Bearing-free doubly salient motor suspension force analysis and compensation control method for eccentric working condition

Abstract

The embodiment of the invention discloses a bearing-free doubly salient motor suspension force analysis and compensation control method for an eccentric working condition, relates to the field of motor control, and can improve system stability and suspension performance. The method comprises the steps of obtaining a motor suspension force analytical model considering rotor eccentricity based on motor inductance characteristics, constructing a double-loop suspension control system comprising the motor suspension force analytical model on the basis, and improving the stability and suspension performance of the system by adopting a feedforward control strategy. The problems of low suspension precision, poor anti-disturbance capability and the like caused by model idealization and compensation deficiency in a traditional method are solved, so that the stability and the suspension performance of a system are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of motor control, in particular to a bearingless doubly salient motor suspension force analysis and compensation control method for eccentric operating conditions, which is especially suitable for high-precision magnetic suspension industrial scenarios, such as high-speed precision machining, flywheel energy storage, and medical equipment fields. BACKGROUND

[0002] As a new type of motor integrating driving and suspension functions, bearingless doubly salient motor has a wide application prospect in high-speed, super-speed, and vacuum environments due to its compact structure and the absence of mechanical bearings. During operation, the rotor suspension force of the bearingless doubly salient motor needs to be dynamically regulated and controlled, so establishing an accurate suspension force calculation model is the core foundation for achieving high-performance control. The current research in this field still lacks exploration in the theoretical aspects of suspension force modeling, and the calculation methods for actual operating conditions (such as dynamic eccentricity) are particularly lacking.

[0003] The current research on suspension force modeling and suspension control of bearingless doubly salient motors has the following limitations: the modeling method is too idealized, existing methods mostly assume that the rotor center coincides, ignoring the eccentric effect under actual operating conditions, leading to suspension force calculation errors, making it difficult for existing related analysis models to accurately follow the true situation of the suspension force of the bearingless doubly salient motor; lack of compensation mechanism, traditional control strategies do not actively compensate for eccentricity and other operating conditions, which can easily lead to suspension instability.

[0004] Therefore, how to solve the problems of low suspension precision and poor disturbance rejection caused by the idealization of traditional methods and the lack of compensation, thereby improving system stability and suspension performance, has become a topic that needs to be studied. SUMMARY

[0005] Embodiments of the present application provide a bearingless doubly salient motor suspension force analysis and compensation control method for eccentric operating conditions, which can improve system stability and suspension performance.

[0006] To achieve the above-mentioned purpose, the embodiments of the present application adopt the following technical solutions:

[0007] A bearingless doubly salient motor suspension force analysis and compensation control method for eccentric operating conditions, comprising:

[0008] S1, a suspension force analytical model considering rotor eccentricity is established, and the suspension force is linearized based on the established suspension force analytical model;

[0009] S2, according to the processing result of S1, the suspension force of the bearingless doubly salient motor is controlled through a double-loop suspension control system, wherein the double-loop suspension control system of the bearingless doubly salient motor is designed according to a motor suspension force analysis model considering rotor eccentricity, and the double-loop suspension control system comprises: an outer loop being a displacement control loop and an inner loop being a current control loop.

[0010] Wherein, the feedforward compensation control strategy is executed in the process of operation of the double-loop suspension control system, the eccentric position of the rotor is detected in real time, and the corresponding feedforward compensation current signal is generated, and the feedforward compensation current signal is superimposed into the suspension current signal, so as to offset the eccentric magnetic pull generated by the eccentric displacement of the rotor.

