Magnetic suspension bearing system compensation parameter self-tuning vibration suppression method

Abstract

The invention discloses a compensation parameter self-tuning vibration suppression method for a magnetic suspension bearing system, which belongs to the field of magnetic suspension bearing control, and comprises the following steps: S1, carrying out a pulse excitation experiment on a magnetic suspension bearing-rotor system by using an electromagnetic vibration exciter, a magnetic suspension bearing-rotor system model is obtained through parameter identification of the frequency response function; s2, obtaining a phase compensation angle according to the mapping relation of the frequency response function; and S3, according to the system model, designing a compensation controller based on a second-order generalized integral-synchronous rotating coordinate system, and through the system model, the phase compensation angle and stability criterion self-tuning compensation control parameters, realizing vibration suppression of the magnetic suspension system. The method can effectively suppress unbalanced mass vibration of the rotor, compensation parameters do not need to be tested and calibrated in advance, the self-tuning process is rapid and convenient, and the method is suitable for any multi-degree-of-freedom magnetic suspension bearing-rotor system and has good practical value and economic value.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of magnetic bearing control, in particular to a magnetic bearing system compensation parameter self-tuning vibration suppression method. BACKGROUND

[0002] Vibration caused by mass imbalance is a common problem in rotating machinery. A large number of studies have shown that most of the failures in rotating machinery are caused by unbalanced vibration, and mass imbalance is the most important unbalance in rotating system vibration. In order to reduce the influence of unbalanced vibration, the common method is to carefully adjust the dynamic balance of the rotor, so that the geometric center of the rotor and its principal axis of inertia are completely coincident. However, this method not only has high cost, but also cannot overcome the problem of distribution change of rotor imbalance during rotation. Therefore, a certain amount of residual imbalance of the rotor will exist. The most important and unique feature of magnetic bearing compared with other bearings is that it can actively adjust the support of the rotor at high frequency in real time. This active control feature can make the magnetic bearing system overcome the vibration caused by residual imbalance, so that the rotor can rotate more stably and with lower loss at high speed.

[0003] In practical applications, the controller needs to introduce additional elements to suppress unbalanced vibration. Among them, it is mainly divided into automatic balancing and unbalance compensation. Based on the second-order generalized integral-synchronous rotating coordinate system, the unbalance compensation needs to be determined according to the actual system. The conventional method uses sinusoidal sweep to obtain the phase angle and obtains the PI control parameters by step-by-step trial. The sinusoidal sweep obtains the frequency domain characteristics of the system by sinusoidal excitation of discrete frequencies. For the requirement of a large range of sweep, under the premise of ensuring identification accuracy, this sweep method is time-consuming and is strongly disturbed by the environment, and cannot quickly and conveniently realize the identification of the system and the self-tuning of the compensation parameters. And due to the uncertainty of the system, the existing compensation parameter adjustment can only adjust the unbalance compensation parameters through trial and error for unknown magnetic bearing-rotor systems, which not only consumes time and effort, but also easily causes system instability and irreversible damage to the equipment. The existence of these problems shows that how to design a magnetic bearing system vibration suppression method that takes into account efficiency, accuracy and convenience of compensation parameter adjustment is a core challenge that needs to be solved in the field of magnetic bearing control. SUMMARY

[0004] The present application is to solve the above technical problems, and proposes a magnetic bearing system compensation parameter self-tuning vibration suppression method. The method realizes the identification and compensation parameter self-tuning of the system based on the electromagnetic pulse excitation method, can increase the vibration suppression efficiency at low cost, and is suitable for any multi-degree-of-freedom magnetic rotor system. At the same time, the method is adapted to the unbalance compensation strategy of the second-order generalized integral-synchronous rotating coordinate system, and has good unbalanced vibration compensation effect.

