A compensation control method of a magnetic bearing based on adaptive natural frequency

Abstract

The application discloses a compensation control method of a magnetic bearing based on adaptive inherent frequency, and comprises the following steps: establishing a dynamic equation of an active electromagnetic bearing according to rotor dynamics theory; constructing a compensation current and extracting an unbalance coefficient according to the dynamic equation of the electromagnetic bearing rotor system; after adding the constructed unbalance compensation signal to the dynamic equation of the active electromagnetic bearing, analyzing the stability of the system; and based on the compensation control method of the magnetic bearing, the adaptive inherent frequency is changed to make the constructed compensation signal stabilize the control of the electromagnetic bearing rotor system within the whole rotating speed. According to the characteristics of the adaptive change of the inherent frequency of the magnetic bearing rotor system, the application solves the problem that the compensation algorithm cannot stably converge near the inherent frequency, and widens the working range of the compensation algorithm.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of magnetic bearing rotor unbalance vibration compensation control, and particularly relates to a compensation control method of a magnetic bearing based on adaptive natural frequency. BACKGROUND

[0002] AMB (Active Magnetic Bearing) makes the rotor suspended by controllable electromagnetic force, and is widely used in the fields of high-speed motor, centrifugal compressor, artificial heart pump and the like due to its long service life and suitability for high speed. In the electromagnetic bearing-rotor system, the mass center of the rotor is offset from the geometric center due to material quality, assembly process and the like. In the process of rotation of the rotor, the mass center offset will cause unbalance force, and the unbalance force acts on the rotor to cause unbalance vibration of the rotor. The unbalance force increases continuously with the increase of the rotation speed, which causes the unbalance vibration to intensify, reduces the stability of the rotor suspension, and even causes instability. Therefore, it is necessary to suppress the unbalance vibration of the rotor.

[0003] At present, the control method of unbalance compensation of the active electromagnetic bearing rotor system mainly includes two types: one type is an unbalance compensation method based on identification of the position of the unbalance mass of the rotor, which calculates the unbalance vibration compensation signal in real time according to the position of the unbalance mass of the rotor and the rotation speed of the rotor, but when the frequency and amplitude of the unbalance disturbance increase, the convergence speed of the search algorithm will slow down, thereby causing the compensation effect to deteriorate; the other type is an unbalance compensation control method based on the unbalance coefficient of the rotor, which generates a compensation signal in real time according to the identification of the unbalance coefficient of the electromagnetic bearing rotor system, but the algorithm cannot converge when the electromagnetic bearing rotor system works at the natural frequency area with constant rotation speed or with small acceleration, and instead causes the rotor amplitude to increase, thereby affecting the stable operation of the system. SUMMARY

[0004] To solve the above technical problems, the present application provides a compensation control method of a magnetic bearing based on adaptive natural frequency, which can stabilize and reduce the amplitude of the rotor.

[0005] To achieve the above purpose, the present application provides a compensation control method of a magnetic bearing based on adaptive natural frequency, which includes:

[0006] According to the rotor dynamics theory, the dynamic equation of the active electromagnetic bearing rotor system is established;

[0007] The compensation current is constructed and the unbalance coefficient is extracted according to the dynamic equation of the electromagnetic bearing rotor system;

[0008] After the constructed unbalance compensation signal is added to the dynamic equation of the active electromagnetic bearing, the stability of the system is analyzed;

[0009] The magnetic bearing compensation control method based on adaptive natural frequency adaptively changes the natural frequency of the electromagnetic bearing rotor system, thereby enabling the constructed compensation signal to stably control the electromagnetic bearing rotor system across the entire speed range.