[0011] In this embodiment, S1 comprises:

[0012] The X, Y coordinate system is established with the geometric center of the rotor as the coordinate origin, the suspension force analysis model considering eccentricity is derived based on the virtual displacement method, the suspension force is expressed as a function of current and inductance partial derivative, and the established suspension force model is: Wherein, F x represents the X-axis suspension force, F y represents the Y-axis suspension force, and the eccentric displacement of the rotor in the X, Y axis is denoted as x, y respectively. The motor contains ABC three-phase armature windings W a , W b , W c , X, Y axis suspension windings W x , W y , and excitation winding W f . Set A={a,b,c,x,y,f}, wherein a, b, c represent A, B, C three-phase armature windings respectively, x, y represent X, Y axis suspension windings, and f represents excitation winding; i j represents the current of the jth phase winding (such as i a is the A-phase armature current, i x is the X-axis suspension winding current, and i f is the excitation current); L j represents the self-inductance of the jth phase winding (such as L a is the self-inductance of A-phase armature winding W a ), and M jk represents the mutual inductance between the jth phase winding and the kth phase winding (such as M ax is the mutual inductance between A-phase armature winding W a and X-axis suspension winding W x ).

[0013] The suspension force considering eccentricity is linearized, Taylor expansion is performed at the equilibrium position (0, 0) (i.e. x=0, y=0), only the first-order small signal term is retained, and the linear expression of the suspension force under the eccentric working condition is obtained: F x0 and F y0 are the initial suspension forces of the rotor in the X-axis and Y-axis at the equilibrium position (0, 0), respectively, x0, y0 represent the X, Y-axis coordinates of the linearized unfolding point, i x , i y are the real-time suspension control currents of the X-axis and Y-axis suspension windings, respectively, i x0 , i y0 represent the static currents required to maintain suspension at the equilibrium position (x = 0, y = 0).

[0014] Further, the suspension force model is established in matrix form according to the linear expression of the suspension force under the eccentric working condition, and the suspension force is expressed as a linear combination of state variables k x-ix and k x-iy are the force-current coefficients in the X-axis; k x-ex and k x-ey are the force-displacement coefficients in the X-axis; k y-ix and k y-iy are the force-current coefficients in the Y-axis; k y-ex and k y-ey are the force-displacement coefficients in the Y-axis. As can be known from the derivation process of the suspension force analytical model of the rotor eccentricity considered above, the radial suspension force mainly includes the radial controllable suspension force F m and the radial eccentric magnetic pull F e . The controllable suspension force can be controlled by passing different amplitudes of current in the suspension winding, and the eccentric magnetic pull only exists when the rotor is radially eccentric, and its amplitude is positively correlated with the eccentric displacement. According to the derived suspension force analytical model considering the rotor eccentricity, the eccentric magnetic pull is fed forwardly compensated to enhance the suspension stability.

[0015] In the allowable process of the double-loop suspension control system, the rotor radial displacements x and y in the XY-axis are continuously detected by a displacement sensor; after comparison with reference displacement signals x* and y*, displacement deviation signals e x = x* - x and e y = y* - y are obtained; a controller generates reference suspension force signals F x * and F y * according to the displacement deviation signals; a force / current conversion module converts the reference suspension force signals into reference suspension current signals i x * and i y * and inputs them into a current control loop; the current control loop is closed loop adjusted to generate suspension control currents i x and i y and pass them into the suspension winding. Under the action of the corresponding suspension force, the rotor is corrected back to the equilibrium position, thereby realizing stable suspension.

