Suspension flux linkage repetitive control method for single-winding bearingless flux switching motor

Abstract

The application discloses a single-winding bearingless flux switching motor's suspension magnetic chain repeat control method, which establishes a suspension magnetic chain model of a rotor dynamic eccentricity according to a magnetic suspension rotor system of a single-winding bearingless flux switching motor; a model compensation repeat controller with an integral element, a model compensator and a same-frequency phase shift notch filter is arranged in the magnetic suspension rotor system; the integral element is used for eliminating a steady-state error, the model compensator is used for obtaining an inverse system output signal so as to obtain an accurate displacement control signal, and the notch filter is used for reducing a same-frequency pulsation of the rotor radial displacement; a desired suspension magnetic chain is calculated and obtained through the model compensation repeat controller, a magnetic chain error is obtained by comparing the desired suspension magnetic chain with an actual magnetic chain obtained by a magnetic chain observer, a desired voltage is calculated through the magnetic chain error, and thus inverter switch signals are obtained. The application effectively handles the rotor radial displacement pulsation under a steady-state condition and the displacement sudden change phenomenon under a dynamic condition, and good control is realized.

Description

Technical Field

[0001] This invention relates to the field of bearingless flux switching motor technology, and more particularly to a method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor. Background Technology

[0002] Magnetic levitation bearing technology boasts advantages such as frictionless operation, long lifespan, zero pollution, and controllable support characteristics, and is considered to have broad application prospects in fields such as vibration reduction and noise reduction, green energy saving, cleanliness, and high speed. In applications such as shipbuilding and marine equipment, aerospace, and CNC machine tools, the size and efficiency requirements of motors are very high, and integration is one of the main technical bottlenecks.

[0003] By winding the magnetic levitation bearing coil and the motor armature winding together on the stator, creating a bearingless structure without magnetic or mechanical bearings, and using dual windings to achieve joint control of magnetic levitation and rotation, this is an effective solution for shortening axial length and increasing power density. Bearingless flux switching motors (BFSPMMs) possess unique magnetic focusing characteristics, a simple and reliable rotor structure, low risk of permanent magnet demagnetization due to temperature rise, and easy direct modulation of the air gap magnetic field. Facing the demands for small size, low noise, and low vibration platforms, higher requirements are placed on the structural integration of BFSPMMs. Single-winding BFSPMMs can achieve independent control of motor rotation and levitation using only the torque current component and levitation current component in one winding, fully utilizing the winding capacity, making them ideal for the small size and high efficiency requirements of small electric drive equipment.

[0004] For a single-winding BFSPMM, achieving high-performance suspension control faces the following challenges: 1) As a doubly salient pole structure motor with stator permanent magnet magnetic field modulation, the radial force fluctuations caused by the magnetic flux hinge and air gap length changes during the stator and rotor tooth-coiling alternation process also have a significant impact on the motor's suspension performance; 2) Vibration signals will generate periodic current disturbances in the windings, and the phase inductance of the single-winding structure is smaller, resulting in a higher content of higher harmonics in the winding current, which makes it easier to cause torque and suspension force pulsations; 3) The torque current component and the suspension current component jointly modulate the initial air gap magnetic field established by the permanent magnet, and the two controlled current components have strong coupling, further highlighting the complex relationship between torque pulsations, suspension force pulsations, and rotor radial displacement pulsations.

[0005] For single-winding BFSPMM, a typical electromechanical coupled system, existing methods are still insufficient to effectively handle rotor radial displacement pulsations under steady-state conditions and sudden displacement changes under dynamic conditions. Therefore, it is necessary to study a control strategy that combines the alternating law of the air gap magnetic field with rotor dynamics. Summary of the Invention

[0006] The purpose of this invention is to provide a method for repeated control of the levitation flux linkage in a single-winding, bearingless flux switching motor.

[0007] The technical solution adopted in this invention is:

[0008] A repetitive control method for levitation flux linkage in a single-winding bearingless flux switching motor is proposed. Based on the magnetic levitation rotor system of the single-winding bearingless flux switching motor, a levitation flux linkage model with rotor dynamic eccentricity is established. Based on the levitation flux linkage model with rotor dynamic eccentricity, a model-compensated repetitive controller with an integral element, a model compensator, and a phase-shifted notch filter is set in the magnetic levitation rotor system. The integral element is used to eliminate steady-state error, the model compensator is used to obtain the output signal of the inverse system in order to obtain an accurate displacement control signal, and the notch filter is used to reduce the phase-shifted pulsation of the rotor radial displacement.

[0009] The desired levitation flux is obtained by calculating the repetitive controller with model compensation. The flux error is obtained by comparing the desired levitation flux with the actual flux obtained by the flux observer. The desired voltage is obtained by calculating the flux error, and thus the inverter switching signal is obtained.

[0010] Specifically, the encoder collects angle information to obtain the desired torque plane voltage based on traditional direct torque control; the desired voltage, together with the desired torque plane voltage obtained based on traditional direct torque control, is used to calculate the duty cycle of each phase arm; and based on the duty cycle of each phase arm, the inverter switching signal is obtained.

