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

Abstract

The invention discloses a suspension flux linkage repetitive control method for a single-winding bearingless flux switching motor. A rotor dynamic eccentric suspension flux linkage model is established according to a magnetic suspension rotor system of the single-winding bearingless flux switching motor; a model compensation repetitive 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 integration element is used for eliminating steady-state errors, the model compensator is used for obtaining inverse system output signals so as to obtain accurate displacement control signals, and the notch filter is used for reducing same-frequency pulsation of rotor radial displacement; an expected suspension flux linkage is obtained through calculation of the model compensation repetitive controller, the expected suspension flux linkage is compared with an actual flux linkage obtained by the flux linkage observer to obtain a flux linkage error, expected voltage is obtained through calculation of the flux linkage error, and therefore an inverter switching signal is obtained. According to the method, the radial displacement pulsation of the rotor under the steady-state working condition and the displacement sudden change phenomenon under the dynamic working condition are effectively treated, and good control is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of bearingless flux switching motors, and in particular to a method for repeatedly controlling the suspended flux of a single-winding bearingless flux switching motor. Background Art

[0002] Magnetic bearing technology has the advantages of no friction, long life, no pollution and controllable bearing characteristics, and is considered to have broad application prospects in the fields of vibration reduction and noise reduction, green energy saving, cleanliness and high speed. In applications such as ships and marine equipment, aerospace and CNC machine tools, the size and efficiency of the motor are very high, which is one of the main technical bottlenecks of integration.

[0003] The coil of the magnetic bearing and the armature winding of the motor are stacked together on the stator. There is no magnetic bearing or mechanical bearing structure, that is, no bearing. Using double windings to achieve magnetic suspension-rotation joint control is an effective solution to shorten the axial length and increase the power density. The bearingless flux switching motor (BFSPMM) has unique magnetic concentration characteristics, a simple and reliable rotor structure, a low risk of permanent magnet temperature rise and demagnetization, and can easily achieve direct modulation of the air gap magnetic field. In the face of the demand for small cabin capacity, low noise, and low vibration platforms, higher requirements are placed on the structural integration of BFSPMM. The single-winding BFSPMM can achieve independent control of motor rotation and suspension by relying on only the torque current component and suspension current component in a set of windings, giving full play to the winding capacity, and is very suitable for the small size and high efficiency requirements of small electric transmission equipment.

[0004] For the single-winding BFSPMM, achieving high-performance suspension control faces the following difficulties: 1) As a double-salient pole structure motor with stator permanent magnet magnetic field modulation, the radial force fluctuation caused by the flux hinge and air gap length change during the stator-rotor tooth slot alternation process also has a great influence on the motor suspension performance; 2) The vibration signal will produce periodic current disturbances in the winding, while the single-winding structure has a small phase inductance and a larger content of high-order harmonics in the winding current, which is more likely 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 there is a strong coupling between the two controlled current components, which further highlights the complex relationship between torque pulsations, suspension force pulsations and rotor radial displacement pulsations.

[0005] For a single-winding BFSPMM, a typical electromechanical coupling system, existing methods are still unable to effectively handle the rotor radial displacement pulsation under steady-state conditions and the displacement mutation phenomenon under dynamic conditions. Therefore, it is necessary to study the control strategy that combines the air gap magnetic field alternation law with the rotor dynamics problem. Summary of the invention

[0006] The object of the present invention is to provide a method for repeatedly controlling the suspended flux of a single-winding bearingless flux switching motor.

[0007] The technical solution adopted by the present invention is:

[0008] A suspension flux repetitive control method for a single-winding bearingless flux switching motor is provided. According to the magnetic suspension rotor system of the single-winding bearingless flux switching motor, a suspension flux model of a rotor with dynamic eccentricity is established. According to the suspension flux model of the rotor with dynamic eccentricity, a model compensation repetitive controller with an integral link, a model compensator and a co-frequency phase shift notch filter is set in the magnetic suspension rotor system. The integral link is used to eliminate steady-state errors, the model compensator is used to obtain an inverse system output signal in order to obtain an accurate displacement control signal, and the notch filter is used to reduce the co-frequency pulsation of the rotor radial displacement.

[0009] The expected suspension flux is calculated by the model compensation repetitive controller, and the expected suspension flux is compared with the actual flux obtained by the flux observer to obtain the flux error. The expected voltage is calculated through the flux error, thereby obtaining the inverter switching signal.

