Compensation control method of magnetic bearing based on self-adaptive inherent frequency

Abstract

The invention discloses a compensation control method of a magnetic bearing based on self-adaptive inherent frequency, which comprises the following steps of: establishing a kinetic equation of an active electromagnetic bearing according to a rotor kinetic theory; according to the kinetic equation of the electromagnetic bearing rotor system, a compensation current is constructed, and an unbalance coefficient is extracted; after the constructed unbalance compensation signal is added into a kinetic equation of the active electromagnetic bearing, the stability of the system is analyzed; according to the magnetic bearing compensation control method based on the self-adaptive inherent frequency, the inherent frequency of an electromagnetic bearing rotor system is changed in a self-adaptive mode, so that the built compensation signal enables the electromagnetic bearing rotor system to be stably controlled within the full rotating speed. According to the characteristic of adaptively changing the inherent frequency of the magnetic bearing rotor system, the problem that a compensation algorithm cannot be stably converged near the inherent frequency is solved, and the working range of the compensation algorithm is widened.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetic bearing rotor unbalance vibration compensation control, and in particular relates to a compensation control method for a magnetic bearing based on adaptive natural frequency. Background Art

[0002] Active electromagnetic bearings (AMBs) use controllable electromagnetic forces to suspend the rotor. Due to their long lifespan and suitability for high speeds, they are widely used in high-speed motors, centrifugal compressors, artificial heart pumps, and other fields. In the electromagnetic bearing-rotor system, issues such as material quality and assembly process can cause the rotor's center of mass to shift from its geometric center. During rotor rotation, this center of mass shift causes an unbalanced force, which reacts on the rotor, causing it to vibrate unbalancedly. This unbalanced force increases with increasing speed, exacerbating the unbalanced vibration and reducing the stability of the rotor suspension, potentially leading to instability. Therefore, it is necessary to suppress the rotor's unbalanced vibration.

[0003] At present, the control methods for imbalance compensation of active electromagnetic bearing rotor systems are mainly divided into two categories: one is an imbalance compensation method based on the identification of the rotor unbalance mass position, which calculates the imbalance vibration compensation signal in real time according to the rotor unbalance mass position and the rotor speed. However, when the frequency and amplitude of the unbalance disturbance increase, the convergence speed of the search algorithm will slow down, resulting in a worse compensation effect; the other is an imbalance compensation control method based on the rotor imbalance coefficient, which generates a compensation signal in real time according to the identification of the imbalance coefficient of the electromagnetic bearing rotor system. However, this algorithm cannot converge when the electromagnetic bearing rotor system operates in the natural frequency region at a constant speed or with a small acceleration. Instead, it causes the rotor amplitude to increase, affecting the stable operation of the system. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention proposes a compensation control method for a magnetic bearing based on an adaptive natural frequency, so as to stably reduce the amplitude of the rotor.

[0005] To achieve the above object, the present invention provides a compensation control method for a magnetic bearing based on adaptive natural frequency, comprising:

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

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

[0008] After adding the constructed imbalance compensation signal into 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 so that the constructed compensation signal can stably control the electromagnetic bearing rotor system within the full speed range.

[0010] Alternatively, the dynamic equation of the electromagnetic bearing rotor system is:

[0011]

[0012] Where J represents the lateral 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 Indicates the distance from the plane where the electromagnetic bearing at end A of the rotor is located to the plane of the rotor's center of mass, f xa represents the electromagnetic force of the electromagnetic bearing A on the rotor in the x direction, L bB Indicates the distance from the plane where the electromagnetic bearing at the B end of the rotor is located to the plane of the rotor center of mass, f xb represents the electromagnetic force of the electromagnetic bearing B on the rotor in the x direction, u z The distance between the center of mass of the unbalanced mass and the center of mass of the rotor is z The projection on z The distance between the unbalanced mass point and the center of mass is z The projection on the axis, m represents the rotor mass, 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 on the rotor in the y direction, f ya represents the electromagnetic force of the electromagnetic bearing A on the rotor in the y direction, 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 ε z With O x The initial angle of the axis, represents the rotor rotation acceleration, Fu is the generalized unbalance vector of the electromagnetic bearing rotor system, Fx represents the unbalance force on the rotor in the x direction, Fy represents the unbalance force on the rotor in the y direction, and F θx It represents the unbalanced force on the rotor when rotating around the x-axis, F θy It represents the unbalanced force on the rotor when it rotates around the y-axis.

