Suspension force control method of magnetic levitation motor considering edge magnetic flux coupling

Abstract

The application discloses a magnetic suspension motor suspension force control method considering edge magnetic flux coupling, suspension current and real-time eccentric displacement are calculated by a position decoupling suspension force model to obtain feedback suspension force; the derivative of suspension current and real-time eccentric displacement with respect to time is input into a sliding mode observer to output a suspension disturbance force observation; after the feedback suspension force and the observation are superposed, the suspension force calculation error is determined to determine the positive and negative of the voltage of a driving power converter, and the suspension system is controlled; the position suspension force decoupling model is established based on a nonlinear model, the sliding mode observer is designed based on the position decoupling model, the nonlinear time-varying coupling component is obtained by the sliding mode observer in real time and online, and the coupling component is fed forward to the suspension control system as external disturbance compensation, the nonlinear time-varying suspension system is effectively converted into a linear time-invariant suspension system, and the suspension stability, reliability and precision of the flywheel battery are greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of automation control technology, and specifically relates to a method for controlling the levitation force of a magnetic levitation motor that considers edge magnetic flux coupling. Background Technology

[0002] Magnetic levitation motors are a core component of flywheel batteries and have broad application prospects in energy-efficient fields such as new energy consumption and regenerative braking of vehicles. Magnetic levitation switched reluctance motors, combined with magnetic levitation bearing technology, replace traditional bearings, reducing frictional losses and maintenance costs in mechanical transmission. They also solve the inherent noise and torque ripple problems of traditional switched reluctance motors, combining the advantages of both magnetic levitation bearings and switched reluctance motors. However, the levitation force displacement stiffness coefficient and current stiffness coefficient of magnetic levitation switched reluctance motors are dynamically coupled by the rotor position, exhibiting nonlinear time-varying characteristics that severely affect the robustness of the levitation system. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a magnetic levitation motor levitation force control method that considers edge magnetic flux coupling, which has the advantages of high reliability, accuracy, and strong robustness, and significantly improves the levitation stability, reliability, and accuracy of flywheel batteries.

[0004] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0005] Methods for controlling the levitation force of magnetic levitation motors considering edge flux coupling include:

[0006] Floating current i y The feedback levitation force is obtained by calculating the real-time eccentric displacement y0 through the position decoupling levitation force model. ;

[0007] Floating current i y The sliding mode observer, which is the differential input of the real-time eccentric displacement y0 with respect to time, outputs the observation of the levitation disturbance force. ;

[0008] Feedback levitation force and observation After superposition, it is equal to the given levitation force F. * The error is calculated to determine the positive or negative voltage of the drive power converter and to control the levitation system.

[0009] Furthermore, the position-decoupled levitation force model is obtained by linearizing the time-varying levitation force model and integrating it over a polar distance to obtain the average value.

[0010] Furthermore, the position-decoupled levitation force model is as follows:

[0011]

[0012] in, and These are the current stiffness coefficient and displacement stiffness coefficient of the position-decoupled suspension model, k. iy (θ) is the radial current stiffness coefficient, k iy (θ) is the radial displacement stiffness coefficient.

[0013] Furthermore, the aforementioned and The specific forms are as follows:

[0014]

[0015] Among them, B r It is the remanence of a permanent magnet, h m S is the magnetization thickness of the permanent magnet ring, N is the number of revolutions of the levitation winding, S3 is the area of ​​the permanent magnet, g1 is the length of the edge magnetic flux air gap, and S m g0 is the main magnetic flux area, g0 is the main magnetic flux air gap length, k0 is the permanent magnet leakage coefficient, and k m1 The levitation force correction coefficient considering the effect of magnetic saturation, where μ0 is the vacuum permeability.

[0016] Furthermore, the sliding mode observer is obtained based on the state-space equations of the y-degree-of-freedom suspension system:

[0017]

[0018] in, For the displacement differential x r2 The estimated value, This is an estimate of the external disturbance f. and Here, x represents the gain of the sliding mode observer, m is the rotor mass, and x is the gain of the sliding mode observer. r1 For displacement state variables.

