A method for suppressing unbalance vibration based on a new multi-frequency resonance controller

Abstract

The application relates to an unbalanced vibration suppression method based on a novel multi-frequency resonance controller. First, a deflection dynamics model of a magnetic suspension rotor containing mass dynamic unbalance and sensor error is established, and then a novel multi-frequency resonance controller is designed, the control current of the deflection channel is taken as an input signal of the controller, the gain at the resonance frequency is adjusted along with the change of the rotating speed, the convergence speed of the algorithm is improved, different phase compensation factors are set in different rotating speed ranges, the stability of the system in the whole rotating speed range is guaranteed, the effect of suppressing harmonic disturbance current and vibration torque is achieved, and the attitude angular rate measurement precision is improved. The application belongs to the field of magnetic suspension rotor control and can be used for suppressing unbalanced vibration caused by mass dynamic unbalance and sensor error in a magnetic suspension rotor system.

Description

Technical Field

[0001] This invention relates to an unbalanced vibration suppression method based on a novel multi-frequency resonant controller, which is applicable to suppressing same-frequency and harmonic frequency disturbance currents and vibration torques in magnetic levitation rotor systems caused by rotor mass dynamic imbalance and sensor errors. Technical Background

[0002] In recent years, magnetic levitation inertial actuators using magnetic bearings have been widely used in aerospace missions due to their advantages such as high speed, active control, frictionless operation, and long lifespan. However, when the magnetically levitated rotor rotates at high speed, various factors can cause unbalanced vibrations in the system. These vibrations not only affect the accuracy of output torque and attitude angular rate measurement, but also severely impact the spacecraft's pointing accuracy and super-agile maneuverability when transmitted to the spacecraft platform. Rotor mass imbalance and sensor errors are the main causes of unbalanced vibrations. Non-uniform material mass distribution and processing errors can lead to rotor mass imbalance. Static imbalance caused by the misalignment of the center of mass and geometric center generates synchronous vibration forces; dynamic imbalance caused by the misalignment of the principal axis of inertia and geometric axis generates synchronous vibration torques. The non-smoothness and non-uniform electromagnetic properties of the sensor surface can lead to sensor errors, resulting in harmonic vibration forces and torques.

[0003] To suppress harmonic vibrations in magnetic levitation rotor systems, researchers have conducted relevant studies. Repetitive control can suppress periodic disturbance signals with known periods, unknown amplitudes, and multiple frequency components, but it suffers from slow response and poor robustness when the frequency changes. The LMS algorithm has advantages such as simple principle, adaptive tracking of interference signal frequency, large notch depth, and strong anti-interference capability, but it has high computational complexity and slow convergence speed. The resonant controller is a periodic suppression technique based on the internal model principle to eliminate fixed-frequency interference, compensating for periodic signals through a finite-dimensional internal model structure. Therefore, it can effectively suppress harmonic signals in magnetic levitation rotor systems and has been successfully applied in power systems and magnetic levitation rotor systems. Summary of the Invention

[0004] The technical problem addressed by this invention is to propose a novel multi-frequency resonant controller-based unbalanced vibration suppression method for magnetic levitation rotor systems, addressing the in-frequency and harmonic-frequency disturbance currents and vibration torques caused by rotor mass dynamic imbalance and sensor errors. This method can independently adjust the gain at different resonant frequencies as the magnetic levitation rotor speed changes, and set different phase compensation factors within different speed ranges. This achieves optimal convergence speed while ensuring system stability across the entire speed range, improving the suppression effect of disturbance currents and the measurement accuracy of attitude angular rates.

[0005] 1. The technical solution of this invention is: by establishing an unbalanced vibration controller based on a novel multi-frequency resonant controller, the same-frequency and harmonic components in the deflection channel control current of the magnetic levitation rotor system are tracked to suppress the same-frequency and harmonic vibration torques. Specifically, the solution includes the following steps:

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

[0007] Rotor mass imbalance caused by uneven material mass distribution and processing errors can be divided into static imbalance and dynamic imbalance. Dynamic imbalance causes the rotor's geometric axis to misalign with its axis of inertia. Since sensors detect the displacement of the geometric center, when the rotor rotates at high speed, the sensors will detect a vibration signal that occurs at the same frequency as the rotational speed.