[0013] Optionally, constructing the compensation current and extracting the unbalance coefficient based on the dynamic equation of the electromagnetic bearing rotor system includes:

[0014]

[0015]

[0016] Among them, α A Indicates the unbalance coefficient of the rotor A end in the x-axis direction, β A Indicates the unbalance coefficient of the rotor A end in the y-axis direction, α B Indicates the unbalance coefficient of the rotor B end in the x-axis direction, β B Indicates the unbalance coefficient of the rotor B end in the y-axis direction, and defines (α A ,β A ) and (α B ,β B ) is the unbalance coefficient between the A and B ends of the rotor.

[0017] Optionally, 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:

[0018]

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

[0020] Optionally, the natural frequency is:

[0021]

[0022] Among them, m A Indicates the rotor mass, k i represents the current stiffness coefficient, k s represents the displacement stiffness coefficient.

[0023] Technical effect of the invention: The present invention discloses a compensation control method for magnetic bearings based on adaptive natural frequency, which solves the problem that the existing technology cannot work in the natural frequency zone. When the rotor accelerates and decelerates at a smaller constant acceleration through the natural frequency zone of the system and works at a constant speed in the natural frequency zone, the adaptive natural frequency compensation control algorithm provided by the present invention can steadily reduce the amplitude of the rotor. Compared with the traditional compensation algorithm, the rotor amplitude is reduced by 95% in the natural frequency zone when using this algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0025] Figure 1 Schematic diagram of a flow chart of a compensation control method for a magnetic bearing based on adaptive natural frequency according to an embodiment of the present invention;

[0026] Figure 2 This is a flow chart of an adaptive natural frequency algorithm according to an embodiment of the present invention;

[0027] Figure 3 Schematic diagram of the unstable interval of the compensation algorithm according to an embodiment of the present invention at the original natural frequency;

[0028] Figure 4 System y of the embodiment of the present invention bA Amplitude curve of the direction, where (a) is the system y in the uniform acceleration process of the algorithm and the traditional algorithm bA (b) is the amplitude curve of the system y in the process of uniform deceleration by this algorithm and the traditional algorithm. bA Amplitude curve graph of direction;

[0029] Figure 5 The axis trajectory diagram of the algorithm according to the embodiment of the present invention, wherein (a) is the axis trajectory diagram of the rotor A end when the speed ω=Ω of the algorithm; (b) is the axis trajectory diagram of the rotor B end when the speed ω=Ω of the algorithm;

[0030] Figure 6 1 is a diagram of the axis trajectory of the traditional algorithm of an embodiment of the present invention; wherein, (a) is the axis trajectory diagram of the rotor A end when the traditional algorithm speed ω = Ω; (b) is the axis trajectory diagram of the rotor B end when the traditional algorithm speed ω = Ω. DETAILED DESCRIPTION

[0031] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. 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 flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0033] like Figure 1-Figure 3 As shown, this embodiment provides a compensation control method for a magnetic bearing based on adaptive natural frequency, including:

[0034] S1. Based on the rotor dynamics theory, establish the dynamic equation of the active electromagnetic bearing;

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

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

[0037] S4. A magnetic bearing compensation control method based on adaptive natural frequency, wherein the compensation signal constructed in step S2 is used to stably control the electromagnetic bearing rotor system within the full speed range by adaptively changing the natural frequency of the electromagnetic bearing rotor system.

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

[0039]

[0040] Where J represents the lateral 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 Indicates the distance from the plane where the electromagnetic bearing at end A of the rotor is located to the plane of the rotor's center of mass, f xa represents the electromagnetic force of the electromagnetic bearing A on the rotor in the x direction, L bB Indicates the distance from the plane where the electromagnetic bearing at the B end of the rotor is located to the plane of the rotor center of mass, f xb represents the electromagnetic force of the electromagnetic bearing B on the rotor in the x direction, u z The distance between the center of mass of the unbalanced mass and the center of mass of the rotor is z The projection on z The distance between the unbalanced mass point and the center of mass is z The projection on the axis, m represents the rotor mass, 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 on the rotor in the y direction, f ya represents the electromagnetic force of the electromagnetic bearing A on the rotor in the y direction, 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 ε z With O x The initial angle of the axis, represents the rotor rotation acceleration, Fu is the generalized unbalance vector of the electromagnetic bearing rotor system, Fx represents the unbalance force on the rotor in the x direction, Fy represents the unbalance force on the rotor in the y direction, and F θx It represents the unbalanced force on the rotor when rotating around the x-axis, F θy It represents the unbalanced force on the rotor when it rotates around the y-axis.