[0016] According to the derived suspension force analytical model considering the rotor eccentricity, the eccentric magnetic pull is fed forwardly compensated, and the suspension stability is enhanced. In the feedforward compensation suspension control strategy, the compensation suspension force F c needs to offset the magnetic pull F e generated by the rotor eccentricity, both satisfying the constraint relationship of equal amplitude and opposite direction, that is, F c =-F e . The system generates a feedforward compensation current signal by real-time detection of the eccentric position, and superimposes it on the suspension current signal for generating the controllable suspension force F m , so as to offset the eccentric magnetic pull generated by the rotor eccentricity and improve the anti-eccentric disturbance ability and position tracking accuracy of the suspension system. The method improves the stability of the motor by real-time correction of the influence of eccentric disturbance on the suspension force. Compared with the traditional method, the present scheme has the characteristics of high model precision and strong anti-eccentric disturbance ability, and provides an effective solution for high-precision control of the bearingless doubly salient motor. Specifically, the corresponding feedforward compensation current signal is generated, and the compensation current i yc-ey for compensating the eccentric magnetic pull generated by the Y-axis radial displacement y is represented as: wherein k y-ey represents the coupling coefficient of the Y-axis direction radial displacement y and the eccentric magnetic pull, k y-iy represents the coupling coefficient of the Y-axis direction suspension current and the radial suspension force. The compensation current i xc-ex for compensating the eccentric magnetic pull generated by the X-axis radial displacement x is represented as: wherein k x-ex represents the coupling coefficient of the X-axis direction radial displacement x and the eccentric magnetic pull, k x-ix represents the coupling coefficient of the X-axis direction suspension current and the radial suspension force.

[0017] In view of the suspension instability problem of the bearingless doubly salient motor caused by the rotor eccentricity in the prior art, the suspension force analysis and compensation control method for the eccentric working condition of the bearingless doubly salient motor provided by the embodiment of the present application obtains a motor suspension force analytical model considering the rotor eccentricity based on the motor inductance characteristics, and on this basis, a double-loop suspension control system containing the motor suspension force analytical model is constructed, and a feedforward control strategy is adopted to improve the system stability and suspension performance, so as to solve the problems of low suspension accuracy and poor disturbance rejection ability caused by the idealization of the traditional method and the lack of compensation, thereby improving the system stability and suspension performance. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0019] Figure 1 is a schematic diagram of the structure of a bearingless electrically excited doubly salient motor of embodiment 12 / 8;

[0020] Figure 2 is a schematic diagram of the suspension principle of the motor of the embodiment;

[0021] Figure 3 is a schematic diagram of the cross-coupling of the suspension forces of the motor of the embodiment;

[0022] Figure 4 is a curve of the change of the inductance caused by the radial displacement of the X-axis of the rotor of the motor of the embodiment;

[0023] Figure 5 is a block diagram of the transfer function of the analytical model of the suspension forces of the motor of the embodiment;

[0024] Figure 6 is a comparison of the finite element simulation results and the calculation results of the analytical model of the Y-axis suspension forces of the motor of the embodiment;

[0025] Figure 7 is a block diagram of the double-loop suspension control system of the motor of the embodiment;

[0026] The labels of the components in the drawings are as follows: 1, stator; 2, rotor; 3, armature winding; 4, field winding; 5, X-axis suspension winding; 6, Y-axis suspension winding. DETAILED DESCRIPTION

[0027] For those skilled in the art to better understand the technical solutions of the present application, the present application will be described in further detail below in combination with the drawings and specific embodiments. In the following, the embodiments of the present application will be described in detail, and the examples of the embodiments are shown in the drawings, wherein the same or similar reference numerals represent the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary and are only used to explain the present application, but cannot be interpreted as a limitation on the present application. Those skilled in the art can understand that, unless specifically stated, the singular forms "a", "an" and "the" used herein can also include the plural forms. It should be further understood that the phrase "comprising" used in the specification of the present application means that the features, integers, steps, operations, elements and / or components exist, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we say an element is "connected" or "coupled" to another element, it can be directly connected or coupled to the other element, or there can be an intermediate element. In addition, "connected" or "coupled" used herein can include wireless connection or coupling. The phrase "and / or" used herein includes any one of the associated listed items and all combinations of the associated listed items. Those skilled in the art can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as that generally understood by those skilled in the art to which the present application belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with those in the prior art, and should not be interpreted with idealized or overly formal meanings unless defined as such.