[0005] A magnetic suspension bearing system compensation parameter self-tuning vibration suppression method, comprising the following steps:

[0006] Step S1, using an electromagnetic exciter to pulse excite the magnetic suspension bearing-rotor system, identifying the frequency response function between the power amplifier input and the sensor output, obtaining the dynamic model of the magnetic suspension bearing-rotor system and the transfer function P(s) of the magnetic suspension bearing-rotor model;

[0007] Step S2, obtaining the mapping relationship between the phase compensation angle and the response frequency of the magnetic suspension bearing-rotor system according to the frequency response function obtained in step S1, and obtaining the required phase compensation angle of the rotor system at different rotational frequencies from the mapping relationship;

[0008] Step S3, designing a compensation controller based on a second-order generalized integral-synchronous rotating coordinate system according to the transfer function P(s) of the magnetic suspension bearing-rotor model obtained in step S1, and obtaining the compensation controller parameters according to the system stability criterion and the phase compensation angle obtained in step S2, and finally obtaining the compensation controller; the preprocessed error signal is input into the compensation controller through feedback, and the compensation controller outputs a control voltage signal after processing, and outputs a control current signal through a power amplifier, so as to realize the compensation and suppression of the magnetic suspension bearing-rotor system to the unbalanced mass.

[0009] Further, in step S1, the magnetic suspension bearing-rotor system is subjected to pulse excitation experiment, and the excitation signal is:

[0010] f(t)=k i I0δ(t)+k s s(t)

[0011] Wherein, k i is the control current stiffness of the magnetic suspension bearing, I0 is the control current intensity, δ(t) is the unit impact function, k s is the displacement stiffness of the magnetic suspension bearing, and s(t) is the rotor displacement; the pulse control current signal is applied to the magnetic suspension bearing-rotor system to obtain the system response signal:

[0012]

[0013] Wherein, φ dr is the damping vibration frequency, φ r is the natural frequency, ζ r is the damping ratio, φ r is the initial phase, A r is the vibration amplitude, and r represents the order;

[0014] The Fourier transform is performed on the excitation signal and the system response signal to obtain the frequency spectrum of the excitation signal and the system response signal:

[0015]

[0016] Further, in the step S1, the frequency response function between the power amplifier input and the sensor output is:

[0017]

[0018] wherein K sensor is the sensor gain, A(s) is the power amplifier transfer function, and C(s) is the controller transfer function.

[0019] Further, in the step S1, the dynamic model of the magnetic bearing-rotor system is:

[0020]

[0021] wherein M is the generalized mass matrix, L b is the magnetic bearing support arm matrix, S is the rotor displacement matrix, is the first-order derivative matrix of the rotor displacement matrix with respect to time, is the second-order derivative matrix of the rotor displacement matrix with respect to time, G is the rotor gyro matrix, K s is the displacement stiffness matrix, K i is the current stiffness matrix, and I is the current matrix, which is expressed as:

[0022]

[0023] wherein I x , I y , and I z are the moments of inertia of the rotor about the x, y, and z axes, respectively, m is the total mass of the rotor, ω is the rotor rotation frequency, l A and l B are the distances from the O point to the positions of the magnetic bearing A and the magnetic bearing B, x bA and y bA are the displacements of the rotor in the x and y directions at the A-end bearing, respectively, x bB and y bB are the displacements of the rotor in the x and y directions at the B-end bearing, respectively, k sA and k sB are the displacement stiffnesses of the A-end and B-end magnetic bearings, respectively, k iA and k iB are the current stiffnesses of the A-end and B-end magnetic bearings, respectively, i xA and i yA are the control current magnitudes of the rotor in the x and y directions at the A-end bearing, respectively.xB , i yB are the control current of the rotor at the B end bearing in the x and y directions, respectively;

[0024] The Laplace transform is performed on the dynamic model of the magnetic bearing-rotor system, and the transfer function of the magnetic bearing-rotor model is obtained as follows:

[0025]

[0026] Further, in the step S2, the frequency response function is calculated based on the excitation signal and the system response signal spectrum, and the compensator parameters are obtained, and the frequency response function is expressed as:

[0027]

[0028] The phase angle defect is expressed as:

[0029]

[0030] The compensation angle parameter in the compensator is obtained as:

[0031]

[0032] Further, the compensation controller in the step S3 is composed of a controller and a compensator, the compensator is connected in parallel with the controller, and the control quantity is compensated to suppress the unbalanced vibration;

[0033] The controller of the compensation controller is a PID controller, and the transfer function of the controller is:

[0034]

[0035] wherein k P is a proportional coefficient, k I is an integral coefficient, and k D is a differential coefficient;

[0036] The compensator of the compensation controller uses a second-order generalized integral-synchronous rotating coordinate system compensation, which is composed of a second-order generalized integral compensation link and a synchronous rotating coordinate system compensation link, and the transfer function of the second-order generalized integral compensation link is:

[0037]

[0038] wherein k is a second-order generalized integral gain constant, and ω0 is a resonant angular frequency;

[0039] The synchronous rotating coordinate system compensation link is composed of a PARK transformation link, a low-pass filter, a PI controller, and a PARK inverse transformation link, and the transfer function is:

[0040]

[0041] wherein, k ppi is a proportional coefficient of the PI controller, k ipi is an integral coefficient of the PI controller, ω1 is a rotating angular frequency of the synchronous coordinate system, θ is a rotating phase angle of the synchronous coordinate system, and τ is a time constant of the low-pass filter;

[0042] In the same frequency suppression, the rotor rotational frequency, the resonant angular frequency, and the rotating angular frequency of the synchronous coordinate system are consistent, that is, ω = ω0 = ω1, and the transfer function of the compensator is:

[0043]

[0044] Further, in the step S3, the system stability criterion is:

[0045]

[0046] wherein, i and j represent imaginary units.

[0047] Compared with the prior art, the present application can achieve the following beneficial effects:

[0048] (1) The present application performs pulse excitation experiments on the magnetic suspension bearing-rotor system through the electromagnetic exciter, and uses the frequency response function to fit the system transfer function, which greatly shortens the test time, reduces the influence of environmental interference, and significantly improves the parameter identification efficiency compared with the traditional sine sweep method.

[0049] (2) The present application combines the electromagnetic pulse excitation method with the unbalance compensation strategy of the second-order generalized integral-synchronous rotating coordinate system, realizes the decoupling control and zero static error tracking control of the magnetic suspension bearing, effectively suppresses the same frequency vibration caused by the unbalanced mass of the rotor, and improves the control precision and system stability.

[0050] (3) The present application can realize compensation parameter self-tuning for unknown systems without manual trial and error or advance testing and calibration, and the parameter tuning process is based on small impact experiments, avoiding the risk of system instability caused by traditional manual parameter adjustment, and is convenient to operate and does not damage the equipment, significantly reducing the debugging cost and time.

[0051] (4) The magnetic suspension bearing system compensation parameter self-tuning vibration suppression method proposed by the present application is applicable to any multi-degree-of-freedom magnetic suspension bearing rotor system, can effectively cover the vibration suppression requirements under different rotational speeds and modes, has good practical value and economic value, and is especially suitable for complex and variable magnetic suspension system applications in industrial scenes. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1A flow chart of a magnetic suspension bearing system compensation parameter self-tuning vibration suppression method according to the present application is provided;

[0053] Figure 2 A compensation control principle block diagram according to the present application is provided;

[0054] Figure 3 A compensator principle diagram according to the present application is provided;

[0055] Figure 4 A fitting curve diagram of a phase compensation angle with respect to a rotating speed according to an embodiment of the present application is provided;

[0056] Figure 5 A rotor vibration amplitude comparison diagram of a magnetic suspension bearing system with and without compensation parameter self-tuning vibration suppression according to an embodiment of the present application is provided. DETAILED DESCRIPTION

[0057] The specific embodiments of the present application will be further described below with reference to the accompanying drawings, and the technical solutions in the embodiments of the present application are described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0058] In combination Figure 1 A magnetic suspension bearing system compensation parameter self-tuning vibration suppression method, comprising the following steps:

[0059] Step S1, a pulse excitation experiment is performed on a magnetic suspension bearing-rotor system by using an electromagnetic exciter, a frequency response function between an input of a power amplifier and an output of a sensor is identified, a dynamic model of the magnetic suspension bearing-rotor system and a transfer function P(s) of the magnetic suspension bearing-rotor model are obtained;

[0060] Step S2, a mapping relationship between a phase compensation angle and a response frequency of the magnetic suspension bearing-rotor system is obtained according to the frequency response function obtained in the pulse excitation experiment in step S1, the required phase compensation angle of the rotor system at different rotating frequencies is obtained from the mapping relationship; a fitting curve diagram of the phase compensation angle with respect to the rotating speed obtained from the frequency response function is as shown in Figure 4 The expression obtained by polynomial fitting is the relationship between the phase compensation angle required by the compensation link and the rotating speed;