[0008] Θ d =ε d cos(Ωt+θ d (1)

[0009] In the formula, Θ d For rotor dynamic imbalance, ε d and θ d These represent the eccentricity between the inertial axis and the geometric axis, and the initial phase, respectively.

[0010] Furthermore, due to material and installation limitations, the detection surface of the displacement sensor is not a smooth circle. When the rotor rotates at high speed, the irregular rotation curve also begins to rotate at the same speed, generating periodic interference with harmonic frequencies, i.e., sensor error. Therefore, the sensor's output signal will also contain harmonic signals of the rotational speed, which can be represented using Fourier series:

[0011]

[0012] In the formula, d x a represents the harmonic components in the sensor output signal caused by sensor error. dk and These represent the amplitude and initial phase of the harmonic vibration signal caused by the sensor.

[0013] Therefore, considering the rotor mass dynamic imbalance and sensor error, the rotor deflection angle detected by the displacement sensor can be expressed as:

[0014]

[0015] In the formula, α and β are the rotor deflection angles under ideal conditions, respectively. r and β r These are the actual deflection angles of the rotor when there is dynamic imbalance of mass, α and β. sand β s These represent the deflection angle disturbances caused by sensor errors, α. m and β m These are the deflection angle disturbances caused by sensor errors;

[0016] Combining equations (1) and (2), equation (3) can be further expressed as:

[0017]

[0018] The deflection displacement signal acquired by the sensor, after passing through the controller and power amplifier, generates a disturbance current with the same frequency and harmonics of the rotor. Therefore, the deflection control current can be expressed as:

[0019]

[0020] In the formula, I α and I β These represent the currents deflecting the α and β channels, respectively, and consist of three parts, i α and i β I represents the deflection control current. αs and I βs I represents the in-frequency disturbance current caused by rotor mass imbalance. αm and I βm This represents the frequency harmonic disturbance current caused by sensor error.

[0021]

[0022]

[0023] Furthermore, from the deflection dynamics equations of the MSCSG and the control principle of the LFMB, we can obtain:

[0024]

[0025] 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... J is the central angle corresponding to the coil. x J y and J z Let 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. Substituting equations (6) and (7) into equation (8) yields:

[0026]

[0027] In the formula,

[0028]

[0029] make

[0030] As can be seen from equation (11), the unbalanced vibration torque of the MSCSG mainly consists of two parts: the same-frequency vibration torque generated by the rotor dynamic imbalance and the harmonic vibration torque generated by the sensor error.

[0031] (2) Establish an unbalanced vibration controller based on a novel multi-frequency resonance.

[0032] The novel multi-frequency resonant controller can be represented as:

[0033]

[0034] Compared with traditional multi-frequency resonant controllers, the introduction of control parameter k i and θ i Among them, k i To control the gain factor, the gain at each resonant frequency can be adjusted independently to achieve optimal convergence speed and improve the suppression of harmonic vibrations. θ i As a phase compensation factor, the phase angle is adjusted within different frequency bands to ensure rotor stability across the entire speed range. Furthermore, by introducing an integral term, not only can the DC component in the input signal be filtered out, but it also facilitates system stability analysis.

[0035] From equation (12), the closed-loop transfer function of the multi-frequency resonant controller can be obtained as follows:

[0036]

[0037] In the formula,

[0038]

[0039]

[0040] From equations (13), (14) and (15), it can be seen that,

[0041]

[0042] Furthermore, the deflection control principle of the magnetic levitation rotor system is as follows:

[0043]

[0044] In the formula, G c G represents a PID controller. w G represents a power amplifier. s S represents a displacement sensor.α and S β The actual displacement signal from the displacement sensor, according to the principle of unbalanced vibration, consists of three parts, which can be expressed as:

[0045]

[0046] In the formula, s α and s β For an ideal sensor displacement signal, s αs and s βs The same-frequency displacement signal s is introduced by the rotor mass imbalance. αm and s βm This is a frequency-doubled displacement signal introduced by sensor error.