[0041] Rewriting the above formula into matrix form yields:

[0042]

[0043] Where 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 rotor mass center, where 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 the gyroscope matrix; F xy is the electromagnetic force vector, L f is the 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] Where diag(·) indicates constructing a diagonal matrix.

[0048] Furthermore, in order to offset the impact of unbalanced disturbances, the following compensation current is constructed:

[0049]

[0050] The unbalance coefficient in the compensation current is further extracted as

[0051]

[0052] Among them, α A Indicates the unbalance coefficient of the rotor A end in the x-axis direction, β A Indicates the unbalance coefficient of the rotor A end in the y-axis direction, α B Indicates the unbalance coefficient of the rotor B end in the x-axis direction, βB Indicates the unbalance coefficient of the rotor B end in the y-axis direction, and defines (α A ,β A ) and (α B ,β B ) is the unbalance coefficient between the rotor ends A and B;

[0053] The unbalance coefficient (α A ,β A ) and the rotor B-end unbalance coefficient (α B ,β B ) is recorded in plural form:

[0054]

[0055] Among them, ε A Indicates the unbalance coefficient of the rotor A end (α A ,β A ), plural form of ε B Indicates the rotor B-end unbalance coefficient (α B ,β B ), where j represents the imaginary unit;

[0056] The unbalance coefficient of the rotor A end (α A ,β A ) identification value and the rotor B-end unbalance coefficient (α B ,β B ) identification value for:

[0057]

[0058] in, Indicates the unbalance coefficient identification value of the rotor A end in the x direction, Indicates the unbalance coefficient identification value of the rotor A end in the y direction, Indicates the unbalance coefficient identification value of the rotor B end in the x direction, Indicates the unbalance coefficient identification value in the y direction of the rotor end B;

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

[0060]

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

[0062]

[0063] in, Represents the second-order derivative of the unbalance coefficient identification value in the x direction at the rotor end A, Represents the first-order derivative of the unbalance coefficient identification value in the x direction at the rotor end A, x bA represents the displacement of the rotor A end in the x direction, y bA represents the displacement of rotor A end in the y direction, k1, k2 and k3 represent the undetermined parameters in the adaptive identification equation of the unbalance coefficient of rotor A end, k4, k5 and k6 represent the undetermined parameters in the adaptive identification equation of the unbalance coefficient of rotor B end, The second derivative of the unbalance coefficient identification value in the y direction at the rotor end A is represented by: Represents the first derivative of the unbalance coefficient identification value in the y direction at the rotor end A; Represents the second-order derivative of the unbalance coefficient identification value in the x direction at the rotor end A, Represents the first-order derivative of the unbalance coefficient identification value in the x direction at the B end of the rotor, x bB represents the displacement in the x direction of the rotor B end, y bB represents the displacement of the rotor end B in the y direction, Represents the second-order derivative of the unbalance coefficient identification value in the y direction at the B end of the rotor, Represents the first-order derivative of the unbalance coefficient identification value in the y direction at the B end of the rotor.

[0064] The estimated error of the unbalance coefficient at the rotor end A is defined as The estimated error of the unbalance coefficient at the rotor end B is

[0065]

[0066] Furthermore, after the compensation current in step S2 is added to the electromagnetic bearing rotor system, the differential equation at end A of the electromagnetic bearing rotor can be expressed as follows (the same applies to ends A and B of the electromagnetic bearing rotor, and end A is taken as an example for detailed analysis below):

[0067]

[0068] Where 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 is expressed as an eighth-order state equation

[0070]

[0071] Its bottom, represents the state matrix of the system, Represents Z A The first-order derivative state matrix of , A(ω,t) is an eighth-order linear time-varying matrix, which is as follows

[0072]