[0011] Furthermore, the control method of the present invention specifically includes the following steps:

[0012] Step 1: Decompose the six-phase current of the single-winding bearingless flux switching motor (BFSPMM) into torque plane current i αT i βT Floating plane current i αS i βS and zero-sequence current i o1 i o2 ;

[0013] Step 2: Calculate the torque current component i in the synchronously rotating coordinate system using the torque equation and the levitation force equation. dT i qT With the levitation current component i dS i qS ;

[0014] Step 3: Based on the torque current components, the levitation plane armature flux and levitation plane flux in the synchronous rotating coordinate system are obtained respectively.

[0015] Step 4: Set up a repetitive controller with an integrator, model compensation, and notch filter; obtain the desired levitation current through the repetitive controller; calculate the desired levitation flux from the desired levitation current.

[0016] Step 5: Compare the desired levitation flux with the flux obtained by the flux observer to obtain the flux error;

[0017] Step 6: The desired voltage is calculated through flux linkage error. Based on the desired voltage in the floating plane and combined with traditional direct torque control, the desired voltage in the torque plane is obtained. The duty cycle of each phase arm is calculated. The inverter is controlled based on the duty cycle of each phase arm to obtain the inverter switching signal. The control of the motor rotation part can be achieved using traditional direct torque control, which is not the technical solution proposed in this invention, but only a way to complete the basic rotation of the motor.

[0018] Furthermore, in step 1, the torque plane current i αT i βT Floating plane current i αS i βS and zero-sequence current i o1 i o2 The expression is as follows:

[0019]

[0020] In the formula,

[0021] Furthermore, in step 2, the torque current component i in the synchronously rotating coordinate system dT i qT With the levitation current component i dS i qS The current in equation (1) has the following relationship:

[0022]

[0023] In the formula, θ re θ is the angle between the torque plane αT axis and dT axis. sus Let α be the angle between the αS-axis and dS-axis of the suspended plane.

[0024] Furthermore, when the αT axis coincides with the αS axis, θ sus Represented as:

[0025]

[0026] In the formula, k d For i qT The amplitude of the levitation force generated by the combined action of the current and the unit levitation current, k q For i qT The amplitude of the levitation force generated by the combined action of the current and the unit levitation current, k PM The amplitude of the levitation force generated by the combined action of the magnetic field established for the permanent magnet and the unit levitation current.

[0027] Furthermore, the expression for the levitation plane armature flux in the synchronously rotating coordinate system in step 3 is as follows:

[0028]

[0029] Where, θ re The angle between the torque plane αT axis and dT axis;

[0030] The expression for the magnetic flux linkage of the levitation plane in a synchronously rotating coordinate system is as follows:

[0031]

[0032] Specifically, when the air gap circumferential angle θ in the inductance of the k-th phase winding points to the corresponding winding axis...

[0033]

[0034] Where v1 and v2 are constants; LL0 and LL e These represent the self-inductance value without eccentricity and the change in self-inductance caused by eccentricity, respectively.

[0035] Furthermore, in step 4, the output of the model compensator in the model compensation repetitive controller is:

[0036]

[0037] Where, Δe x and Δe y These represent the displacement errors in the x and y directions, respectively. The low-pass filter Q(z) in the model compensator is used to suppress high-frequency noise caused by the differential action.

[0038] The control parameters for suppressing synchronous pulsation at the rotational speed under unbalanced magnetic pull are as follows:

[0039]

[0040] In the formula,

[0041]

[0042] Where, θ rm H(z) represents the mechanical angle; H(z) represents the notch filter.

[0043] The steady-state error elimination component in the unbalanced magnetic pull is as follows:

[0044]

[0045] In the formula, p0 is the proportionality coefficient.

[0046] Furthermore, step 4 specifically includes the following steps:

[0047] Step 4-1: Collect the DC bus voltage information, rotor displacement information, and angle information of the single-winding bearingless flux switching current.

[0048] Step 4-2: Calculate and obtain the expected displacement for comparison based on the rotor displacement information;

[0049] Step 4-3: Calculate the desired floating current signal based on the model-compensated repetitive controller; the desired floating current based on the model-compensated repetitive controller is:

[0050]

[0051] in, and For the output of the model compensator; and This is the control quantity for suppressing rotational frequency pulsation; and Eliminate components of steady-state error;

[0052] Step 4-4, when using i dT When the =0 control strategy is applied, the desired flux linkage in the levitation flux linkage control is calculated as follows:

[0053]

[0054] Where Δx and Δy are the displacement distances of the rotor in the x and y directions, respectively; LL0 and LL e These represent the self-inductance value without eccentricity and the change in self-inductance caused by eccentricity, respectively. The angle between the rotating coordinate system of the suspended plane and the stationary coordinate system;

[0055] Steps 4-5: Compare the desired levitation flux with the actual flux obtained by the flux observer to obtain the flux error. Calculate the desired voltage using the flux error to obtain the inverter switching signal.