[0061] Step S3, designing a compensation controller based on the second-order generalized integral-synchronous rotating coordinate system according to the transfer function P(s) of the magnetic suspension bearing-rotor model obtained in step S1, and obtaining the compensation controller parameters according to the system stability criterion and the phase compensation angle obtained in step S2; the preprocessed error signal is input into the compensation controller through feedback, the control voltage signal is output after the compensation controller is processed, the control current signal is output through the power amplifier, the compensation and suppression of the unbalanced mass of the magnetic suspension bearing-rotor system are realized, and the vibration amplitude of the rotor of the magnetic suspension bearing system after the vibration suppression with the self-adjusting compensation parameters is compared with the vibration amplitude of the rotor without the vibration suppression, as shown in FIG. Figure 5 .

[0062] Further, in step S1, the magnetic suspension bearing-rotor system is excited by a pulse, and the excitation signal is:

[0063] f(t)=k i I0δ(t)+k s s(t)

[0064] wherein k i is the control current stiffness of the magnetic suspension bearing, I0 is the control current intensity, δ(t) is the unit impact function, k s is the displacement stiffness of the magnetic suspension bearing, and s(t) is the rotor displacement; the rotor displacement does not change in a short time, so that a pulse control current signal of a certain size can be applied to obtain the required system response; the pulse control current signal is applied to the magnetic suspension bearing-rotor system to obtain the system response signal, and the system response signal is:

[0065]

[0066] wherein φ dr is the damping vibration frequency, φ r is the natural frequency, ζ r is the damping ratio, φ r is the initial phase, A r is the vibration amplitude, and r represents the order;

[0067] The Fourier transform is performed on the excitation signal and the system response signal to obtain the frequency spectrum of the excitation signal and the system response signal:

[0068]

[0069] Further, in step S1, the frequency response function between the power amplifier input and the sensor output is:

[0070]

[0071] wherein K sensorA(s) is a power amplifier transfer function, and C(s) is a controller transfer function.

[0072] Further, the dynamic model of the magnetic suspension bearing-rotor system in step S1 is:

[0073]

[0074] where M is a generalized mass matrix, L b is a magnetic suspension bearing support arm matrix, S is a rotor displacement matrix, is a first-order derivative matrix of the rotor displacement matrix with respect to time, is a second-order derivative matrix of the rotor displacement matrix with respect to time, G is a rotor gyro matrix, K s is a displacement stiffness matrix, K i is a current stiffness matrix, I is a current matrix, and is expressed as:

[0075]

[0076] where I x , I y , and I z are the moments of inertia of the rotor about the x, y, and z axes, respectively, m is the total mass of the rotor, ω is the rotor rotation frequency, l A , and l B are the distances from the O point to the positions of the magnetic suspension bearing A and the magnetic suspension bearing B, x bA , y bA are the displacements of the rotor in the x and y directions at the A-end bearing, x bB , y bB are the displacements of the rotor in the x and y directions at the B-end bearing, k sA , and k sB are the displacement stiffnesses of the A-end and B-end magnetic suspension bearings, k iA , and k iB are the current stiffnesses of the A-end and B-end magnetic suspension bearings, i xA , i yA are the control current magnitudes of the rotor in the x and y directions at the A-end bearing, i xB , i yB are the control current magnitudes of the rotor in the x and y directions at the B-end bearing.

[0077] The Laplace transform is performed on the dynamic model of the magnetic suspension bearing-rotor system, and the transfer function of the magnetic suspension bearing-rotor model is:

[0078]

[0079] Further, in the step S2, the frequency response function is calculated based on the excitation signal and the system response signal spectrum, and the compensator parameters are obtained, and the frequency response function is expressed as:

[0080]

[0081] The phase missing angle is expressed as:

[0082]

[0083] The compensation angle parameter in the compensator is obtained as:

[0084]

[0085] Further, in combination with Figure 2 , the compensation controller in the step S3 is composed of a controller and a compensator, the compensator is connected in parallel with the controller, and the control quantity is compensated to suppress the unbalanced vibration;

[0086] The controller of the compensation controller is a PID controller, and the controller transfer function is:

[0087]

[0088] wherein k P is a proportional coefficient, k I is an integral coefficient, and k D is a differential coefficient;