[0047] From equations (15) and (16), it can be seen that when s = jiw, N IMRSC (jiω)→0, at this point, the harmonic disturbance current caused by rotor mass dynamic imbalance and sensor error can be completely suppressed, i.e., I αs →0,I αm →0,I βs →0,I βm →0. As shown in equation (8), the disturbance torques at the same frequency and harmonics are also completely suppressed, i.e., T αs →0,T αm →0,T βs →0,T βm →0.

[0048] (3) Improve the accuracy of attitude angular rate measurement

[0049] Taking a magnetically levitated sensitive gyroscope as an example, its angular rate measurement principle can be expressed as:

[0050]

[0051] In the formula, ω x and ω y These are the two-axis attitude angular velocities of the MSCSG. The torque coefficient is h = J z Ω, α, and β are the angular velocities of the magnetically levitated rotor, respectively. and These represent the angular acceleration of the magnetically levitated rotor. It can be seen that by measuring the angular velocity and angular acceleration of the magnetically levitated rotor relative to the stator, as well as the control current of the deflection channel, the attitude angular velocity of the spacecraft in the inertial coordinate system can be measured.

[0052] When considering the effects of rotor mass dynamic imbalance and sensor error, the angular rate measurement model can be expressed as:

[0053]

[0054] In the formula, and These are the angular velocity measurement errors caused by the dynamic imbalance of the rotor mass and the sensor error, respectively.

[0055] Substituting equations (6) and (7) into equation (19), we get:

[0056]

[0057] In the formula, the first part represents the influence of harmonic current, and the second part represents the influence of deflection angle jitter, which can be expressed as follows:

[0058]

[0059]

[0060] As can be seen from the above equation, the influence of rotor mass dynamic imbalance and sensor error on MSCSG attitude angular rate measurement includes two parts: harmonic currents of the same frequency and multiple frequencies and the jitter of rotor deflection angle. According to the principle of the influence of unbalanced vibration on the accuracy of MSCSG attitude angular rate measurement, when only the influence of harmonic current is considered, equation (20) can be simplified to:

[0061]

[0062] From equations (16), (17), and (24), it can be seen that when a multi-frequency resonant controller is introduced into the magnetic levitation rotor system, the same-frequency and harmonic currents of the deflection channel can be completely suppressed, resulting in I... α →i α I β →i β ,and This can improve the accuracy of attitude angular rate.

[0063] The principle of this invention is as follows: For the same-frequency and harmonic-frequency disturbance currents caused by rotor mass dynamic imbalance and sensor errors in a magnetic levitation rotor system, the control current of the deflection channel is used as the input signal of the multi-frequency resonant unbalanced vibration controller. As the rotational speed changes, the gain at the resonant frequency is adjusted, and different phase compensation factors are set within different speed ranges to fully track harmonic disturbance currents, improve the convergence speed of the algorithm, and ensure the stability of the system across the entire speed range. This achieves the effect of suppressing harmonic disturbance currents and vibration torque, thereby improving the accuracy of attitude angular rate measurement.