[0056] Furthermore, step 5 specifically includes the following steps:

[0057] Step 5-1: Calculate and obtain the back electromotive force of the suspended plane based on the DC bus voltage information;

[0058] Step 5-2: Compensate the observation results of the low-pass filter flux linkage observer by the orthogonality of the flux linkage vector and the back electromotive force vector to obtain the levitated flux linkage observed by the link observer; the levitated flux linkage observed by the low-pass filter flux linkage observer is:

[0059]

[0060] Where, ω c The cutoff frequency is γ, and the adjustment coefficient is e. αS and eβS These are the back electromotive forces along the αS and βS axes of the suspended plane, respectively; and The actual magnetic flux linkage ψ is observed. αS ψ βS That is, e S and These are the back electromotive force vector of the suspended plane and the magnetic flux linkage vector, respectively.

[0061] Step 5-3, specifically, calculates the flux linkage error between the desired flux linkage and the actual flux linkage in the aS and βS axes based on the levitation flux linkage signal:

[0062]

[0063] Where, Δψ αS Δψ represents the flux linkage error between the desired and actual flux linkage along the αS-axis. αS This represents the flux linkage error between the desired flux linkage and the actual flux linkage in the βS-axis.

[0064] Based on the output of the flux linkage observer, the flux linkage error can be rewritten as:

[0065]

[0066] in, This represents the flux linkage error between the desired flux linkage and the observed actual flux linkage along the αS-axis. This represents the flux linkage error between the expected flux linkage and the observed actual flux linkage in the βS-axis.

[0067] Furthermore, the desired voltage of the suspended plane in step 6 is:

[0068]

[0069] In the formula, R s T is the stator resistance. K To control the cycle.

[0070] Furthermore, the general solution for the duty cycle of each phase arm in step 6 is:

[0071]

[0072] In the formula,

[0073] Therefore, when D A When representing the duty cycle of D0 within a control cycle, it is through D A =0 can be used to solve for D B -D F The value can be obtained by simply limiting the duty cycle to achieve the required duty cycle for a six-phase inverter.

[0074] This invention employs the above technical solution, incorporating a model-compensated repetitive controller with an integrator, a model compensator, and a phase-shift notch filter within the magnetic levitation rotor system. The integrator eliminates steady-state errors, the model compensator acquires the inverse system output signal to obtain accurate displacement control signals, and the notch filter reduces the in-frequency pulsation of the rotor's radial displacement. Furthermore, voltage information is collected by voltage sensors to calculate the electromotive force generated in the levitation plane. Simultaneously, based on the observed flux linkage signal obtained by the observer, displacement information is collected by displacement sensors to calculate the expected displacement. The expected levitation flux linkage is then calculated by the model-compensated repetitive controller. The expected levitation flux linkage is compared with the actual flux linkage observed by the flux linkage observer to obtain the flux linkage error. The expected voltage is calculated using the flux linkage error. An encoder collects angle information to obtain the torque plane expected voltage based on conventional direct torque control. The expected voltage, combined with the torque plane expected voltage, is used to calculate the duty cycle of each phase arm. Based on the duty cycle of each phase arm, the inverter switching signal is obtained.

[0075] This invention effectively addresses rotor radial displacement pulsation under steady-state conditions and displacement abrupt changes under dynamic conditions, achieving excellent control. Attached Figure Description

[0076] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0077] Figure 1 This is a schematic diagram of the topology of the single-winding bearingless flux switching motor of the present invention;

[0078] Figure 2 This is a schematic diagram of rotor eccentricity in the single-winding bearingless flux switching motor of the present invention;

[0079] Figure 3 This is a schematic diagram of the principle structure of the magnetic flux observer of the present invention;

[0080] Figure 4 This is a schematic diagram of the principle structure of the model compensation repetitive controller of the present invention. Detailed Implementation

[0081] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0082] like Figures 1 to 4As shown in the figure, this invention discloses a method for repetitive control of levitation flux linkage in a single-winding bearingless flux switching motor. Based on the magnetic levitation rotor system of the single-winding bearingless flux switching motor, a levitation flux linkage model with rotor dynamic eccentricity is established. Based on the levitation flux linkage model with rotor dynamic eccentricity, a model compensation repetitive controller with an integral element, a model compensator, and a phase-shifted notch filter is set in the magnetic levitation rotor system. The integral element is used to eliminate steady-state error, the model compensator is used to obtain the output signal of the inverse system in order to obtain an accurate displacement control signal, and the notch filter is used to reduce the phase-shifted pulsation of rotor radial displacement.

[0083] The desired levitation flux is obtained by calculating the repetitive controller with model compensation. The flux error is obtained by comparing the desired levitation flux with the actual flux obtained by the flux observer. The desired voltage is obtained by calculating the flux error, and thus the inverter switching signal is obtained.