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

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

[0012] Step 1: Decompose the six-phase current of the single-winding bearingless flux switching motor (BFSPMM) into the torque plane current i αT i βT , suspension 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 synchronous rotating coordinate system through the torque equation and the suspension force equation dT i qT and the suspension current component i dS i qS ;

[0014] Step 3, based on the torque current component, respectively transform the suspension plane armature flux and the suspension plane flux in the synchronous rotating coordinate system,

[0015] Step 4, set up a repetitive controller with an integral link, model compensation and notch filter; obtain the desired suspension current through the repetitive controller; calculate the desired suspension flux from the desired suspension current,

[0016] Step 5, comparing the expected suspension flux with the flux obtained by the flux observer to obtain the flux error;

[0017] Step 6, obtain the expected voltage through the flux error calculation, obtain the expected voltage of the torque plane based on the expected voltage of the suspension plane combined with the traditional direct torque control, calculate the duty cycle of each phase bridge arm, and control the inverter based on the duty cycle of each phase bridge arm to obtain the inverter switching signal. The control of the rotating part of the motor can be controlled by traditional direct torque control, which is not the technical solution proposed by the present invention, but only as a way to complete the basic rotation of the motor.

[0018] Furthermore, in step 1, the torque plane current i αT i βT , suspension 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, the torque current component i in the synchronous rotating coordinate system in step 2 is dT i qT and the suspension current component i dS i qS The current in equation (1) has the following relationship:

[0022]

[0023] In the formula, θ re is the angle between the torque plane αT axis and dT axis, θ sus is the angle between the αS axis and the dS axis of the suspension plane.

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

[0025]

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

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

[0028]

[0029] Among them, θ re is the angle between the αT axis and the dT axis of the torque plane;

[0030] The expression of the suspension plane magnetic flux in the synchronously rotating coordinate system is as follows:

[0031]

[0032] Among them, when the air gap circular angle θ in the k-th phase winding inductance points to the corresponding winding axial direction,

[0033]

[0034] Among them, v1 and v2 are constants; LL0 and LL e are the self-inductance value without eccentricity and the change of self-inductance caused by eccentricity respectively;

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

[0036]

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

[0038] The control quantity for suppressing the pulsation of the same frequency in the unbalanced magnetic pull is as follows:

[0039]

[0040] In the formula,

[0041]

[0042] Among them, θ rm is the mechanical angle; H(z) is the notch filter;

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

[0044]

[0045] Where p0 is the proportionality coefficient.

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

[0047] Step 4-1, respectively collecting and acquiring DC bus voltage information, rotor displacement information and angle information of the single-winding bearingless flux switching circuit;

[0048] Step 4-2, calculating and obtaining the comparison expected displacement based on the rotor displacement information;

[0049] Step 4-3, the expected suspension current signal is calculated based on the model-compensated repetitive controller; the expected suspension current based on the model-compensated repetitive controller is:

[0050]

[0051] in, and is the model compensator output; and It is the speed same frequency pulsation suppression control quantity; and Eliminate the component for steady-state error;

[0052] Step 4-4, when using i dT = 0 control strategy, the expected magnetic flux in the suspension magnetic flux control is calculated as:

[0053]

[0054] Among them, Δx and Δy are the displacement distances of the rotor in the x direction and y direction respectively; LL0 and LL e are the self-inductance without eccentricity and the change of self-inductance caused by eccentricity respectively; is the angle between the rotating coordinate system of the suspension plane and the stationary coordinate system;

[0055] Step 4-5, compare the expected suspension flux with the actual flux obtained by the flux observer to obtain the flux error, calculate the expected voltage through the flux error, and thus obtain the inverter switching signal.

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

[0057] Step 5-1, calculating and obtaining the back electromotive force of the suspension plane based on the DC bus voltage information;

[0058] Step 5-2, the observation result of the low-pass filter flux observer is compensated by the orthogonality of the flux vector and the back electromotive force vector to obtain the suspension flux observed by the link observer; the suspension flux observed by the low-pass filter flux observer is:

[0059]

[0060] Among them, ω c is the cut-off frequency, γ is the adjustment coefficient; e αS and eβS are the back EMFs of the αS and βS axes of the suspension plane, respectively; and and is the observed actual magnetic flux ψ αS , βS ; That is e S and They are the suspension plane back electromotive force vector and the suspension flux vector respectively.

[0061] Step 5-3, specifically, the flux error between the expected flux and the actual flux in the aS and βS axes is calculated based on the suspension flux signal:

[0062]

[0063] Among them, Δψ αS represents the flux error between the expected flux and the actual flux in the αS axis; Δψ αS It represents the flux error between the expected flux and the actual flux in the βS axis;

[0064] According to the output of the flux observer, the flux error is rewritten as:

[0065]

[0066] in, It represents the flux error between the expected flux in the αS axis and the observed actual flux; It represents the flux error between the expected flux in the βS axis and the observed actual flux.