[0010] Optionally, the dynamic equations of the electromagnetic bearing rotor system are as follows:

[0011]

[0012] Where J represents the lateral moment of inertia, J z L represents the moment of inertia of the rotor about the z-axis, ω represents the rotor's rotational speed, and L represents the moment of inertia of the rotor about the z-axis. bA f represents the distance from the plane containing the electromagnetic bearing at rotor end A to the rotor's center of mass plane. xa L represents the electromagnetic force exerted by electromagnetic bearing A on the rotor in the x-direction. bB f represents the distance from the plane containing the electromagnetic bearing at rotor end B to the rotor's center of mass plane. xb u represents the electromagnetic force exerted by electromagnetic bearing B on the rotor in the x-direction. z The distance between the unbalanced mass center and the rotor mass center is O z The projection on, ε z The distance between the unbalanced mass point and the center of mass in O z The projection onto the shaft, where m represents the rotor mass. This represents the acceleration of the rotor in the x-direction. This represents the angular acceleration of the rotor about the x-axis. This represents the angular velocity of the rotor about the x-axis. This represents the angular acceleration of the rotor about the y-axis. f represents the angular velocity of the rotor about the y-axis. yb f represents the electromagnetic force exerted by electromagnetic bearing B on the rotor in the y-direction. ya This represents the electromagnetic force exerted by electromagnetic bearing A on the rotor in the y-direction. The acceleration of the rotor in the y-direction is represented by m. e Indicates unbalanced mass. Indicates the rotor rotation speed. α represents the rotor rotation angle. ur ε z With O x The initial included angle of the axis, Let Fx represent the rotor rotational acceleration, Fy represent the generalized unbalance vector of the electromagnetic bearing rotor system, Fx represent the unbalanced force on the rotor in the x-direction, and Fy represent the unbalanced force on the rotor in the y-direction. θx F represents the unbalanced force acting on the rotor as it rotates about the x-axis. θy This represents the unbalanced force experienced by the rotor as it rotates around the y-axis.

[0013] Optionally, constructing the compensation current and extracting the unbalance coefficient according to the dynamic equation of the electromagnetic bearing rotor system comprises:

[0014]

[0015]

[0016] wherein, α A represents the unbalance coefficient of the rotor A end in the x-axis direction, β A represents the unbalance coefficient of the rotor A end in the y-axis direction, α B represents the unbalance coefficient of the rotor B end in the x-axis direction, β B represents the unbalance coefficient of the rotor B end in the y-axis direction, and (α A , β A ) and (α B , β B ) are defined as the unbalance coefficients of the rotor A end and the rotor B end.

[0017] Optionally, after the compensation current is added to the electromagnetic bearing rotor system, the differential equation of the electromagnetic bearing rotor A end is represented as:

[0018]

[0019] wherein, P is the proportional coefficient of the PD controller, D is the differential coefficient of the PD controller, and ω is the system rotating speed.

[0020] Optionally, the natural frequency is:

[0021]

[0022] wherein, m A represents the rotor mass, k i represents the current stiffness coefficient, and k s represents the displacement stiffness coefficient.

[0023] Technical effects of the present application: the present application discloses a compensation control method of a magnetic bearing based on an adaptive natural frequency, solves the problem that the existing technology cannot work in the natural frequency area, when the rotor accelerates and decelerates through the natural frequency area of the system at a small constant acceleration and works in the natural frequency area at a constant rotating speed, the adaptive natural frequency compensation control algorithm provided by the present application can stabilize and reduce the amplitude of the rotor, compared with the traditional compensation algorithm, the rotor amplitude is reduced by 95% when working in the natural frequency area. BRIEF DESCRIPTION OF DRAWINGS

[0024] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments illustrated in the drawings are provided to explain the present application and should not be considered limiting of the present application. In the drawings:

[0025] Figure 1 A flowchart of an embodiment of the adaptive natural frequency-based compensation control method of the magnetic bearing of the application;

[0026] Figure 2 A flowchart of the adaptive natural frequency algorithm of an embodiment of the application;

[0027] Figure 3 A schematic diagram of the unstable interval of the compensation algorithm at the original natural frequency of an embodiment of the application;