[0084] Specifically, the encoder acquires angle information to obtain the desired torque plane voltage based on conventional direct torque control; the desired voltage, combined with the desired torque plane voltage obtained based on conventional direct torque control, is used to calculate the duty cycle of each phase arm; based on the duty cycle of each phase arm, the inverter switching signal is obtained. Further, the control method of the present invention specifically includes the following steps:

[0085] Step 1: Decompose the six-phase current of the single-winding bearingless flux switching motor (BFSPMM) into torque plane current i αT i βT Floating plane current i αS i βS and zero-sequence current i o1 i o2 ;

[0086] Step 2: Calculate the torque current component i in the synchronously rotating coordinate system using the torque equation and the levitation force equation. dT i qT With the levitation current component i dS i qS ;

[0087] Step 3: Based on the torque current components, the levitation plane armature flux and levitation plane flux in the synchronous rotating coordinate system are obtained respectively.

[0088] Step 4: Set up a repetitive controller with an integrator, model compensation, and notch filter; obtain the desired levitation current through the repetitive controller; calculate the desired levitation flux from the desired levitation current.

[0089] Step 5: Compare the desired levitation flux with the flux obtained by the flux observer to obtain the flux error;

[0090] Step 6: The desired voltage is calculated through flux linkage error. Based on the desired voltage in the floating plane and combined with traditional direct torque control, the desired voltage in the torque plane is obtained. The duty cycle of each phase arm is calculated. The inverter is controlled based on the duty cycle of each phase arm to obtain the inverter switching signal. The control of the motor rotation part can be achieved using traditional direct torque control, which is not the technical solution proposed in this invention, but only a way to complete the basic rotation of the motor.

[0091] The specific principles of this invention will be explained in detail below:

[0092] The motor studied in this invention is as follows Figure 1 As shown, its stator and rotor structure is the same as that of the mechanical bearing FSPMM, but the thickness of the permanent magnet is reduced to facilitate adjustment of the air gap magnetic field. The permanent magnets are embedded between the U-shaped iron cores using alternating magnetization, and 12 coils form a six-phase winding. Each phase winding consists of coils connected in series that are spatially perpendicular to each other; for example, phase A winding consists of coils A1 and A2 connected in series, with each phase winding differing by 60 degrees. θ rm For mechanical angles, θ is the electrical angle. re =10θ rm .

[0093] The single-winding BFSPMM rotor has no mechanical bearings for fixation, and the rotor is always in a dynamic eccentric state during motor operation, such as... Figure 2 As shown. Define the x-direction as being directly opposite coil A1 and the y-direction as being directly opposite coil A2. The stator inner diameter of the motor is s. ro The outer diameter of the rotor is r ro The air gap length when the rotor is eccentric is g o When the rotor is statically eccentric, the rotor's geometric center shifts from the motor's mechanical center O to point P, with an initial eccentricity distance of e and an initial eccentricity angle of [value missing]. When the motor rotates, the rotor precesses synchronously, and the rotor's geometric center shifts from point P to point Q, with a deflection angle of ω. rm ·t, ω rm It is the mechanical angular frequency.

[0094] Figure 2 In a spatially symmetrical series winding, the centerline of the vertically connected coil is the corresponding winding axis. Generating a bias magnetic field in the same direction on the axis of the spatially symmetrical winding can break the air gap magnetic field balance in that direction, thus generating a levitation force. The single-winding BFSPMM utilizes the multi-degree-of-freedom advantage of multi-phase motors, with the torque current component i flowing through the k-th phase winding. kT and suspending current component i kS , k = AF. To maximize motor control performance, the torque current components in the spatially symmetrical winding are in opposite directions, while the floating current components are in the same direction, i.e., i k =i kT +i kS i AS=i DS i BS =i ES i CS =i FS i AT =-i DT i ET =-i BT and i CT =-i FT The windings are connected in a star configuration. Using the T6 transformation matrix, the six-phase current can be decomposed into torque plane currents i. αT i βT Floating plane current i αS i βS and zero-sequence current i o1 i o2 :

[0095]

[0096] in,

[0097] By decoupling the control functions of the αTβT plane and the αSβS plane, the stable rotation and levitation operation of a single-winding bearingless motor can be achieved.

[0098] Operating principle: Currently, the single-winding BFSPMM operation control mainly uses vector control. The speed regulator (ASR) and displacement regulator (ADR) output the desired torque and desired levitation force, respectively, and calculate the torque current component i in the synchronous rotating coordinate system through the torque equation and levitation force equation. dT i qT With the levitation current component i ds i qS Δx and Δy are the displacement distances of the rotor in the x and y directions, respectively. The current in the synchronous rotating coordinate system has the following relationship with the current in equation (1):

[0099]

[0100] In the formula, θ re θ is the angle between the torque plane aT axis and the dT axis. sus Let α be the angle between the αS-axis and dS-axis of the suspended plane.

[0101] When the αT axis coincides with the αS axis, θ sus It can be represented as:

[0102]

[0103] In the formula, k d For i qTThe amplitude of the levitation force generated by the combined action of the current and the unit levitation current, k q For i qT The amplitude of the levitation force generated by the combined action of the current and the unit levitation current, k PM The amplitude of the levitation force generated by the combined action of the magnetic field established for the permanent magnet and the unit levitation current.