[0067] Furthermore, the expected voltage of the suspension plane in step 6 is:

[0068]

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

[0070] Furthermore, the duty cycle of each phase bridge arm in step 6 is generally solved as follows:

[0071]

[0072] In the formula,

[0073] Therefore, when D A When the duty cycle of D0 is expressed in a control cycle, D A = 0, we can solve for D B -D F The duty cycle of the six-phase inverter that meets the control requirements can be obtained by only limiting the duty cycle.

[0074] The present invention adopts the above technical scheme, and sets a model compensation repetitive controller with an integral link, a model compensator and a same-frequency phase-shift notch filter in a magnetic suspension rotor system; the integral link is used to eliminate steady-state errors, the model compensator is used to obtain the inverse system output signal so as to obtain an accurate displacement control signal, and the notch filter is used to reduce the same-frequency pulsation of the radial displacement of the rotor; further, voltage information is collected by a voltage sensor to calculate and obtain the generated electromotive force of the suspension plane, and at the same time, the observed flux signal is obtained according to the observer, the displacement sensor collects the displacement information to calculate and obtain the expected displacement for comparison, and at the same time, the expected suspension flux is calculated by the model compensation repetitive controller, and the expected suspension flux is compared with the actual flux obtained by the flux observer to obtain the flux error, and the expected voltage is calculated by the flux error, and the encoder collects angle information to obtain the expected voltage of the torque plane based on traditional direct torque control; the expected voltage is combined with the expected voltage of the torque plane to calculate the duty cycle of each phase bridge arm, and the inverter switching signal is obtained based on the duty cycle of each phase bridge arm.

[0075] The present invention effectively handles the radial displacement pulsation of the rotor under steady-state conditions and the displacement mutation phenomenon under dynamic conditions, thereby achieving good control. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0077] Figure 1 A schematic diagram of the topological structure of a single-winding bearingless flux switching motor according to the present invention;

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

[0079] Figure 3 Schematic diagram of the principle structure of the flux observer of the present invention;

[0080] Figure 4 It is a schematic diagram of the principle structure of the model compensation repetitive controller of the present invention. DETAILED DESCRIPTION

[0081] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0082] like Figures 1 to 4As shown in one, the present invention discloses a method for repeatedly controlling the suspended flux of a single-winding bearingless flux switching motor. According to the magnetic suspension rotor system of the single-winding bearingless flux switching motor, a suspended flux model of a rotor with dynamic eccentricity is established; according to the suspended flux model of the rotor with dynamic eccentricity, a model compensation repeated controller with an integral link, a model compensator and a same-frequency phase-shift notch filter is arranged in the magnetic suspension rotor system; the integral link is used to eliminate steady-state errors, the model compensator is used to obtain an inverse system output signal so as to obtain an accurate displacement control signal, and the notch filter is used to reduce the same-frequency pulsation of the rotor radial displacement;

[0083] The expected suspension flux is calculated by the model compensation repetitive controller, and the expected suspension flux is compared with the actual flux obtained by the flux observer to obtain the flux error. The expected voltage is calculated through the flux error, thereby obtaining the inverter switching signal.

[0084] Specifically, the encoder collects angle information to obtain the expected voltage of the torque plane based on the traditional direct torque control; the expected voltage is combined with the expected voltage of the torque plane obtained based on the traditional direct torque control to jointly calculate the duty cycle of each phase bridge arm, and the inverter switching signal is obtained based on the duty cycle of each phase bridge arm. 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 the torque plane current i αT i βT , suspension 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 synchronous rotating coordinate system through the torque equation and the suspension force equation dT i qT and the suspension current component i dS i qS ;

[0087] Step 3, based on the torque current component, respectively transform the suspension plane armature flux and the suspension plane flux in the synchronous rotating coordinate system,

[0088] Step 4, set up a repetitive controller with an integral link, model compensation and notch filter; obtain the desired suspension current through the repetitive controller; calculate the desired suspension flux from the desired suspension current,

[0089] Step 5, comparing the expected suspension flux with the flux obtained by the flux observer to obtain the flux error;

[0090] Step 6, obtain the expected voltage through the flux error calculation, obtain the expected voltage of the torque plane based on the expected voltage of the suspension plane combined with the traditional direct torque control, calculate the duty cycle of each phase bridge arm, and control the inverter based on the duty cycle of each phase bridge arm to obtain the inverter switching signal. The control of the rotating part of the motor can be controlled by traditional direct torque control, which is not the technical solution proposed by the present invention, but only as a way to complete the basic rotation of the motor.

[0091] The specific principle of the present invention is described 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 in order to facilitate the adjustment of the air gap magnetic field, the thickness of the permanent magnet is reduced. The permanent magnet is embedded between the U-shaped iron core in the form of alternating magnetization, and 12 coils form a six-phase winding. Each phase winding is composed of coils connected in series perpendicular to each other in space. For example, the A phase winding is composed of coils A1 and A2 connected in series, and each phase winding is 60 degrees apart. rm is the mechanical angle, the electrical angle θ re =10θ rm .