[0064] Compared with existing solutions, the main advantages of this invention are: the resonant controller has the characteristic of eliminating fixed-frequency interference, but when applied to a magnetic levitation rotor system, it can cause potential instability in the original system. To address this problem, this method changes the gain of the controller at different frequencies, so that the convergence speed of the algorithm adapts to the changes in rotor speed, ensuring control effect across the entire speed range. At the same time, the introduction of a phase compensation factor can adjust the phase angle in different speed ranges, ensuring system stability. In addition, the integral element in the controller can not only filter out the DC component in the input signal, but also facilitate the stability analysis of the system. Attached Figure Description

[0065] Figure 1 Detailed implementation plan diagram;

[0066] Figure 2 A schematic diagram of a novel multi-frequency resonant controller;

[0067] Figure 3 Block diagram of deflection control for a magnetically levitated rotor using a novel unbalanced vibration suppression method based on a multi-frequency resonant controller;

[0068] Figure 4 Experimental results of current magnitude before and after using this method in the deflection α channel;

[0069] Figure 5 Experimental results of current magnitude before and after using this method to deflect the β channel; Detailed Implementation Plan

[0070] By establishing an unbalanced vibration controller based on a novel multi-frequency resonant controller, the same-frequency and harmonic components in the deflection channel control current of the magnetic levitation rotor system are tracked, thereby suppressing the same-frequency and harmonic vibration torques. The specific steps include:

[0071] (1) Establish a dynamic model of the deflection of the magnetically levitated rotor affected by the dynamic imbalance of rotor mass and sensor error.

[0072] Rotor mass imbalance caused by uneven material mass distribution and processing errors can be divided into static imbalance and dynamic imbalance. Dynamic imbalance causes the rotor's geometric axis to misalign with its axis of inertia. Since sensors detect the displacement of the geometric center, when the rotor rotates at high speed, the sensors will detect a vibration signal that occurs at the same frequency as the rotational speed.

[0073] Θ d =ε d cos(Ωt+θ d (4)

[0074] In the formula, Θ d For rotor dynamic imbalance, ε d and θd These represent the eccentricity between the inertial axis and the geometric axis, and the initial phase, respectively.

[0075] Furthermore, due to material and installation limitations, the detection surface of the displacement sensor is not a smooth circle. When the rotor rotates at high speed, the irregular rotation curve also begins to rotate at the same speed, generating periodic interference with harmonic frequencies, i.e., sensor error. Therefore, the sensor's output signal will also contain harmonic signals of the rotational speed, which can be represented using Fourier series:

[0076]

[0077] In the formula, d x a represents the harmonic components in the sensor output signal caused by sensor error. dk and These represent the amplitude and initial phase of the harmonic vibration signal caused by the sensor.

[0078] Therefore, considering the rotor mass dynamic imbalance and sensor error, the rotor deflection angle detected by the displacement sensor can be expressed as:

[0079]

[0080] In the formula, α and β are the rotor deflection angles under ideal conditions, respectively. r and β r These are the actual deflection angles of the rotor when there is dynamic imbalance of mass, α and β. s and β s These represent the deflection angle disturbances caused by sensor errors, α. m and β m These are the deflection angle disturbances caused by sensor errors;

[0081] Combining equations (1) and (2), equation (3) can be further expressed as:

[0082]

[0083] The deflection displacement signal acquired by the sensor, after passing through the controller and power amplifier, generates a disturbance current with the same frequency and harmonics of the rotor. Therefore, the deflection control current can be expressed as:

[0084]

[0085] In the formula, I α and I β These represent the currents deflecting the α and β channels, respectively, and consist of three parts, i α and i β I represents the deflection control current. αs and I βsI represents the in-frequency disturbance current caused by rotor mass imbalance. αm and I βm This represents the frequency harmonic disturbance current caused by sensor error.

[0086] in,

[0087]

[0088]

[0089] Furthermore, from the deflection dynamics equations of the MSCSG and the control principle of the LFMB, we can obtain:

[0090]

[0091] 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... J is the central angle corresponding to the coil. x J y and J z Let 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. Substituting equations (6) and (7) into equation (8) yields:

[0092]

[0093] In the formula,

[0094]

[0095] make

[0096] As can be seen from equation (11), the unbalanced vibration torque of the MSCSG mainly consists of two parts: the same-frequency vibration torque generated by the rotor dynamic imbalance and the harmonic vibration torque generated by the sensor error.