[0104] When using i dT When the =0 control strategy is applied, the electromagnetic torque T required for stable operation of a single-winding BFSPMM is... e and controllable levitation force F cx F cy The linear relationship between the current and the corresponding control current can be expressed as:

[0105]

[0106] In the formula, k t k is the torque current coefficient. sx and k sy These are the levitation current stiffness coefficients in the x and y directions, respectively.

[0107]

[0108] The performance of a motor in levitation operation depends on the design of the ADR (Action Control Regulator) and the accuracy of the levitation force equation. Removing the levitation force equation and directly controlling the balance of the air gap magnetic field within the ADR can effectively reduce internal disturbances caused by model inaccuracies, while also facilitating ADR optimization to improve its ability to suppress external disturbances. The following section will elaborate on how to achieve levitation flux control.

[0109] (1) Air gap magnetic flux density of the levitation flux linkage model with rotor dynamic eccentricity: According to Figure 2 As shown, the dynamic change of the air gap length when the rotor is eccentric is represented as follows:

[0110]

[0111] In the formula, θ is the circumferential angle of the air gap. Since the air gap permeability is negatively correlated with the air gap length, and the air gap permeability is directly proportional to the magnetic flux density, the slotless air gap magnetic flux density B under dynamic eccentricity is... re It can be represented as:

[0112]

[0113] In the formula, B r The air gap magnetic flux density is the value when there is no eccentricity.

[0114] According to the Maclaurin expansion formula and ignoring terms of order two and above, equation (8) can be simplified to:

[0115]

[0116] According to the theory of air gap magnetic field modulation, the air gap magnetic flux density of a motor can be expressed as the product of the magnetic field modulation function and the air gap magnetomotive force:

[0117]

[0118] In the formula, μ0 is the air permeability, and F m M represents the air gap magnetomotive force. sr The magnetic field modulation function is derived from the stator modulation function M. s Rotor modulation function M r The product of M consists of s and M r The values ​​were obtained by calculating the stator and rotor tooth space distributions using Fourier series, respectively.

[0119] (2) Armature flux linkage: According to equation (10), the mutual inductance between the i-th phase winding and the j-th phase winding when the rotor is eccentric can be derived as follows:

[0120]

[0121] In the formula, r sro l is the air gap radius. stk For the length of the iron core shaft, W i and W j These are the winding functions for phase i and phase j, respectively. The winding function W for phase k is... k For conductor distribution function C k Through the stator modulation function M s The modulated result, i.e. W k =M s ·C k Because each phase winding of a single-winding BFSPMM consists of two coils connected in series that are symmetrical about the spatial axis, C k The conductor distribution function C of coil k1 k1 and the conductor distribution function C of coil k2 k2 Composition, namely C k =C k1 +C k2 The conductor distribution function C of the k1 coil of the k-th phase winding. k1 The Fourier series expansion can be written as:

[0122]

[0123] In the formula, N w For the number of coil turns, c = 0 to 5 corresponds to k = A to F, a w With b w These are the coefficients of the Fourier series.

[0124] Coil k2 is spatially ahead of coil k1 by 90°, therefore the conductor distribution function C of coil k2 is... k2 Represented as:

[0125]

[0126] Substituting equations (12)-(13) into equation (11), and combining with equation (9), we can obtain the mutual inductance between the i-th phase winding and the j-th phase winding of the single-winding BFSPMM as follows:

[0127]

[0128] In the formula, LM0 and LM e These represent the unbiased mutual inductance value and the change in mutual inductance caused by eccentricity, respectively, ignoring the inductance pulsation with rotor position.

[0129] Similarly, when i = j, the self-inductance of the i-th phase winding of a single-winding BFSPMM is:

[0130]

[0131] In the formula, LL0 and LL e These represent the self-inductance value without eccentricity and the change in self-inductance caused by eccentricity, respectively.

[0132] Using the T6 transformation matrix, the armature flux linkages in the torque plane, levitation plane, and zero-sequence plane can be obtained as follows:

[0133]

[0134] According to equation (17), the armature flux linkage can be obtained as follows:

[0135]

[0136] In the formula, when the air gap circumferential angle θ in the inductance of the k-th phase winding points to the corresponding winding axis,

[0137]

[0138] In the formula, v1 and v2 are constants.

[0139] Furthermore, according to equations (3)-(4), the levitation plane armature flux in the synchronous rotating coordinate system can be obtained as follows:

[0140]

[0141] (3) Permanent magnet flux linkage: According to equation (10), the permanent magnet flux linkage of the i-th phase winding when the rotor is eccentric can be derived as follows:

[0142]

[0143] In the formula, F pm The initial permanent magnet magnetomotive force distribution of BFSPMM:

[0144] F pm =∑ n≥1 F m a m sinn(n p_pm θ) (22)

[0145] In the formula, n p_pm =6 represents the number of permanent magnet pole pairs, F m a is the magnetomotive force amplitude. m These are the coefficients of the Fourier series.

[0146] Substituting equations (12)-(13) into equation (21), and combining with equation (9), we can obtain the permanent magnet flux linkage of the i-th phase winding of the single-winding BFSPMM as:

[0147]

[0148] In the formula, ψ fe This represents the change in amplitude of the permanent magnet flux linkage caused by eccentricity.