[0028] Figure 4 A system y bA direction amplitude curve of the algorithm and the traditional algorithm in the uniform acceleration process, wherein (a) is the amplitude curve of the system y bA direction amplitude curve of the algorithm and the traditional algorithm in the uniform acceleration process, wherein (a) is the amplitude curve of the system y bA direction amplitude curve of the algorithm and the traditional algorithm in the uniform acceleration process, wherein (a) is the amplitude curve of the system y

[0029] Figure 5 A schematic diagram of the algorithm of an embodiment of the application, wherein (a) is the rotor A end shaft center trajectory diagram when the rotational speed of the algorithm is ω=Ω; (b) is the rotor B end shaft center trajectory diagram when the rotational speed of the algorithm is ω=Ω.

[0030] Figure 6 A schematic diagram of the traditional algorithm of an embodiment of the application, wherein (a) is the rotor A end shaft center trajectory diagram when the rotational speed of the traditional algorithm is ω=Ω; (b) is the rotor B end shaft center trajectory diagram when the rotational speed of the traditional algorithm is ω=Ω. DETAILED DESCRIPTION

[0031] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0032] It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0033] As Figures 1-3 shown, the present embodiment provides a compensation control method of a magnetic bearing based on adaptive natural frequency, comprising:

[0034] S1, according to the rotor dynamics theory, the dynamic equation of the active electromagnetic bearing is established;

[0035] S2, according to the dynamic equation of the electromagnetic bearing rotor system, the compensation current is constructed and the unbalance coefficient is extracted;

[0036] S3, adding the unbalance compensation signal constructed in step S2 to step S1, analyzing the stability of the system;

[0037] S4, the magnetic bearing compensation control method based on adaptive natural frequency, through adaptively changing the natural frequency of the electromagnetic bearing rotor system, the compensation signal constructed in step S2 makes the electromagnetic bearing rotor system stable control in full speed.

[0038] Further, in S1, according to the rotor dynamics theory, the dynamic equation of the active electromagnetic bearing is established as follows:

[0039]

[0040] Where, J represents the transverse moment of inertia, J z represents the moment of inertia of the rotor around the z axis, ω represents the rotor rotation speed, L bA represents the distance from the plane of the electromagnetic bearing A at the end of the rotor to the plane of the center of mass of the rotor, f xa represents the electromagnetic force of the electromagnetic bearing A in the x direction to the rotor, L bB represents the distance from the plane of the electromagnetic bearing B at the end of the rotor to the plane of the center of mass of the rotor, f xb represents the electromagnetic force of the electromagnetic bearing B in the x direction to the rotor, u z is the projection of the distance between the center of mass of the unbalanced mass and the center of mass of the rotor on O z , ε z is the projection of the distance between the unbalanced mass point and the center of mass on O z axis, m represents the mass of the rotor, represents the acceleration of the rotor in the x direction, represents the angular acceleration of the rotor around the x axis, represents the angular velocity of the rotor around the x axis, represents the angular acceleration of the rotor around the y axis, represents the angular velocity of the rotor around the y axis, f yb represents the electromagnetic force of the electromagnetic bearing B in the y direction to the rotor, f ya represents the electromagnetic force of the electromagnetic bearing A in the y direction to the rotor, represents the acceleration of the rotor in the y direction, m e represents the unbalanced mass, represents the rotor rotation speed, represents the rotor rotation angle, α ur represents the initial angle between ε z and O x axis, represents the acceleration of the rotor, Fu is the generalized unbalance vector of the rotor system of the electromagnetic bearing, Fx represents the unbalance force of the rotor in the x direction, Fy represents the unbalance force of the rotor in the y direction, F θx represents the unbalance force of the rotor in the rotation around the x axis, F θy represents the unbalance force of the rotor in the rotation around the y axis.