[0097] (2) Establish an unbalanced vibration controller based on a novel multi-frequency resonance.

[0098] like Figure 2 As shown, the novel multi-frequency resonant controller can be represented as:

[0099]

[0100] Compared with traditional multi-frequency resonant controllers, the introduction of control parameter k i and θ i Among them, k iTo control the gain factor, the gain at each resonant frequency can be adjusted independently to achieve optimal convergence speed and improve the suppression of harmonic vibrations. θ i As a phase compensation factor, the phase angle is adjusted within different frequency bands to ensure rotor stability across the entire speed range. Furthermore, by introducing an integral term, not only can the DC component in the input signal be filtered out, but it also facilitates system stability analysis.

[0101] From equation (12), the closed-loop transfer function of the multi-frequency resonant controller can be obtained as follows:

[0102]

[0103] In the formula,

[0104]

[0105]

[0106] From equations (13), (14) and (15), it can be seen that,

[0107]

[0108] Depend on Figure 3 It can be seen that the deflection control principle of the magnetic levitation rotor system is as follows:

[0109]

[0110] In the formula, G c G represents a PID controller. w G represents a power amplifier. s S represents a displacement sensor. α and S β The actual displacement signal from the displacement sensor, according to the principle of unbalanced vibration, consists of three parts, which can be expressed as:

[0111]

[0112] In the formula, s α and s β For an ideal sensor displacement signal, s αs and s βs The same-frequency displacement signal s is introduced by the rotor mass imbalance. αm and s βm This is a frequency-doubled displacement signal introduced by sensor error.

[0113] From equations (16) and (17), it can be seen that when s = jiw, N IMRSC (jiω)→0, at this point, the harmonic disturbance current caused by rotor mass dynamic imbalance and sensor error can be completely suppressed, i.e., Iαs →0,I αm →0,I βs →0,I βm →0. As shown in equation (8), the disturbance torques at the same frequency and harmonics are also completely suppressed, i.e., T αs →0,T αm →0,T βs →0,T βm →0.

[0114] (3) Improve the accuracy of attitude angular rate measurement

[0115] Taking a magnetically levitated sensitive gyroscope as an example, its angular rate measurement principle can be expressed as:

[0116]

[0117] In the formula, ω x and ω y These are the two-axis attitude angular velocities of the MSCSG. The torque coefficient is h = J z Ω, α, and β are the angular velocities of the magnetically levitated rotor, respectively. and These represent the angular acceleration of the magnetically levitated rotor. It can be seen that by measuring the angular velocity and angular acceleration of the magnetically levitated rotor relative to the stator, as well as the control current of the deflection channel, the attitude angular velocity of the spacecraft in the inertial coordinate system can be measured.

[0118] When considering the effects of rotor mass dynamic imbalance and sensor error, the angular rate measurement model can be expressed as:

[0119]

[0120] In the formula, and These are the angular velocity measurement errors caused by the dynamic imbalance of the rotor mass and the sensor error, respectively.

[0121] Substituting equations (6) and (7) into equation (20), we get:

[0122]

[0123] In the formula, the first part represents the influence of harmonic current, and the second part represents the influence of deflection angle jitter, which can be expressed as follows:

[0124]

[0125]

[0126] As can be seen from the above equation, the influence of rotor mass dynamic imbalance and sensor error on MSCSG attitude angular rate measurement includes two parts: harmonic currents of the same frequency and multiple frequencies and the jitter of rotor deflection angle. According to the principle of the influence of unbalanced vibration on the accuracy of MSCSG attitude angular rate measurement, when only the influence of harmonic current is considered, equation (20) can be simplified to:

[0127]

[0128] From equations (16), (17), and (24), it can be seen that when a multi-frequency resonant controller is introduced into the magnetic levitation rotor system, the same-frequency and harmonic currents of the deflection channel can be completely suppressed, resulting in I... α →i α I β →i β ,and This can improve the accuracy of attitude angular rate.