[0028] The specific scheme provided by the embodiment of the present application, as shown in Figures 1 to 7 , includes:

[0029] A bearingless doubly salient electromagnetic motor (BDSEM) suspension force modeling method and compensation control strategy under eccentric operating conditions, mainly including: a BDSEM suspension force analytical model considering rotor eccentricity, a double-loop suspension control system, and a feedforward compensation control strategy. The structure of a 12 / 8-pole BDSEM is shown in Figure 1 . The excitation winding, armature winding and suspension winding are arranged in the stator slot, and every three stator poles form a stator pole unit. The excitation winding W f is composed of four series coils and is wound around the periphery of the four stator pole units; the X-axis suspension winding W x and the Y-axis suspension winding W y are respectively composed of two groups of coils and are wound around the stator pole units in the Y-axis and X-axis directions, respectively.

[0030] Figure 2 It shows different mechanical rotor angles θ r The principle of levitation force generation: When W f With W y Current direction as follows Figure 2 As shown, W f The generated excitation magnetic field ψ f With W y The generated levitation magnetic field ψ y The magnetic flux density is enhanced when the magnetic flux is superimposed in the same direction in the air gap above the rotor; while in the air gap below the rotor, ψ f With ψ y The opposing forces cancel each other out, resulting in a decrease in magnetic flux density. This unbalanced air gap magnetic flux density generates a Y-axis levitation force F on the rotor. y X-axis levitation force F x The principle behind this is similar. Due to the salient pole structure of the motor, except for specific mechanical rotor angles (such as 0° and 22.5°) where the coupling effect is eliminated due to geometric symmetry, the X / Y axis levitation forces exhibit cross-coupling. For example... Figure 3 As shown, when the rotor angle θ r When the angle is 30°, let the X-axis suspending current i x =0, only the Y-axis levitation current i is applied y The resulting levitation force is as follows Figure 3 As shown by the green arrow. Even at this time, the X-axis floating current i x Even at zero, due to cross-coupling, an undesirable levitation force component will still be generated in the X-axis direction, leading to instability of the levitation control system. The total levitation force of the BDSEM in the X and Y axes is determined by multiple parameters, including the winding currents, rotor position angle, and rotor radial displacement. To further analyze the variation characteristics of the levitation force under rotor eccentricity, the levitation force under rotor eccentricity can be decomposed according to the inductance and its deflection. The levitation forces F in the X and Y axes are... x and F y It can be represented as:

[0031]

[0032] In the formula, A = {a,b,c,x,y,f}.

[0033] Select excitation inductance L f and X-axis levitation excitation mutual inductance M xf As the object of analysis, its relationship with the radial displacement x along the X-axis is as follows: Figure 4 As shown. By analyzing the variation trend of inductance with radial displacement and combining it with the effect of current, the variation law of the corresponding levitation force component with radial displacement can be clarified, thereby reducing the complexity of the analysis. The total levitation force F along the X-axis is shown. x The components are shown in Table 1.

[0034] Table 1. X-axis levitation force component

[0035]

[0036]

[0037] Y-axis total levitation force F y The components are shown in Table 2.

[0038] Table 2. Y-axis levitation force component

[0039]

[0040]

[0041] where x, y are the eccentric displacements of the rotor in the X / Y axis respectively. The motor contains armature windings W a , W b , W c , levitation windings W y , W x and field windings W f . Wherein, armature currents i a , i b , i c are passed in the armature windings, levitation currents i y , i x are passed in the levitation windings, field currents i f are passed in the field windings. L f represents the self-inductance of the field windings W f , L x , L y represent the self-inductance of the X, Y axis levitation windings W x , W y , L a , L b , L c represent the self-inductance of the three-phase armature windings W a , W b , W c , M xf , M yf represent the mutual inductance of the X, Y axis levitation windings W x , W y and the field windings W f , M af , M bf , M cf represent the mutual inductance of the three-phase armature windings W a , W b , W c and the field windings W f , M xy represents the mutual inductance of the X, Y axis levitation windingsx , W y ax , M bx , M cx a , W b , W c x , M ay , M by , M cy a , W b , W c y , M ab , M bc , M ca

[0042] Under the condition of constant field current, the average suspension force is generated by the interaction of suspension current and rotor radial displacement. The analytical model of suspension force of BDSEM is a double-input double-output system, whose inputs are the X-axis and Y-axis suspension currents i x and i y , and outputs are the X-axis and Y-axis radial displacements x and y.