[0041] Rewriting the above formula into a matrix form can obtain:

[0042]

[0043] wherein M represents the generalized mass matrix of the rotor system; q0 = [θ y xθ x y] T represents the 4-DOF displacement vector of the center of mass of the rotor, wherein θ y represents the angle of rotation around the y axis, x represents the displacement in the x direction, θ x represents the angle of rotation around the x axis, y represents the displacement in the y direction; G is a gyro matrix; F xy is an electromagnetic force vector, L f is an electromagnetic force coefficient matrix.

[0044]

[0045] M = diag(J, m, J, m);

[0046] F xy = [f xA f xB f yA f yB ] T ;

[0047] wherein diag(·) represents constructing a diagonal matrix.

[0048] Further, in order to offset the influence of the unbalance disturbance, the following compensation current is constructed:

[0049]

[0050] Further, the unbalance coefficients in the compensation current are extracted as

[0051]

[0052] wherein α A represents the unbalance coefficient of the rotor A end in the x axis direction, β A represents the unbalance coefficient of the rotor A end in the y axis direction, α B represents the unbalance coefficient of the rotor B end in the x axis direction, βB denotes the unbalance coefficient in the y-axis direction of the rotor B end, and is defined as (α A ,β A ) and (α B ,β B ) are the unbalance coefficients of the rotor A end and the rotor B end, respectively;

[0053] The rotor A end unbalance coefficient (α A ,β A ) and the rotor B end unbalance coefficient (α B ,β B ) are denoted as complex numbers:

[0054]

[0055] wherein ε A denotes the complex number of the rotor A end unbalance coefficient (α A ,β A ), ε B denotes the complex number of the rotor B end unbalance coefficient (α B ,β B ), and j denotes the imaginary unit;

[0056] The identified value of the rotor A end unbalance coefficient (α A ,β A ) is denoted as and the identified value of the rotor B end unbalance coefficient (α B ,β B ) is denoted as

[0057]

[0058] wherein denotes the identified value of the unbalance coefficient in the x direction of the rotor A end, denotes the identified value of the unbalance coefficient in the y direction of the rotor A end, denotes the identified value of the unbalance coefficient in the x direction of the rotor B end, denotes the identified value of the unbalance coefficient in the y direction of the rotor B end;

[0059] The adaptive identification equation of the rotor A end unbalance coefficient is:

[0060]

[0061] The adaptive identification equation of the rotor B end unbalance coefficient is:

[0062]

[0063] wherein denotes the second-order derivative of the identified value of the unbalance coefficient in the x direction of the rotor A end,​ denotes the first derivative of the identified imbalance coefficient in the x direction of rotor A, x bA denotes the displacement in the x direction of rotor A, y bA denotes the displacement in the y direction of rotor A, k1, k2 and k3 denote undetermined parameters in the adaptive identification equation of the imbalance coefficient of rotor A, k4, k5 and k6 denote undetermined parameters in the adaptive identification equation of the imbalance coefficient of rotor B, denotes the second derivative of the identified imbalance coefficient in the y direction of rotor A, denotes the first derivative of the identified imbalance coefficient in the y direction of rotor A; denotes the second derivative of the identified imbalance coefficient in the x direction of rotor A, denotes the first derivative of the identified imbalance coefficient in the x direction of rotor B, x bB denotes the displacement in the x direction of rotor B, y bB denotes the displacement in the y direction of rotor B, denotes the second derivative of the identified imbalance coefficient in the y direction of rotor B, denotes the first derivative of the identified imbalance coefficient in the y direction of rotor B.

[0064] the estimation error of the imbalance coefficient of rotor A is defined as the estimation error of the imbalance coefficient of rotor B is

[0065]

[0066] Further, after the compensation current in step S2 is added to the electromagnetic bearing rotor system, the differential equation of the electromagnetic bearing rotor A can be expressed as (the electromagnetic bearing rotor A and B are the same, and the following is analyzed in detail taking the A end as an example):

[0067]

[0068] wherein P is the proportional coefficient of the PD controller, D is the differential coefficient of the PD controller, and ω is the system speed.