[0019] Furthermore, the state-space equation of the y-degree-of-freedom suspension system is:

[0020]

[0021] Among them, matrix ,matrix ,matrix ,matrix , u is the suspending current i y y1 is the output rotor displacement of the suspension system.

[0022] Furthermore, the error function of the sliding mode observer is:

[0023]

[0024] in, For x r2 The estimation error, Let f be the estimation error.

[0025] Going further:

[0026] based on and The conditions for convergence of rotor eccentric velocity observation are obtained as follows:

[0027]

[0028] Where L represents the Lyapunov function;

[0029] when The observed rotor eccentricity velocity converged;

[0030] satisfy:

[0031]

[0032] Where: C is the coefficient of the solution to the differential equation, and t is the time variable;

[0033] When k2>0, the disturbance quantity observation converges.

[0034] Furthermore, the positive or negative voltage is determined by the error through a hysteresis comparator.

[0035] Furthermore, the observation of the levitation disturbance force It can simultaneously observe nonlinear time-varying coupled levitation force and external disturbances.

[0036] The beneficial effects of this invention are as follows:

[0037] (1) By establishing a position-decoupled suspension force model, the present invention effectively converts the nonlinear time-varying suspension system into a linear time-invariant system, effectively solving the dynamic coupling of rotor position to the suspension system, reducing the motor rotor offset, increasing the system's anti-interference performance, and verifying its robustness.

[0038] (2) The sliding mode observer of the present invention is designed based on the position decoupled suspension force model, which makes the observation of rotor eccentric speed converge quickly and the observation of disturbance quantity converge quickly, and accurately tracks the nonlinear time-varying coupling components. Attached Figure Description

[0039] Figure 1 This is a block diagram of the magnetic levitation motor levitation force control method considering edge magnetic flux coupling as described in this invention;

[0040] Figure 2This is a flowchart illustrating the design of the sliding mode observer described in this invention. Detailed Implementation

[0041] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the scope of protection of the present invention is not limited thereto.

[0042] This embodiment uses a 12 / 14 magnetic levitation switched reluctance motor (12 / 14BSRM) as an example to specifically illustrate the levitation force control method of a magnetic levitation motor considering edge magnetic flux coupling.

[0043] like Figure 1 As shown, the magnetic levitation motor levitation force control system of the present invention, considering edge magnetic flux coupling, includes a PID controller, a hysteresis comparator, a power converter, a position decoupling model, a sliding mode observer, and the motor body. The position decoupling model and the sliding mode observer constitute a decoupling compensation system; feedback levitation force From the floating current i y The real-time eccentric displacement y0 is obtained through position decoupling levitation force model calculation; the input of the sliding mode observer is the real-time detected levitation current i. y The derivative of the real-time eccentric displacement y0 with respect to time is used to output the observation of the levitation disturbance force. The output levitation disturbance force observation of the sliding mode observer It can observe both nonlinear time-varying coupled levitation force and external disturbances; it can also provide feedback on levitation force. and observation The superimposed levitation force F of the PID controller is then combined with the output levitation force F of the PID controller. * (The error is obtained from the real-time eccentric displacement y0 and the given displacement y*, and the specific process is the existing technology.) The error is calculated, and then the positive and negative voltage of the driving power converter is determined through the hysteresis comparator to achieve the purpose of controlling the suspension system.

[0044] Position decoupled levitation force model calculates feedback levitation force The specific steps are as follows:

[0045] Step (1), taking the y-direction of the rotor coordinate system as an example, the levitation force of the magnetic levitation switched reluctance motor is divided into the main levitation force generated by the main magnetic flux and the auxiliary levitation force generated by the edge magnetic flux. The general analytical expression of the levitation force model can be expressed as follows:

[0046] (1)

[0047] Where, k m This is the levitation force correction coefficient that takes into account the effects of magnetic saturation; F my+ It is the main levitation force generated by the stator main magnetic flux in the positive y direction of the rotor coordinate system; F my— It is the main levitation force generated by the main flux of the stator in the negative y-direction of the rotor coordinate system; F fy+It is the auxiliary levitation force generated by the edge magnetic flux of the stator in the positive y-direction of the rotor coordinate system; F my— It is the auxiliary levitation force generated by the edge magnetic flux of the stator in the negative y direction of the rotor coordinate system, ΔF. my It is F my+ and F my— Resultant force, ΔF fy It is F fy+ and F fy— The combined force.