[0043] To simplify the analysis, it is assumed that the field current i f is constant i f0 , and the motor operates in the no-load state, i.e., the armature currents (i a , i b , i c ) are 0. Under this condition, F m , F mf , F my , F mx , F mm are 0. Under the condition of no torque and radial force load, the suspension current is very small. Therefore, the suspension self-inductance suspension force F s and the suspension mutual inductance suspension force F xy can be ignored. At this time, the X-axis suspension force F x and the Y-axis suspension force F y can be expressed as:

[0044]

[0045] Using the Taylor linearization method, the first-order approximation of F x and F y at the equilibrium position (0, 0) (i.e., x = 0, y = 0) can be obtained as:

[0046] ​​​​​​

[0047] In the formula, the partial derivatives of inductance with respect to the relevant variables are all taken at the point (0, 0) and only vary with the rotor angle. Let k θ-xi (i = 1, 2, …, 8) and k θ-yi (i = 1, 2, …, 8) represent these partial derivatives, and their corresponding relationships with the partial derivatives of inductance are shown in Table 3 and Table 4, respectively.

[0048] Table 3. Corresponding relationship between X-axis direction suspension force representation symbol and first to eighth inductance partial derivatives

[0049]

[0050]

[0051] Table 4. Corresponding relationship between Y-axis direction suspension force representation symbol and first to eighth inductance partial derivatives

[0052]

[0053] According to the above derivation, F x and F y can be arranged as follows:

[0054]

[0055] Based on the above derivation, the transfer function block diagram of the suspension force analytical model of the bearingless electrically excited doubly salient motor is shown in Figure 5 For the X-axis direction suspension force, f x-d represents the disturbance force in the X-axis direction, and the suspension forces f x-ix , f x-iy , f x-ex and f x-ey are generated by the X-axis suspension current i x , the Y-axis suspension current i y , the X-axis radial displacement x and the Y-axis radial displacement y, respectively. For the Y-axis direction suspension force, f y-d represents the disturbance force in the Y-axis direction, and the suspension forces f y-ix , f y-iy , f y-ex and f y-ey are generated by the X-axis suspension current i x , the Y-axis suspension current i y , the X-axis radial displacement x and the Y-axis radial displacement y, respectively. This block diagram reflects the influence of different factors on the suspension force.

[0056] The rotor motion equations in the X and Y-axis directions can be expressed in the following linear form:

[0057]

[0058] where m is the rotor mass; k x-ix , k x-iy and k y-ix are the force-current coefficients in X, Y axes respectively; k y-iy , k x-ex and k x-ey are the force-displacement coefficients in X, Y axes respectively; f y-ex is the disturbance force; k y-ey and k d are the disturbance coefficients in X, Y axes respectively. By combining (6), (7) and (8), the force-current coefficients k x-d , k y-d and k x-ix , k x-iy , the force-displacement coefficients k y-ix , k y-iy and k x-ex , k x-ey in X, Y axes can be derived as: y-ex y-ey

[0059]

[0060] Taking the radial displacements y and x, the radial velocities and as the state variables x1-x4, and the inputs i y and i x , the state space equation of the bearingless electrically excited doubly salient motor can be expressed as:

[0061]

[0062] where , respectively, represent the first order derivatives of the four state variables, the radial displacements y and x, and the radial velocities and .