[0149] When the air gap circumferential angle θ in the inductance of the i-th phase winding points to the corresponding winding axis, the permanent magnet flux linkage of the levitation plane can be obtained by using the T6 transformation matrix:

[0150]

[0151] According to equations (3)-(4), the levitation plane permanent magnet flux in the synchronous rotating coordinate system can be obtained as follows:

[0152]

[0153] In the formula,

[0154]

[0155] Combining equations (20) and (25), the expression for the magnetic flux linkage of the suspended plane in the synchronous rotating coordinate system can be obtained as follows:

[0156]

[0157] Therefore, in the flux linkage, the torque current component and the levitation flux linkage and rotor radial displacement caused by the permanent magnet magnetomotive force are linearly related, and the levitation current component can regulate the levitation flux linkage. Thus, a control based on the levitation flux linkage is constructed, as follows.

[0158] Suspended flux linkage control based on model-compensated repetitive controller:

[0159] (1) Suspension magnetic flux control: According to equation (28), when At that time, the desired levitation planar magnetic flux can be expressed as:

[0160]

[0161] Among them, the controllable levitation force is generated by adjusting the air gap magnetic field. and It can be obtained from ADR.

[0162]

[0163] Therefore, the error between the desired flux linkage and the actual flux linkage in the αS and βS axes is:

[0164]

[0165] The desired voltage of the suspended plane is:

[0166]

[0167] In the formula, R s T is the stator resistance. K To control the cycle.

[0168] By obtaining the inverter switching signal based on the desired voltage vector, motor levitation can be achieved. The phase voltage control equation is:

[0169]

[0170] In the formula, U DC It is the DC bus voltage, u NO If the voltage is at the center point, and the upper arm of the k-phase bridge is open while the lower arm is closed, then S... k =1, otherwise S k =0.

[0171] Using the T6 matrix, the six-phase voltage in the stationary coordinate system can be expressed as:

[0172]

[0173] in,

[0174]

[0175] To maintain a constant switching frequency, the switching device of each phase bridge arm switches only once per control cycle. For a six-phase inverter, there are a maximum of 5 effective voltage vectors in one control cycle, defined as V. a (a = 1-5). V a The duration of action is set to τ a Furthermore, the duration of the zero voltage vector V0 is t0. The desired equivalent voltage vector... It is synthesized from five effective voltage vectors. Based on the volt-second balance principle, The relationship with duty cycle can be written as:

[0176]

[0177] In the formula, S ia τ a D is a 6×1 matrix representing the product of the switching states and their durations in a 6-phase inverter. i This represents a 6×1 matrix representing the duty cycles of the i-th phase arm, where i = AF.

[0178] From equation (36), the general solution for the duty cycle of each phase arm can be obtained as follows:

[0179]

[0180] In the formula,

[0181]

[0182] Therefore, when D A When representing the duty cycle of V0 within a control cycle, it is done through D A =0 can be used to solve for D B -D F The value can be obtained by simply limiting the duty cycle to achieve the required duty cycle for a six-phase inverter.

[0183] (2) Flux flux observer: In formula (31), the actual flux flux ψ is accurately obtained. αS ψ βS This is crucial. In traditional flux observation methods, the direct integration method suffers from DC bias and integration drift. Low-pass filter flux observers can effectively filter the DC component, but the amplitude and phase of the observed flux vary with the observer's cutoff frequency, making them unsuitable for high-speed applications. This invention considers the orthogonality between the flux vector and the back EMF vector to compensate for the observation results. The flux observer is as follows... Figure 3 As shown. It is well known that the magnetic flux angle... Angle with back electromotive force The included angle between them should always be 90°, that is, it is necessary to... The control is zero. Its expression is:

[0184]

[0185] Among them, e S and These are the back electromotive force vector of the levitation plane and the levitation flux vector, respectively, e αS e βSLet be the back electromotive force of the levitation plane αS and βS axes, with the superscript "^" indicating the observed value. Based on the low-pass filter flux linkage observer, the levitation flux linkage in equation (39) can be obtained as follows:

[0186]

[0187] Where, ω c The cutoff frequency is γ, and the adjustment coefficient is γ, which can be obtained using the angle adjuster (AAR) according to equation (39). αS and e βS These are the back electromotive forces along the αS and βS axes of the suspended plane, respectively; and The actual magnetic flux linkage ψ observed αS ψ βS That is, e S and are the back electromotive force vector of the levitation plane and the levitation flux vector, respectively. s is the differential of the complex field expression of the transfer function.

[0188] Therefore, based on the output of the magnetic flux observer, equation (31) can be rewritten as:

[0189]

[0190] Model-compensated repetitive controller: The relationship between the radial displacement and radial magnetic pull of a single-winding BFSPMM rotor can be written as:

[0191]

[0192] In the formula, l m and l s These are the rotor centroid length and shaft length, respectively. g The length of the center of gravity, m a and g a J represents the rotor mass and gravitational acceleration, respectively. xy F is the moment of inertia at the rotor's equator. mpx and F mpy The unbalanced magnetic pull in the x and y directions, respectively, f ux and f uy These represent the unmodeled dynamics in the x and y directions, respectively.