[0048] Step (2): Calculate the main magnetic flux area and the edge magnetic flux area respectively.

[0049] Main flux area S m The value of ah (where a represents the rotor tooth width and h represents the rotor axial length) is a constant; the edge magnetic flux area S f The value of the side flux width A f (The acquisition process is based on existing technology) shows a positive correlation, A f The analytical model is as follows:

[0050] (2)

[0051] In equation (2), θ represents the real-time position of the rotor, and b0, b1, and b2 are all constants, and:

[0052] (3)

[0053] Where w is A f The mathematical relationship between the pulsation frequency w and the rotational speed n is as follows:

[0054] (4)

[0055] T is the period of the rotor pole pitch, which is related to the rotational speed n and the number of rotor teeth m. r The mathematical relationship is as follows:

[0056] (5)

[0057] From equations (2), (3), (4) and (5), the edge magnetic flux area S can be obtained. f The specific expression is:

[0058] (6)

[0059] Step (3): Calculate the main levitation force ΔF in the y-direction of the rotor coordinate system. my and auxiliary levitation force △F fy And linearization is performed at the rotor balance position, ΔF my and △F fyThe relationship between air gap magnetic flux density and levitation magnetic flux area is expressed as follows:

[0060] (7)

[0061] In the formula, B pm B is the bias magnetic flux density generated by the permanent magnet; imy It is the control magnetic flux density generated by the levitation winding; B ify It is the edge control magnetic flux density generated by the levitation winding; μ0 is the free permeability; S m It is the area of ​​the main magnetic flux, S f It is the edge magnetic flux area;

[0062] B imy and B ify The specific expression is as follows:

[0063] (8)

[0064] In the formula, g0 is the length of the main magnetic flux air gap; N is the number of revolutions of the levitation winding; i y It is the levitation current in the y direction; g1 is the edge flux air gap length, which is approximately expressed as:

[0065] (9)

[0066] Substitute formulas (7)-(9) into formula (1), and adjust F at the rotor balance position. y After linearization (the specific process is based on existing technology), the y-direction levitation force model (time-varying levitation force model) of the rotor coordinate system of the 12 / 14BSRM levitation system is obtained as follows:

[0067] (10)

[0068] In the formula, k iy (θ) is the radial current stiffness coefficient, k y (θ) is the radial displacement stiffness coefficient, and their specific forms are as follows:

[0069] (11)

[0070] In the formula, B r It is the remanence of a permanent magnet, h m S3 is the magnetization thickness of the permanent magnet ring, S4 is the area of ​​the permanent magnet, k0 is the leakage flux coefficient of the permanent magnet, and k m1 Suspension force correction coefficient considering the effect of magnetic saturation.

[0071] Step (4) Calculate the mechanical angle k at 2π. iy (θ) and k yThe average value of (θ) can be used to transform equation (10) into a time-invariant levitation force model, as shown below:

[0072] (12)

[0073] In the formula, It is the output of the position-decoupled suspension model; and These are the current stiffness coefficients and displacement stiffness coefficients of the position-decoupled suspension model, specifically in the following forms:

[0074] (13)

[0075] The design process of the sliding mode observer is as follows: Figure 2 As shown, the specific design steps are as follows:

[0076] Step (1), the state-space equations of the y-degree-of-freedom suspension system are established based on the position-decoupled suspension force model as follows:

[0077] (14)

[0078] Among them, matrix ,matrix ,matrix ,matrix , u is the suspending current i y f is the external disturbance, m is the rotor mass, and x is the rotor mass. r1 Let x be the displacement state variable. r2 y1 is the displacement derivative (i.e., rotor eccentricity velocity) and y1 is the output rotor displacement of the suspension system.

[0079] Step (2): Based on the state-space equations established in step (1), the sliding mode observer is designed as follows:

[0080] (15)

[0081] In the formula and For x r2 The estimated value of f, and These represent the gains of the sliding mode observer.