[0063] For the 12 / 8-pole BDSEM, the rotor rotates one revolution corresponding to 8 electrical periods, so one electrical period corresponds to the rotor mechanical angle r of 45°. In one electrical period, to verify the accuracy of the analytical model of the levitation force, the finite element simulation results of the levitation force are compared with the analytical model calculation results. As shown in Figure 6 , for the two working conditions of x=0 μm, y=50 μm and x=0 μm, y=100 μm, the finite element simulation results of the Y-axis levitation force are compared with the analytical model calculation results (i a , b , c =0, i f ​​= 1A, i x = 1A, i y = 1A). By Figure 6 It can be seen that the analytical model calculation results of Y-axis suspension force are consistent with the finite element simulation results overall. When the radial displacement is small, the analytical model has high accuracy; as the radial displacement increases, its accuracy decreases slightly.

[0064] According to the suspension force analytical model considering rotor eccentricity, the BDSEM double-loop suspension control system is designed. As shown in Figure 7 , the system is a double-loop control structure, the outer loop is a displacement control loop based on a PID controller, and the inner loop is a current control loop based on a PI controller. In the double-loop suspension control system, the displacement sensor continuously detects the radial displacement x and y of the X / Y axis. After comparing the detection signal with the reference displacement signal x* and y*, the displacement error signal e x = x* - x and e y = y* - y is generated. The PID controller generates the reference suspension force signal F x * and F y * according to the displacement error signal. The reference suspension force signal is converted into the reference suspension current signal i mm * and i x * through the force / current conversion module G y (s). Then, the current is closed-loop regulated based on the current control loop of the PI controller, considering the electrical parameters (inductance L, resistance R) of the suspension winding, to generate the final suspension control current i x and i y . Under the action of the corresponding suspension force, the rotor is corrected to the equilibrium position, thereby realizing stable suspension.

[0065] From the derivation process of the suspension force analytical model considering rotor eccentricity, it can be known that the radial suspension force mainly includes the radial controllable suspension force F m and the radial eccentric magnetic pull F e . The controllable suspension force can be controlled by passing different amplitudes of current in the suspension winding, and the eccentric magnetic pull only exists when the rotor is radially eccentric, and its amplitude is positively related to the size of the radial displacement.

[0066] According to the derived suspension force analytical model considering rotor eccentricity, the eccentric magnetic pull is fed forwardly compensated to enhance the suspension stability. In the feedforward compensation suspension control strategy, the compensation suspension force F c needs to offset the magnetic pull F e generated by the rotor eccentricity, and they satisfy the constraint relationship of equal amplitude and opposite direction, i.e. F c = -F e . As Figure 7As shown, the dotted line is the eccentric magnetic pull generation channel, and the dashed line is the eccentric magnetic pull feedforward compensation channel. The system generates a feedforward compensation current signal by real-time detection of the eccentric position, and superimposes it on the generation of the controllable suspension force F m , thereby canceling the eccentric magnetic pull generated by the radial displacement. For suspension control, the main compensation is the eccentric magnetic pull generated by the X-axis radial displacement x and the Y-axis radial displacement y, and the compensation currents i xc-ex and i yc-ey may be represented as:

[0067]

[0068] The feedforward compensation can cancel the eccentric disturbance and improve the anti-eccentric interference ability and position tracking accuracy of the suspension system. Compared with the traditional method, the present scheme has the characteristics of high model accuracy and strong anti-eccentric interference ability.

[0069] Each of the embodiments in the specification is described in a progressive manner, and the same and similar parts between the embodiments can be referred to each other. Each embodiment focuses on the difference from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, it is described relatively simply, and the relevant part can be referred to the part of the method embodiment. The above is merely a specific implementation of the present application, but the protection scope of the present 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 present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for analyzing and compensating for the levitation force of a bearingless doubly salient pole motor under eccentric conditions, characterized in that, include: S1. Establish an analytical model of suspension force taking into account rotor eccentricity, and linearize the suspension force based on the established analytical model of suspension force. S2. Based on the processing result of S1, the levitation force of the bearingless doubly salient pole motor is controlled by a dual-ring levitation control system, wherein the dual-ring levitation control system includes: an outer ring as a displacement control ring and an inner ring as a current control ring.