[0193] When the rotor is dynamically eccentric, the radial resultant force F generated by the magnetic field established by the permanent magnet is... p (t) is:

[0194]

[0195] Substituting equation (9) into equation (43), the unbalanced magnetic pull force during dynamic eccentricity of a single-winding BFSPMM rotor can be derived as follows:

[0196]

[0197] In the formula, when the motor topology is determined, k e1 k e2 k e3 It is a constant.

[0198] According to equation (44), the rotor radial displacement includes a rotational speed-frequency pulsation signal. If the inverse characteristic of the phase-frequency characteristic of the controlled object can be obtained, phase compensation and amplitude compensation can be provided for the ADR to a certain extent. Since the actual system model cannot be very accurate, and the model parameters cannot remain unchanged, this invention constructs an ADR based on the principle of repetitive control to reduce rotational speed-frequency pulsations with unmodeled dynamics. Model-compensated repetitive controllers, such as... Figure 4 As shown.

[0199] exist Figure 4 In the diagram, part ① is a repetitive signal generator, which is an integrator with the fundamental period of the signal as the step size. To improve stability, a low-pass filter Q(z) is used to reduce the integration effect.

[0200] Part ② is the model compensator, and the floating current i is derived according to equation (42). ds i qS The inverse transfer function between the rotor radial displacement and the repetitive signal generator, combined with the repetitive signal generator, results in the following model compensator output:

[0201]

[0202] In the formula, Δe x and Δe y These represent the displacement errors in the x and y directions, respectively. The low-pass filter Q(z) in the model compensator is used to suppress high-frequency noise caused by the differential action.

[0203] To reduce rotational frequency ripple, a Least Mean Square (LMS) notch filter H(z) is used to enhance ω. rm The control signal strength in the frequency band. Since the displacement is very small, the displacement square term in equation (44) is ignored. Combining with equation (5), the control quantity for suppressing the same frequency pulsation of the rotational speed in the unbalanced magnetic pull is as follows:

[0204]

[0205] In the formula,

[0206]

[0207] Since the above control loop does not include an integral element, steady-state error still exists due to the DC component of the unbalanced magnetic pull caused by factors such as rotor gravity and mass imbalance. Furthermore, through... Eliminate steady-state error:

[0208]

[0209] In the formula, p0 is the proportionality coefficient.

[0210] Therefore, the expected floating current of the model-compensated repetitive controller is:

[0211]

[0212] When using i dT When the control strategy is =0, the desired flux linkage in the levitation flux linkage control proposed in this invention is:

[0213]

[0214] In summary, by combining equations (32), (41) and (50), the levitation flux control based on the model-compensated repetitive controller can be realized.

[0215] This invention employs the above technical solution, incorporating a model-compensated repetitive controller with an integrator, a model compensator, and a phase-shift notch filter within the magnetic levitation rotor system. The integrator eliminates steady-state errors, the model compensator acquires the inverse system output signal to obtain accurate displacement control signals, and the notch filter reduces the in-frequency pulsation of the rotor's radial displacement. Furthermore, voltage information is collected by voltage sensors to calculate the electromotive force generated in the levitation plane. Simultaneously, based on the observed flux linkage signal obtained by the observer, displacement information is collected by displacement sensors to calculate the expected displacement. The expected levitation flux linkage is then calculated by the model-compensated repetitive controller. The expected levitation flux linkage is compared with the actual flux linkage observed by the flux linkage observer to obtain the flux linkage error. The expected voltage is calculated using the flux linkage error. An encoder collects angle information to obtain the torque plane expected voltage based on conventional direct torque control. The expected voltage, combined with the torque plane expected voltage, is used to calculate the duty cycle of each phase arm. Based on the duty cycle of each phase arm, the inverter switching signal is obtained.

[0216] This invention effectively addresses rotor radial displacement pulsation under steady-state conditions and displacement abrupt changes under dynamic conditions, achieving excellent control.