[0073] in,

[0074] The stability of is equivalent to the system stability under unbalanced vibration displacement control, and tends to (0, 0), in other words yes The 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 to determine the appropriate k1, k2, k3 so that the formula Asymptotically stable. Observing the above formula, we find that the matrix A(ω,t) is a linear time-varying matrix. Transforming it into a time-invariant matrix will facilitate the value analysis of the above formula. To achieve the above purpose, the following theory is introduced:

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

[0076]

[0077] For any value of t, A(t+T)=A(t). Such a linear time-varying system has the following properties:

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

[0079] 2. Existence of a constant matrix Make Established;

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

[0081]

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

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

[0084] By transforming z A =P(t)z A Substituting into formula (4.13), we can derive

[0085]

[0086] in

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

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

[0089]

[0090] Among them, Q(ω,t) is the rotation matrix related to the speed

[0091]

[0092] Take the transformation,

[0093] z A =P(ω,t)Z A ;

[0094] After sorting, we get:

[0095]

[0096] In the formula, the time-invariant matrix after transformation is:

[0097]

[0098] in

[0099]

[0100] When the rotor speed ω is constant, the above equation is a constant matrix. Therefore, the system is converted into a linear steady-state system. Using Lyapunov's first method, we know that the stability criterion for the free motion of a linear steady-state system is: 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] in

[0103] a8=1;

[0104] a7=2D+2k1;

[0105]

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

[0107] a0=k2k3ω 4 .

[0108] Furthermore, the specific reasons for the instability of the system in step S3 are:

[0109] In order to ensure the system can be stably controlled, P = 60000, D = 500, a8 = 1 is pre-set. According to the Routh criterion, it is necessary to ensure that the first column elements of all Routh tables are positive numbers, a0 = k2k3ω 4 , then k2 and k3 must have the same sign. On this basis, the condition to ensure the stability of the system is that all the characteristics of the system must have negative real parts.

[0110] The expression for the natural frequency is:

[0111]

[0112] Where m A represents the rotor mass, k i represents the current stiffness coefficient, k s Represents the displacement stiffness coefficient. When the above parameters are determined, the natural frequency of the system will no longer 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 are taken, it cannot be guaranteed All the characteristic roots have negative real parts, which means that the system cannot remain stable at this time.

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

[0114] The rotor mass of the system m A , current stiffness coefficient k i and displacement stiffness coefficient k s Once determined, the natural frequency of the rotor system is only related to the PD controller parameter P. Therefore, we only need to consider when the rotor is operating at a constant speed and accelerating in the rotor natural frequency range. Changing the rotor natural frequency at this time so that the speed at this time is out of the current rotor natural frequency range can make the compensation algorithm converge stably in this speed range.

[0115] During the acceleration process, when the rotor is in the unstable region of the rotor's natural frequency, the range of the unstable region of the natural frequency is changed by reducing the value of the proportional coefficient P in the PD controller, thereby achieving the purpose of stabilizing the system. Similarly, during the deceleration process, the range of the unstable region of the natural frequency is changed by increasing the value of the proportional coefficient P in the PD controller, thereby achieving the purpose of stabilizing the system, that is:

[0116] P=P+a1P;

[0117] Where a1 is the adaptive natural frequency coefficient. The sign of a1 is negative during acceleration and positive during deceleration. It is recommended that a1 = 0.25.

[0118] Therefore, through the above-mentioned adaptive natural frequency compensation algorithm, when the rotor passes through the system's natural frequency unstable area with a small acceleration or works in the original natural frequency unstable area, the compensation algorithm can be stably converged, thereby effectively reducing the rotor amplitude.

[0119] The following simulation experiments are used to verify the effect of the control method described in the embodiment of the present invention:

[0120] In the acceleration motion model of the electromagnetic bearing rotor system, the rotor speed is accelerated from ω = 1500 rpm / min to ω = 3000 rpm / min, with an acceleration of 1 (rad / min) / s, and the compensation algorithm is started in the first second; Figure 4 As can be seen from (a), when the traditional algorithm passes through the system's natural frequency unstable zone with a small acceleration, the rotor's amplitude will increase rapidly, while the algorithm of the present invention can make the rotor stably pass through the system's natural frequency unstable zone. Compared with the traditional algorithm, the algorithm of the present invention reduces the amplitude in the system's natural frequency unstable zone by 99%.