2. The method according to claim 1, characterized in that, Also includes: During the operation of the dual-ring suspension control system, the eccentric position of the rotor is detected in real time, and a corresponding feedforward compensation current signal is generated. The feedforward compensation current signal is then superimposed on the suspension current signal to counteract the eccentric magnetic pull caused by the eccentric displacement of the rotor.

3. The method according to claim 1, characterized in that, S1 includes: Establish an X and Y coordinate system with the geometric center of the rotor as the origin, and create a levitation force model: Among them, F x F represents the levitation force along the X-axis. y The levitation force along the Y-axis is represented by x, and the eccentric displacements of the rotor along the X and Y axes are denoted as x and y, respectively. The motor consists of armature windings W for each of the three phases A, B, and C. a W b W c The suspension windings W on the X and Y axes x W y and excitation winding W f Let A = {a, b, c, x, y, f}, where a, b, c represent the three-phase armature windings A, B, and C respectively, x and y represent the X and Y axis levitation windings, and f represents the excitation winding; j L represents the current in the j-th phase winding; j M represents the self-inductance of the j-th phase winding. jk This represents the mutual inductance between the j-th phase and the k-th phase windings.

4. The method according to claim 3, characterized in that, The linearization of the levitation force includes performing a Taylor expansion at the equilibrium position while retaining the first-order small-signal term and ignoring higher-order nonlinear terms.

5. The method according to claim 1 or 4, characterized in that, The linearized levitation force under eccentric conditions is: F x0 and F y0 These represent the initial levitation forces along the X and Y axes of the rotor at the equilibrium position, respectively, where x0 and y0 represent the X and Y coordinates of the linearized expansion point, and i x i y These are the real-time levitation control currents for the X-axis and Y-axis levitation windings, respectively. x0 i y0 This represents the static current required to maintain levitation at the equilibrium position.

6. The method according to claim 5, characterized in that, Also includes: Based on the linearized levitation force under the eccentric condition, a matrix-form levitation force model is obtained. k x-ix and k x-iy k is the force-current coefficient on the X-axis. x-ex and k x-ey k is the force-displacement coefficient on the X-axis. y-ix and k y-iy k is the force-current coefficient on the Y-axis. y-ex and k y-ey This is the force-displacement coefficient on the Y-axis.

7. The method according to claim 5, characterized in that, The permitted process of the dual-ring suspension control system includes: The radial displacements x and y of the rotor along the X and Y axes are continuously detected by displacement sensors. After comparison with the reference displacement signals x* and y*, the displacement deviation signal e is obtained. x =x*-x and e y =y*-y; The controller generates a reference levitation force signal F based on the displacement deviation signal. x * and F y *; The reference levitation force signal is converted into a reference levitation current signal i using a force / current conversion module. x * and i y *And input current control loop; The current is regulated in a closed loop through a current control loop to generate a floating control current i. x and i y And it is fed into the suspension winding.

8. The method according to claim 6, characterized in that, In the feedforward compensation current signal, the compensation current i is used to compensate for the eccentric magnetic pull generated by the radial displacement y of the Y-axis. yc-ey Represented as: Where k y-ey k represents the coupling coefficient between the radial displacement y in the Y-axis direction and the eccentric magnetic pull. y-iy This represents the coupling coefficient between the levitation current in the Y-axis direction and the radial levitation force.

9. The method according to claim 8, characterized in that, In the feedforward compensation current signal, the compensation current i is used to compensate for the eccentric magnetic pull generated by the radial displacement x of the X-axis. xc-ex Represented as: Where k x-ex k represents the coupling coefficient between the radial displacement x along the X-axis and the eccentric magnetic pull. x-ix This represents the coupling coefficient between the levitation current in the X-axis direction and the radial levitation force.

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