[0069] The above closed-loop system can be expressed by an eight-order state equation

[0070]

[0071] Among them, denotes the state matrix of the system, denotes the first derivative state matrix of Z A , and A(ω, t) is an eight-order linear time-varying matrix, which has the following form

[0072]

[0073] where,

[0074] is stable equivalent to the system stability under the control of unbalanced vibration displacement, and tends to (0, 0), in other words is an asymptotic estimate of , then the vibration displacement of the rotor will tend to zero under this compensation. Therefore, the stability index of the closed loop system is guaranteed to be stable in determining the appropriate k1, k2, k3 so that the formula is asymptotically stable. Observing the above formula, it is found that the matrix A(ω, t) is a linear time-varying matrix, and it will be beneficial to the value analysis of the above formula by transforming it into a time-invariant matrix. In order to achieve the above purpose, the following theory is introduced:

[0075] For an n-order linear time-varying system with a periodically varying matrix A(t),

[0076]

[0077] where, for any t, there exists A(t+T) = A(t). Such a linear time-varying system has the following properties:

[0078] 1. Let ψ(t) be a basic solution system of the system formula, then ψ(t+T) is still a basic solution system of the system;

[0079] 2. There exists a constant matrix such that holds;

[0080] 3. For the time-varying system formula (4.13), take the transformation matrix

[0081]

[0082] P(t) is continuous and bounded on [t0, ∞), and for any t ≥ t0, the following formula holds:

[0083] |detP(t)| > 0.

[0084] By transforming z A = P(t)z A into formula (4.13), it can be derived that,

[0085]

[0086] where

[0087] 4. Periodically varying linear time-varying system and the transformed linear time-invariant system is a Lyapunov sense equivalent transformation, in other words, a sufficient and necessary condition for the system to be asymptotically stable is that the transformed linear time-invariant system is asymptotically stable.

[0088] Since the regular part of the time-varying matrix A(ω, t) contains sinωt and cosωt, according to the theorem, take the transformation matrix P(ω, t) as

[0089]

[0090] where Q(ω, t) is a rotation matrix related to the rotational speed

[0091]

[0092] Take the transformation

[0093] z A = P(ω, t) Z A ;

[0094] After rearrangement, we get

[0095]

[0096] In the formula, the transformed time-invariant matrix is

[0097]

[0098] where

[0099]

[0100] When the rotational speed ω of the rotor is a constant value, the above formula is a constant matrix. Therefore, the system is transformed into a linear constant system. Using the first method of Lyapunov, it is known that the stability criterion for free motion of a linear constant system is that all eigenvalues of have negative real parts. For this system, the characteristic polynomial of

[0101] a8x 8 +a7x 7 +a6x 6 +a5x 5 +a4x 4 +a3x 3 +a2x 2 +a1x 1 +a0x 0 = 0.

[0102] where

[0103] a8 = 1.

[0104] a7 = 2D + 2k1 ;

[0105]

[0106] a1 = -k1k2ω 4 -k1k3ω 4 +k1k2Pω 2 +k1k3Pω 2 ;

[0107] a0 = k2k3ω 4 .

[0108] Further, the specific cause of the instability of the system in step S3 is:

[0109] In order to make the system stable control, P = 60000, D = 500, a8 = 1 are set in advance, according to the Routh criterion, it is necessary to ensure that all the elements in the first column of the Routh table are positive, a0 = k2k3ω 4 , then k2 and k3 must be of the same sign, on this basis, the condition for ensuring the stability of the system is that all the characteristics of the system must have negative real parts.

[0110] The expression of the natural frequency is:

[0111]

[0112] In the formula, m A represents the rotor mass, k i represents the current stiffness coefficient, and k s represents the displacement stiffness coefficient. When the above parameters are determined, the natural frequency of the system does not change when the system is running. When the speed ω ≈ Ω, it is found through calculation that no matter what values k1, k2 and k3 take, it is impossible to ensure that all the characteristic roots have negative real parts, which means that the system cannot remain stable at this time.