[0089] The compensator of the compensation controller uses a second-order generalized integral-synchronous rotating coordinate system compensation, which is composed of a second-order generalized integral compensation link and a synchronous rotating coordinate system compensation link, as shown in Figure 3 The second-order generalized integral compensation link can realize decoupling control of the magnetic suspension bearing, and the synchronous rotating coordinate system compensation link can realize zero-error tracking control of the magnetic suspension bearing system;

[0090] The transfer function of the second-order generalized integral compensation link is:

[0091]

[0092] wherein k is a second-order generalized integral gain constant, and ω0 is a resonant angular frequency;

[0093] The compensation link of the synchronous rotating coordinate system is composed of a PARK transformation link, a low-pass filter, a PI controller, and a PARK inverse transformation link, and the transfer function is:

[0094]

[0095] wherein k ppi is a proportional coefficient of the PI controller, and k ipiis an integral coefficient of the PI controller, ω1 is a rotating angular frequency of the synchronous coordinate system, θ is a rotating phase angle of the synchronous coordinate system, and τ is a time constant of the low-pass filter;

[0096] In the same frequency suppression, the rotor rotation frequency, the resonance angular frequency and the rotating angular frequency of the synchronous coordinate system are consistent, i.e., ω = ω0 = ω1, and the transfer function of the compensator is:

[0097]

[0098] Further, in the step S3, the system stability criterion is:

[0099]

[0100] wherein i and j each represent an imaginary unit.

[0101] As long as the parameters meeting the stability criterion can make the system realize stable non-compensation control, but in practice, additional constraints are required according to different system requirements to meet the system working requirements.

[0102] The fitting curve diagram of the phase compensation angle obtained from the frequency response function about the rotating speed in the embodiment of the application is as shown in Figure 4 The expression obtained by polynomial fitting is the relationship between the phase compensation angle required by the compensation element and the rotating speed. The rotor model is built by the finite element method. After identification and self-tuning of the compensation controller parameters of the simulation model, the phase compensation angle is:

[0103]

[0104] The self-tuned compensation controller parameters are shown in Table 1:

[0105] Table 1: Self-tuned compensation controller parameters

[0106]

[0107] The comparison diagram of the vibration amplitude of the magnetic suspension bearing system after compensation parameter self-tuning vibration suppression and the vibration amplitude of the rotor without vibration suppression is as shown in Figure 5 It can be seen that the magnetic suspension bearing system compensation parameter self-tuning vibration suppression method realizes a large suppression of the same frequency vibration, and improves the stability of the magnetic suspension bearing-rotor system working process.

[0108] The above only describes the preferred embodiments of the application, and the application is not limited to the above embodiments. It can be understood that other improvements and changes directly derived or thought by those skilled in the art without departing from the spirit and concept of the application should be considered to be included in the protection scope of the application.

Claims

1. A method for self-tuning vibration suppression of compensation parameters of a magnetic bearing system, characterized in that: The following steps are involved: Step S1: Using an electromagnetic exciter, perform a pulse excitation experiment on the magnetic bearing-rotor system to identify the frequency response function between the power amplifier input and the sensor output, and obtain a dynamic model of the magnetic bearing-rotor system and a transfer function P(s) of the magnetic bearing-rotor model; Step S2: obtaining a mapping relationship between a phase compensation angle and a response frequency of the magnetic bearing-rotor system according to the frequency response function obtained from the pulse excitation experiment in step S1, and obtaining a required phase compensation angle at different rotational frequencies of the rotor system from the mapping relationship; Step S3, designing a compensation controller based on the second-order generalized integral-synchronous rotating coordinate system according to the transfer function P(s) of the magnetic bearing-rotor model obtained in step S1, and obtaining compensator parameters according to the system stability criterion and the phase compensation angle obtained in step S2, and finally obtaining the compensation controller; the preprocessed error signal is fed back into the compensation controller, and the compensation controller outputs a control voltage signal after processing, and outputs a control current signal through the power amplifier, thereby realizing compensation and suppression of the unbalanced mass of the magnetic bearing-rotor system.

