in the fixed sensor coordinate system are: The coordinates in the same frequency rotating coordinate system are When the rotor rotates at a speed of During high-speed rotation, the relationship of synchronous rotational coordinate transformation can be expressed as: (7) In equation (7), This is a phase compensation factor used to ensure the stability of the system across the entire speed range; the signal after synchronous rotating coordinate transformation. and Theoretically, the signal is a DC signal, containing both the signal with the same frequency as the rotational speed and high-frequency noise. Therefore, it is necessary to filter out the high-frequency noise and detect the signal with the same frequency as the rotational speed. Thus, a high-precision closed-loop signal detection method is designed. Part of the DC signal after SRF conversion directly enters the output of the high-precision closed-loop detection, while the other part is connected in series with a PI controller and a low-pass filter, providing negative feedback from the output to the input, thus forming a closed-loop signal detection mechanism. Indicates a PI controller. A low-pass filter can be represented as: （8） Therefore, the closed-loop transfer function of the high-precision closed-loop synchronous signal detection (HCSD) stage is: （9） Finally, the DC signal, after passing through the high-precision closed-loop same-frequency signal detection stage, is converted back into an AC signal using the inverse SRF transformation matrix: （10） The transformation relationship between equations (7) and (10) can be obtained by Laplace transform: （11） Signal after synchronous rotational coordinate transformation and After the high-precision closed-loop same-frequency signal detection process, it can be expressed as: （12） From equations (11) and (12), it can be seen that the open-loop transfer function of the same-frequency vibration controller based on the high-precision closed-loop synchronous rotating coordinate transformation method can be expressed as: （13） Therefore, its closed-loop transfer function can be expressed as: （14） In the formula, k is the closed-loop gain of the high-precision closed-loop same-frequency vibration signal suppression method, and: （15） From equation (14), the frequency characteristic of the closed-loop transfer function of the same-frequency vibration controller based on the high-precision closed-loop synchronous rotating coordinate transformation method (HCSRF) is: （16） From equation (16), it can be seen that when Sometimes, Furthermore, the notch depth is related to the gain k of the High-Precision Closed-Loop Synchronous Rotating Coordinate Transformation (HCSRF) method, and the scaling factor in the High-Precision Closed-Loop Same-Frequency Signal Detection (HCSD) stage. and the time constant of LPF related; (3) Suppressing co-frequency disturbance current and co-frequency vibration torque Based on the principle of rotor mass imbalance, the current in the LFMB consists of two parts: one part controls the stable levitation and deflection of the rotor, and the other part is a disturbance current with the same frequency as the rotor. That is, the rotor deflection control current can be expressed as: （17） In equation (17), and This represents the rotor deflection control current. and This represents the current used to control the stable levitation and deflection of the rotor. and This represents the disturbance current that has the same frequency as the rotor. With the introduction of an HCSRF controller into the original deflection control system, the output currents of the x-channel and y-channel power amplifiers are expressed as follows: （18） in, （19） In the formula, and For an ideal sensor displacement signal, and This is a synchronous vibration signal introduced due to rotor mass imbalance. and The actual displacement signal of the displacement sensor; from equations (16)-(19), we can obtain: （20） when hour, ,but , That is, the harmonic current of the same frequency in the deflection control current is completely suppressed. As can be seen from equation (20), at this time we have , This effectively suppresses the same-frequency disturbance current in the deflection control current; From equation (1), the expression for the torque of vibration at the same frequency is: （21） From equation (21), it can be seen that when the same-frequency disturbance current is suppressed, i.e. , Sometimes, , That is, when the same frequency disturbance current is effectively suppressed, the same frequency vibration torque is also completely suppressed.

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