[0113] Further, in step S4, the algorithm of the adaptive natural frequency is as follows:

[0114] After the rotor mass m A , the current stiffness coefficient k i and the displacement stiffness coefficient k s of the system are determined, the natural frequency of the rotor system is only related to the parameter P of the PD controller. Therefore, we only need to consider that when the rotor works at the natural frequency range of the rotor at a constant speed or acceleration, the natural frequency of the rotor at this time is changed, so that the speed at this time is separated from the natural frequency of the rotor at this time, that is, the compensation algorithm can be stable and convergent at the speed range at this time.

[0115] In the acceleration process, when the rotor is in the inherent frequency unstable region of the rotor, the purpose of stabilizing the system is achieved by reducing the value of the proportional coefficient P in the PD controller to change the range of the inherent frequency unstable region; similarly, in the deceleration process, the purpose of stabilizing the system is achieved by increasing the value of the proportional coefficient P in the PD controller to change the range of the inherent frequency unstable region, that is:

[0116] P=P+a1P;

[0117] Wherein a1 is an adaptive inherent frequency coefficient, a1 is negative in acceleration, a1 is positive in deceleration, and a1 is recommended to be 0.25.

[0118] Therefore, by the above-mentioned adaptive inherent frequency compensation algorithm, when the rotor passes through the inherent frequency unstable region of the system at a small acceleration or works in the original inherent frequency unstable region, the compensation algorithm can be stably converged, thereby effectively reducing the amplitude of the rotor.

[0119] The effect of the control method described in the embodiment of the application is verified by simulation experiments as follows:

[0120] In the acceleration model of the electromagnetic bearing rotor system, the rotor speed is accelerated from ω=1500rpm / min to ω=3000rpm / min with an acceleration of 1(rad / min) / s, and the compensation algorithm is started at the first second; from Figure 4 As shown in (a) of the above formula, the amplitude of the rotor will rapidly increase when the traditional algorithm passes through the inherent frequency unstable region of the system at a small acceleration, and the algorithm of the application can make the rotor pass through the inherent frequency unstable region of the system stably. Compared with the traditional algorithm, the amplitude of the system inherent frequency unstable region is reduced by 99% in the algorithm of the application.

[0121] In the acceleration model of the electromagnetic bearing rotor system, the rotor speed is accelerated from ω=1500rpm / min to ω=3000rpm / min with an acceleration of 1(rad / min) / s, and the compensation algorithm is started at the first second; from Figure 4 As shown in (a) of the above formula, the amplitude of the rotor will rapidly increase when the traditional algorithm passes through the inherent frequency unstable region of the system at a small acceleration, and the algorithm of the application can make the rotor pass through the inherent frequency unstable region of the system stably. Compared with the traditional algorithm, the amplitude of the system inherent frequency unstable region is reduced by 99% in the algorithm of the application.

[0122] The compensation algorithm of the application embodies the effective control of the rotor in the acceleration operation.

[0123] In the flywheel rotor constant speed model, simulation is carried out under the condition that the rotor speed ω=Ω, and the compensation algorithm is started at the first second, and from Figures 5-6It can be seen that when the rotor works in the inherent frequency unstable zone of the system, the amplitude of the rotor A and B gradually increases with time, and the compensation algorithm is invalid; and after the compensation algorithm of the application is started, the amplitude of the rotor A and B is reduced by more than 95%, compared with the traditional algorithm, the application algorithm effectively reduces the amplitude of the rotor.