[0129] To verify the effectiveness of the proposed method, Figure 4 and Figure 5 Experimental results before and after applying this method at 5000 rpm are presented. The FFT analysis results show the control current spectra of the deflection α-channel and β-channel before and after applying this method. The same-frequency disturbance current of the α-channel decreased from -31.29 dB to -45.33 dB, the third harmonic component decreased from -40.94 dB to -50.76 dB, and the fifth harmonic component decreased from -44.9 dB to -53.84 dB, representing reductions of 97.54%, 88.35%, and 83.73%, respectively. The same-frequency disturbance current of the β-channel decreased from -28.32 dB to -43.38 dB, the third harmonic component decreased from -42.33 dB to -56.58 dB, and the fifth harmonic component decreased from -47.65 dB to -56.08 dB, representing reductions of 98.59%, 94.51%, and 80.39%, respectively. Therefore, the method of the present invention can effectively suppress the same-frequency and harmonic-frequency disturbance currents in the deflection channel of the magnetic levitation rotor system.

Claims

1. A method for suppressing unbalanced vibration based on a novel multi-frequency resonant controller, characterized in that: To address the same-frequency and harmonic-frequency disturbance currents introduced by rotor mass dynamic imbalance and sensor errors in a magnetic levitation rotor system, an unbalanced vibration controller based on a novel multi-frequency resonant controller is established. This controller uses the same-frequency and harmonic-frequency resonant currents in the two deflection channels of the magnetic levitation rotor system as signals to be eliminated, thereby suppressing vibration torque. The specific steps include: (1) Establish a dynamic model of the deflection of the magnetically levitated rotor affected by the dynamic imbalance of rotor mass and sensor error. Rotor mass imbalance caused by uneven material mass distribution and processing errors can be divided into static imbalance and dynamic imbalance. Dynamic imbalance causes the rotor's geometric axis to not coincide with its axis of inertia. The sensor detects the displacement of the geometric center. When the rotor rotates at high speed, the sensor will detect a jump at the same frequency as the rotational speed, i.e., a vibration signal at the same frequency. (1) In the formula, For rotor dynamic imbalance, and These represent the eccentricity between the inertial axis and the geometric axis, and the initial phase, respectively. Furthermore, due to material and installation limitations, the detection surface of the displacement sensor is not a smooth circle. When the rotor rotates at high speed, the irregular rotation curve also begins to rotate at the same speed, generating periodic interference at multiples of the rotational speed, i.e., sensor error. Therefore, the sensor's output signal will also contain a frequency harmonic of the rotational speed, which can be represented by a Fourier series. (2) In the formula, The harmonic components in the sensor output signal caused by sensor error. a dk and These represent the amplitude and initial phase of the harmonic vibration signal caused by the sensor's harmonics, respectively. Therefore, considering the rotor mass dynamic imbalance and sensor error, the rotor deflection angle detected by the displacement sensor can be expressed as: (3) In the formula, and These are the rotor deflection angles under ideal conditions. and These represent the actual deflection angles of the rotor when there is dynamic imbalance due to mass. and These are the deflection angle disturbances caused by sensor errors. and These are the deflection angle disturbances caused by sensor errors; Combining equations (1) and (2), equation (3) can be further expressed as: (4) The deflection displacement signal acquired by the sensor, after passing through the controller and power amplifier, generates a disturbance current with the same frequency and harmonics of the rotor; therefore, the deflection control current can be expressed as: (5) In the formula, and They represent deflection respectively. Channels and The current in the channel consists of three parts. and Indicates the deflection control current. and This represents the same-frequency disturbance current caused by rotor mass imbalance. and This represents the frequency harmonic disturbance current caused by sensor error; in, (6) (7) Furthermore, from the deflection dynamics equations of the MSCSG and the control principle of the LFMB, we can obtain: (8) In the formula, N The number of coil turns. I x and I y These represent the coil current magnitudes for the radial X and Y channels, respectively. B The magnitude