[0121] In the acceleration motion model of the electromagnetic bearing rotor system, the rotor speed is decelerated from ω = 3300 rpm / min to ω = 1900 rpm / min, with an acceleration of -1 (rad / min) / s, and the compensation algorithm is started in the first second; Figure 4 As shown in (b), the traditional algorithm will also cause the rotor amplitude to increase rapidly when decelerating the rotor through the system's natural frequency unstable zone at a small acceleration. However, the algorithm of the present invention can make the rotor stably pass through the system's natural frequency unstable zone. Compared with the traditional algorithm, the algorithm of the present invention reduces the amplitude in the system's natural frequency unstable zone by 99%.

[0122] This demonstrates the effective control of the compensation algorithm of the present invention under rotor acceleration operation.

[0123] In the flywheel rotor constant speed model, the simulation is performed under the condition of rotor speed ω = Ω, and the compensation algorithm is turned on at the 1st second. Figure 5-Figure 6It can be seen that when the rotor operates in the unstable region of the system's natural frequency, the amplitude at both ends of the rotor A and B gradually increases over time with the traditional algorithm, and the compensation algorithm becomes ineffective; however, after the compensation algorithm of the present invention is started, the amplitude at both ends of the rotor A and B is reduced by more than 95%; compared with the traditional algorithm, the algorithm of the present invention effectively reduces the rotor amplitude.

[0124] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A compensation control method for a magnetic bearing based on adaptive natural frequency, characterized in that: include: According to the rotor dynamics theory, the dynamic equations of the active electromagnetic bearing rotor system are established; According to the dynamic equation of the electromagnetic bearing rotor system, the compensation current is constructed and the unbalance coefficient is extracted; After adding 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 so that the constructed compensation signal can stably control the electromagnetic bearing rotor system within the full speed range.

2. The compensation control method of a magnetic bearing based on adaptive natural frequency according to claim 1, characterized in that: The dynamic equation of the electromagnetic bearing rotor system is: Where J represents the lateral 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 Indicates the distance from the plane where the electromagnetic bearing at end A of the rotor is located to the plane of the rotor's center of mass, f xa represents the electromagnetic force of the electromagnetic bearing A on the rotor in the x direction, L bB Indicates the distance from the plane where the electromagnetic bearing at the B end of the rotor is located to the plane of the rotor center of mass, f xb represents the electromagnetic force of the electromagnetic bearing B on the rotor in the x direction, u z The distance between the center of mass of the unbalanced mass and the center of mass of the rotor is z The projection on z The distance between the unbalanced mass point and the center of mass is z The projection on the axis, m represents the rotor mass, 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 on the rotor in the y direction, f ya represents the electromagnetic force of the electromagnetic bearing A on the rotor in the y direction, 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 ε z With O x The initial angle of the axis, represents the rotor rotation acceleration, Fu is the generalized unbalance vector of the electromagnetic bearing rotor system, Fx represents the unbalance force on the rotor in the x direction, Fy represents the unbalance force on the rotor in the y direction, and Fθ x Indicates the unbalanced force on the rotor when rotating around the x-axis, Fθ y It represents the unbalanced force on the rotor when it rotates around the y-axis.

3. The compensation control method of a magnetic bearing based on adaptive natural frequency according to claim 1, characterized in that: Constructing the compensation current and extracting the unbalance coefficient based on the dynamic equation of the electromagnetic bearing rotor system includes: Among them, α A Indicates the unbalance coefficient of the rotor A end in the x-axis direction, β A Indicates the unbalance coefficient of the rotor A end in the y-axis direction, α B Indicates the unbalance coefficient of the rotor B end in the x-axis direction, β B Indicates the unbalance coefficient of the rotor B end in the y-axis direction, and defines (α A ,β A ) and (α B ,β B ) is the unbalance coefficient between the rotor ends A and B.

4. The compensation control method of a magnetic bearing based on adaptive natural frequency according to 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 differential coefficient of the PD controller, and ω is the system speed.

5. The compensation control method of a magnetic bearing based on adaptive natural frequency according to claim 1, characterized in that: The natural frequency is: Among them, m A Indicates the rotor mass, k i represents the current stiffness coefficient, k s represents the displacement stiffness coefficient.

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