[0124] The above is only a preferred specific embodiment of the application, but the protection scope of the application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the application, which should be covered in the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A compensation control method for a magnetic bearing based on adaptive natural frequency, characterized in that, include: Based on rotor dynamics theory, the dynamic equations of the active electromagnetic bearing rotor system are established; The compensation current is constructed and the unbalance coefficient is extracted based on the dynamic equations of the electromagnetic bearing rotor system. After incorporating the constructed imbalance compensation signal into the dynamic equation of the active electromagnetic bearing, the stability of the system is analyzed. The magnetic bearing compensation control method based on adaptive natural frequency adaptively changes the natural frequency of the electromagnetic bearing rotor system, thereby enabling the constructed compensation signal to stably control the electromagnetic bearing rotor system across the entire speed range.

2. The compensation control method for a magnetic bearing based on adaptive natural frequency as described in claim 1, characterized in that, The dynamic equations of the electromagnetic bearing rotor system are: Where J represents the lateral moment of inertia, J z L represents the moment of inertia of the rotor about the z-axis, ω represents the rotor's rotational speed, and L represents the moment of inertia of the rotor about the z-axis. bA f represents the distance from the plane containing the electromagnetic bearing at rotor end A to the rotor's center of mass plane. xa L represents the electromagnetic force exerted by electromagnetic bearing A on the rotor in the x-direction. bB f represents the distance from the plane containing the electromagnetic bearing at rotor end B to the rotor's center of mass plane. xb u represents the electromagnetic force exerted by electromagnetic bearing B on the rotor in the x-direction. z The distance between the unbalanced mass center and the rotor mass center is O z The projection on, ε z The distance between the unbalanced mass point and the center of mass in O z The projection onto the shaft, where m represents the rotor mass. This represents the acceleration of the rotor in the x-direction. This represents the angular acceleration of the rotor about the x-axis. This represents the angular velocity of the rotor about the x-axis. This represents the angular acceleration of the rotor about the y-axis. f represents the angular velocity of the rotor about the y-axis. yb f represents the electromagnetic force exerted by electromagnetic bearing B on the rotor in the y-direction. ya This represents the electromagnetic force exerted by electromagnetic bearing A on the rotor in the y-direction. The acceleration of the rotor in the y-direction is represented by m. e Indicates unbalanced mass. Indicates the rotor rotation speed. α represents the rotor rotation angle. ur ε z With O x The initial included angle of the axis, Let Fx represent the rotor rotational acceleration, Fy represent the generalized unbalance vector of the electromagnetic bearing rotor system, Fx represent the unbalanced force on the rotor in the x-direction, Fy represent the unbalanced force on the rotor in the y-direction, and Fθ represent the unbalanced force on the rotor in the y-direction. x Fθ represents the unbalanced force acting on the rotor as it rotates about the x-axis. y This represents the unbalanced force experienced by the rotor as it rotates around the y-axis.

3. The compensation control method for a magnetic bearing based on adaptive natural frequency as described in claim 1, characterized in that, Based on the dynamic equations of the electromagnetic bearing rotor system, a compensation current is constructed and the unbalance coefficient is extracted, including: Where, α A β represents the unbalance coefficient along the x-axis at rotor end A. A α represents the unbalance coefficient in the y-axis direction at rotor end A. B β represents the unbalance coefficient in the x-axis direction at rotor end B. B Let α represent the unbalance coefficient in the y-axis direction at rotor end B, and define (α) A ,β A ) and (α B ,β B ) represents the imbalance coefficient between rotor ends A and B.

4. The compensation control method for a magnetic bearing based on adaptive natural frequency as described in claim 1, characterized in that, After adding the compensation current to the electromagnetic bearing rotor system, the differential equation at end A of the electromagnetic bearing rotor is expressed as: Where P is the proportional coefficient of the PD controller, D is the derivative coefficient of the PD controller, and ω is the system speed.

5. The compensation control method for a magnetic bearing based on adaptive natural frequency as described in claim 1, characterized in that, The natural frequency is: Where, m A k represents the rotor mass. i k represents the current stiffness coefficient. s This represents the displacement stiffness coefficient.

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