2. The method for self-tuning vibration suppression of a magnetic bearing system compensation parameter according to claim 1, characterized in that: In step S1, a pulse excitation experiment is performed on the magnetic bearing-rotor system, and the excitation signal is: f(t)=k i I0δ(t)+k s s(t) Among them, k i is the control current stiffness of the magnetic bearing, I0 is the control current intensity, δ(t) is the unit impact function, k s is the displacement stiffness of the magnetic bearing, s(t) is the rotor displacement; a pulse control current signal is applied to the magnetic bearing-rotor system to obtain the system response signal, which is: Among them, ω dr is the damped vibration frequency, ω r is the natural frequency, ζ r is the damping ratio, φ r is the initial phase, A r is the vibration amplitude, r represents the order; Perform Fourier transform on the excitation signal and the system response signal, and obtain the spectrum of the excitation signal and the system response signal as follows:

3. The method for self-tuning vibration suppression of compensation parameters of a magnetic bearing system according to claim 1, characterized in that: In step S1, the frequency response function between the power amplifier input and the sensor output is: Among them, K sensor is the sensor gain, A(s) is the power amplifier transfer function, and C(s) is the controller transfer function.

4. The method for self-tuning vibration suppression of compensation parameters of a magnetic bearing system according to claim 1, characterized in that: The dynamic model of the magnetic bearing-rotor system in step S1 is: Where M is the generalized mass matrix, L b is the magnetic bearing support arm matrix, S is the rotor displacement matrix, is the first-order derivative matrix of the rotor displacement matrix with respect to time, is the second-order derivative matrix of the rotor displacement matrix with respect to time, G is the rotor gyroscope matrix, K s is the displacement stiffness matrix, K i is the current stiffness matrix, I is the current matrix, expressed as: Among them, I x , I y and I z are the moments of inertia of the rotor around the x, y and z axes respectively, m is the total mass of the rotor, ω is the rotor speed, l A With l B x is the distance between the magnetic bearing A and the magnetic bearing B and point O, bA 、y bA They are the displacements of the rotor at the A-end bearing in the x and y directions, respectively. bB 、y bB are the displacements of the rotor at the B-end bearing in the x and y directions, k sA and k sB are the displacement stiffness of the magnetic bearing at end A and end B, k iA and k iB are the current stiffness of the magnetic bearing at end A and end B, i xA 、i yA are the control currents of the rotor at the A-end bearing in the x and y directions, i xB 、i yB are the magnitudes of the control current of the rotor at the B-end bearing in the x and y directions respectively; The Laplace transform is performed on the dynamic model of the magnetic bearing-rotor system, and the transfer function of the magnetic bearing-rotor model is obtained as follows:

5. The method for self-tuning vibration suppression of compensation parameters of a magnetic bearing system according to claim 1, characterized in that: In step S2, a frequency response function is fitted and calculated based on the excitation signal and the system response signal spectrum to obtain compensator parameters. The frequency response function is expressed as: The phase defect is expressed as: The compensation angle parameters in the compensator are obtained as follows:

6. The method for self-tuning vibration suppression of a magnetic bearing system compensation parameter according to claim 1, characterized in that: In step S3, the compensation controller is composed of a controller and a compensator, and the compensator is connected in parallel with the controller to compensate the control amount to suppress unbalanced vibration; The controller of the compensation controller is a PID controller, and the controller transfer function is: Among them, k P is the proportionality coefficient, k I is the integration coefficient, k D is the differential coefficient; The compensator of the compensation controller uses the second-order generalized integral-synchronous rotating coordinate system compensation, which consists of a second-order generalized integral compensation link and a synchronous rotating coordinate system compensation link. The transfer function of the second-order generalized integral compensation link is: Where k is the second-order generalized integral gain constant, ω0 is the resonant angular frequency; The synchronous rotating coordinate system compensation link consists of a PARK transformation link, a low-pass filter, a PI controller, and a PARK inverse transformation link. The transfer function is: Among them, k ppi is the proportional coefficient of the PI controller, k ipi is the integral coefficient of the PI controller, ω1 is the rotation angular frequency of the synchronous coordinate system, θ is the rotation phase angle of the synchronous coordinate system, and τ is the time constant of the low-pass filter; In the same-frequency suppression, the rotor rotation frequency, the resonant angular frequency and the rotation angular frequency of the synchronous coordinate system are consistent, that is, ω=ω0=ω1, and the transfer function of the compensator is:

7. The method for self-tuning vibration suppression of a magnetic bearing system compensation parameter according to claim 1, characterized in that: In step S3, the system stability criterion is: Among them, i and j both represent imaginary units.

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