[0082] Step (3): Based on the sliding mode observer designed in step (2), the error function is obtained, which can be expressed as:

[0083] (16)

[0084] x r2 The estimation error is expressed as The estimation error of f is expressed as Then the above formula can be written as:

[0085] (17)

[0086] Design Lyapunov functions based on the Lyapunov criterion. The condition for convergence of rotor eccentric velocity observation is:

[0087] (18)

[0088] From the above formula, we can obtain that when the following conditions are met... Rotor eccentricity speed x r2 The observations converged, and the observation error eventually became 0;

[0089] Eliminate by the error function (17) The differential equation can be obtained as follows:

[0090] (19)

[0091] Solving the differential equation yields the observation error:

[0092] (20)

[0093] In the formula: C is the coefficient of the solution to the differential equation, and t is the time variable;

[0094] From equation (20), we can obtain that when k2>0, the disturbance observation converges, and the observation error is... The convergence speed and observation error can be adjusted by changing the values ​​of k1 and k2.

[0095] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A levitation force control method for a magnetic levitation motor considering edge magnetic flux coupling, characterized in that, include: Floating current i y The feedback levitation force is obtained by calculating the real-time eccentric displacement y0 through the position decoupling levitation force model. ; Floating current i y The sliding mode observer, which is the differential input of the real-time eccentric displacement y0 with respect to time, outputs the observation of the levitation disturbance force. ; Feedback levitation force and observation After superposition, it is equal to the given levitation force F. * Calculate the error, determine the voltage sign of the drive power converter, and control the levitation system; The position-decoupled levitation force model is obtained by linearizing the time-varying levitation force model and integrating it over a polar distance to obtain the average value. The position-decoupled levitation force model is as follows: in, and These are the current stiffness coefficient and displacement stiffness coefficient of the position-decoupled suspension model, k. iy (θ) is the radial current stiffness coefficient, k y (θ) is the radial displacement stiffness coefficient.

2. The levitation force control method for a magnetic levitation motor according to claim 1, characterized in that, The and The specific forms are as follows: Among them, B r It is the remanence of a permanent magnet, h m S is the magnetization thickness of the permanent magnet ring, N is the number of revolutions of the levitation winding, S3 is the area of ​​the permanent magnet, g1 is the length of the edge magnetic flux air gap, and S m g0 is the main magnetic flux area, g0 is the main magnetic flux air gap length, k0 is the permanent magnet leakage coefficient, and k m1 The levitation force correction coefficient considering the effect of magnetic saturation, where μ0 is the vacuum permeability.

3. The levitation force control method for a magnetic levitation motor according to claim 2, characterized in that, The sliding mode observer is obtained based on the state-space equations of the y-degree-of-freedom suspension system: in, For the displacement differential x r2 The estimated value, and Here, x represents the gain of the sliding mode observer, m is the rotor mass, and x is the gain of the sliding mode observer. r1 For displacement state variables.

4. The levitation force control method for a magnetic levitation motor according to claim 3, characterized in that, The state-space equation of the y-degree-of-freedom suspension system is: Among them, matrix ,matrix ,matrix ,matrix , u=i y y1 is the output rotor displacement of the suspension system, and f is the external disturbance.

5. The levitation force control method for a magnetic levitation motor according to claim 3, characterized in that, The error function of the sliding mode observer is: in, For x r2 The estimation error, Let f be the estimation error.

6. The levitation force control method for a magnetic levitation motor according to claim 5, characterized in that: based on and The conditions for convergence of rotor eccentric velocity observation are obtained as follows: Where L represents the Lyapunov function; when The observed rotor eccentricity velocity converged; satisfy: Where: C' is the coefficient of the solution to the differential equation, and t is the time variable; When k2>0, the disturbance quantity observation converges.

7. The levitation force control method for a magnetic levitation motor according to claim 1, characterized in that, The positive or negative voltage is determined by the error through a hysteresis comparator.

8. The levitation force control method for a magnetic levitation motor according to claim 1, characterized in that, The observation of the suspension disturbance force It can simultaneously observe nonlinear time-varying coupled levitation force and external disturbances.

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