[0217] Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Without conflict, the embodiments and features in the embodiments of this application can be combined with each other. The components of the embodiments of this application described and illustrated herein can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A repetitive control method for levitation flux linkage in a single-winding bearingless flux switching motor: Based on the magnetic levitation rotor system of the single-winding bearingless flux switching motor, a levitation flux linkage model with rotor dynamic eccentricity is established; based on the levitation flux linkage model with rotor dynamic eccentricity, a model-compensated repetitive controller with an integral element, a model compensator, and a phase-shifted notch filter is set in the magnetic levitation rotor system; the integral element is used to eliminate steady-state error, the model compensator is used to obtain the output signal of the inverse system in order to obtain an accurate displacement control signal, and the notch filter is used to reduce the same-frequency pulsation of the rotor radial displacement; The desired levitation flux is calculated using a model-compensated repetitive controller. The desired levitation flux is compared with the actual flux obtained by a flux observer to obtain the flux error. The desired voltage is then calculated from the flux error, thus obtaining the inverter switching signal. The key feature is that: The control method includes the following steps: Step 1: Decompose the six-phase current of the single-winding bearingless flux switching motor into torque plane currents. Floating plane current and zero-sequence current ; Step 2: Calculate the torque and current components in the synchronously rotating coordinate system using the torque equation and the levitation force equation. With suspending current component ; Step 3: Based on the torque current components, the levitation plane armature flux and levitation plane flux in the synchronous rotating coordinate system are obtained respectively. Step 4: Set up a repetitive controller with an integrator, model compensation, and notch filter; obtain the desired levitation current through the repetitive controller; calculate the desired levitation flux using the desired levitation current. Step 4 specifically includes the following steps: Step 4-1: Collect the DC bus voltage information, rotor displacement information, and angle information of the single-winding bearingless flux switching current. Step 4-2: Calculate and obtain the expected displacement for comparison based on the rotor displacement information; Step 4-3: Calculate the desired floating current signal based on the model-compensated repetitive controller; the desired floating current based on the model-compensated repetitive controller is: （50）； in, and For the output of the model compensator; and This is the control quantity for suppressing rotational frequency pulsation; and Eliminate components of steady-state error; Step 4-4, when using When the =0 control strategy is applied, the desired flux linkage in the levitation flux linkage control is calculated as follows: （51）； in, and The rotor is respectively in direction and Displacement distance in the direction; and These represent the self-inductance value without eccentricity and the change in self-inductance caused by eccentricity, respectively. The initial eccentricity distance, The angle between the rotating coordinate system of the suspended plane and the stationary coordinate system; Step 5: Compare the desired levitation flux with the flux obtained by the flux observer to obtain the flux error; Step 6: Calculate the desired voltage through flux linkage error, obtain the desired voltage in the torque plane based on the desired voltage in the floating plane combined with traditional direct torque control, calculate the duty cycle of each phase arm, and control the inverter based on the duty cycle of each phase arm to obtain the inverter switching signal.

2. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 1, characterized in that: Torque plane current in step 1 Floating plane current and zero-sequence current The expression is as follows: （1）； In the formula, (2).

3. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 1, characterized in that: Torque and current components in the synchronous rotating coordinate system in step 2 With suspending current component The currents have the following relationship: （3）； In the formula, Torque plane shaft and The angle between axes Floating plane shaft and The angle between axes; shaft and When the axes coincide, Represented as: （4）； In the formula, for The amplitude of the levitation force generated by the combined action of the electric current and the unit levitation current. for The amplitude of the levitation force generated by the combined action of the electric current and the unit levitation current. The amplitude of the levitation force generated by the combined action of the magnetic field established for the permanent magnet and the unit levitation current.

4. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 1, characterized in that: The expression for the levitation plane armature flux in the synchronously rotating coordinate system in step 3 is as follows: （20）； in, Floating plane shaft and The angle between axes; The expression for the magnetic flux linkage of the levitation plane in a synchronously rotating coordinate system is as follows: （28）； Among them, when the first Air gap circumference angle in phase winding inductance When pointing to the corresponding winding axis, （19）； in, , All are constants; and These represent the self-inductance value without eccentricity and the change in self-inductance caused by eccentricity, respectively. The initial eccentricity distance, This is the initial eccentricity angle.

5. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 1, characterized in that: In step 4, the output of the model compensator in the model compensation repetitive controller is: （46）； in, and They are respectively in direction and Displacement error in direction; low-pass filter in the model compensator Used to suppress high-frequency noise caused by differential action; The control parameters for suppressing synchronous pulsation at the rotational speed under unbalanced magnetic pull are as follows: （47）； In the formula, , For mechanical angles; It is a notch filter; The steady-state error elimination component in the unbalanced magnetic pull is as follows: （49）； In the formula, This is the proportionality coefficient.

6. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 1, characterized in that: Step 5 specifically includes the following steps: Step 5-1: Calculate and obtain the back electromotive force of the suspended plane based on the DC bus voltage information; Step 5-2: Compensate the observation results of the low-pass filter flux linkage observer by the orthogonality between the flux linkage vector and the back electromotive force vector to obtain the levitated flux linkage observed by the flux linkage observer; the levitated flux linkage observed by the low-pass filter flux linkage observer is: （40）； in, The cutoff frequency, This is the adjustment coefficient; and They are floating planes and Shaft back electromotive force; The actual magnetic flux Observed values; and These are the back electromotive force vector of the suspended plane and the magnetic flux linkage vector, respectively. Step 5-3, based on the output of the magnetic flux observer... , The flux linkage error between the desired and actual flux linkage in the shaft is transformed as follows: （41）； in, express The flux linkage error between the expected flux linkage and the observed actual flux linkage in the axis; express The flux error between the expected flux linkage and the observed actual flux linkage in the axis.

7. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 6, characterized in that: The desired voltage of the suspended plane in step 6 is: （32）； In the formula, For stator resistance, To control the cycle.

8. The method for repeated control of levitation flux linkage in a single-winding bearingless flux switching motor according to claim 7, characterized in that: The general solution for the duty cycle of each phase arm in step 6 is: （37）； In the formula, (38).

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