of the magnetic field in the LFMB air gap. L r The radius of the LFMB stator frame is... The central angle corresponding to the coil. , and Let Ω be the moment of inertia of each shaft of the rotor, and Ω be the rotor speed; substituting equations (6) and (7) into equation (8) yields: (9) In the formula, (10) make (11) As can be seen from equation (11), the unbalanced vibration torque of the MSCSG mainly consists of two parts: the same-frequency vibration torque generated by the rotor dynamic imbalance and the harmonic vibration torque generated by the sensor error. (2) Establish an unbalanced vibration controller based on a novel multi-frequency resonance. The novel multi-frequency resonant controller can be represented as: (12) Compared with traditional multi-frequency resonant controllers, the introduction of control parameters and ;in, To control the gain factor, the gain at each resonant frequency can be adjusted independently to achieve the optimal convergence speed and improve the suppression effect of harmonic vibration. As a phase compensation factor, the phase angle in different frequency bands is adjusted to ensure the stability of the rotor across the entire speed range; in addition, by introducing an integral term, not only can the DC component in the input signal be filtered out, but it also facilitates the stability analysis of the system. From equation (12), the closed-loop transfer function of the multi-frequency resonant controller can be obtained as follows: (13) In the formula, (14) (15) From equations (13), (14) and (15), it can be seen that, (16) Furthermore, the deflection control principle of the magnetic levitation rotor system is as follows: (17) In the formula, This indicates a PID controller. Indicates a power amplifier. Indicates displacement sensor, and The actual displacement signal from the displacement sensor, according to the principle of unbalanced vibration, consists of three parts, which can be expressed as: (18) In the formula, and For an ideal sensor displacement signal, and This is the same-frequency displacement signal introduced by rotor mass imbalance. and This is a frequency-harmonic displacement signal introduced by sensor error; From equations (15) and (16), it can be seen that when hour, At this point, the harmonic disturbance current caused by rotor mass dynamic imbalance and sensor error can be completely suppressed, i.e. , , , As can be seen from equation (8), the disturbance torques at the same frequency and harmonics are also completely suppressed, i.e. , , , ; (3) Improve the accuracy of attitude angular rate measurement Taking a magnetically levitated sensitive gyroscope as an example, its angular rate measurement principle can be expressed as: (19) In the formula, and These are the two-axis attitude angular velocities of the MSCSG. , is the torque coefficient. , and These are the angular velocities of the magnetically levitated rotor. and These are the deflection angular accelerations of the magnetically levitated rotor; it can be seen that by measuring the deflection angular velocity and angular acceleration of the magnetically levitated rotor relative to the stator, as well as the control current of the deflection channel, it is possible to measure the attitude angular velocity of a spacecraft in an inertial coordinate system. When considering the effects of rotor mass dynamic imbalance and sensor error, the angular rate measurement model can be expressed as: (20) In the formula, and These are the angular velocity measurement errors caused by rotor mass dynamic imbalance and sensor error, respectively. Substituting equations (6) and (7) into equation (19), we get: (21) In the formula, the first part represents the influence of harmonic current, and the second part represents the influence of deflection angle jitter, which can be expressed as follows: (22) (23) As can be seen from the above equation, the influence of rotor mass dynamic imbalance and sensor error on MSCSG attitude angular rate measurement includes two parts: harmonic currents of the same frequency and multiple frequencies and the jitter of rotor deflection angle. According to the principle of the influence of unbalanced vibration on the accuracy of MSCSG attitude angular rate measurement, when only the influence of harmonic current is considered, equation (20) can be simplified to: (24) From equations (16), (17), and (24), it can be seen that when a multi-frequency resonant controller is introduced into the magnetic levitation rotor system, the same-frequency and harmonic currents of the deflection channel can be completely suppressed. , ,and , This can improve the accuracy of attitude angular rate.

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