[0093] The single-winding BFSPMM rotor has no mechanical bearing to fix it. When the motor is running, the rotor is always in a dynamic eccentric state. Figure 2 As shown. Define the x direction to be directly opposite to coil A1 and the y direction to be directly opposite to coil A2. The inner diameter of the motor stator is s ro , the rotor outer diameter is r ro , the air gap length when the rotor is not eccentric is g o When the rotor is statically eccentric, the rotor geometric center shifts from the motor mechanical center point O to point P. The initial eccentric distance is e and the initial eccentric angle is When the motor rotates, the rotor produces synchronous precession, and the rotor geometric center shifts from point P to point Q, with a deflection angle of ω rm t,ω rm is the mechanical angular frequency.

[0094] Figure 2 The center line of the vertical series coil in the middle space is the corresponding winding axis. The same-direction bias magnetic field generated on the spatially symmetrical winding axis can break the air gap magnetic field balance in that direction, thereby generating a suspension force. The single-winding BFSPMM takes advantage of the multi-degree-of-freedom advantage of the multi-phase motor. The torque current component i is passed into the k-th phase winding. kT and the suspension current component i kS , k = AF. In order to maximize the motor control performance, the torque current components in the spatially symmetrical windings are opposite and the suspension current components are in the same direction, that is, 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 star-connected, and the six-phase current can be decomposed into the torque plane current i through the T6 transformation matrix. αT i βT , suspension plane current i αS i βS and zero sequence current i o1 i o2 :

[0095]

[0096] in,

[0097] By realizing the decoupling of the αTβT plane and αSβS plane control functions, the single-winding bearingless motor can rotate and suspend stably.

[0098] Operation principle: At present, the operation control of single-winding BFSPMM is mainly based on vector control. The speed regulator (ASR) and displacement regulator (ADR) output the desired torque and the desired suspension force respectively, and calculate the torque current component i in the synchronous rotating coordinate system through the torque equation and the suspension force equation. dT 、i qT and the suspension current component i ds 、i qS Δx and Δy are the displacement distances of the rotor in the x-direction and y-direction 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 dT axis. sus is the angle between the αS axis and the dS axis of the suspension plane.

[0101] When the αT axis and the αS axis coincide, θ sus It can be expressed as:

[0102]

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

[0104] When using i dT = 0 control strategy, the electromagnetic torque T required for the single-winding BFSPMM to operate stably e and controllable suspension force F cx F cy The linear relationship between and the corresponding control current can be expressed as:

[0105]

[0106] In the formula, k t is the torque current coefficient, k sx and k sy are the suspension current stiffness coefficients in the x-direction and y-direction,

[0107]

[0108] The motor suspension operation performance depends on the design of the ADR and the accuracy of the suspension force equation. If the suspension force equation is removed and the air gap magnetic field balance is directly controlled in the ADR, the internal disturbance caused by the inaccurate model can be effectively reduced, and the ADR can be conveniently optimized to improve the ability to suppress external disturbances. The following will explain in detail how to achieve suspension flux control.

[0109] (1) Air gap flux density of the suspended flux linkage model with dynamic rotor eccentricity: Figure 2 As shown in the figure, the air gap length changes dynamically when the rotor is eccentric, which can be expressed as:

[0110]

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

[0112]

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

[0114] According to the Maclaurin expansion and ignoring the higher-order terms above the second order, equation (8) can be simplified to:

[0115]

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

[0117]

[0118] Where μ0 is the magnetic permeability of air, F m M is the air gap magnetomotive force. sr is the magnetic field modulation function, which is the stator modulation function M s , rotor modulation function M r The product of s and M r They are calculated by Fourier series from the stator and rotor slot distributions respectively.

[0119] (2) Armature flux: According to formula (10), the mutual inductance between the i-th phase winding and the j-th phase winding when the rotor is not eccentric can be deduced as:

[0120]

[0121] In the formula, r sro is the air gap radius, l stk is the core axis length, W i and W j The winding functions of the i-phase winding and the j-phase winding are respectively. The winding function of the k-th phase winding is W k is the conductor distribution function C k Through the stator modulation function M s The result after modulation, namely W k =M s ·C k Since each phase winding of the single-winding BFSPMM is composed of two coils symmetrically connected in series along the spatial axis, C k The k1 coil conductor distribution function C k1 and k2 coil conductor distribution function C k2 Composition, namely C k =C k1 +C k2 . The conductor distribution function C of the k1 coil of the kth phase winding k1 The Fourier series expansion of can be written as:

[0122]

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

[0124] The k2 coil is 90° ahead of the k1 coil in space, so the k2 coil conductor distribution function C k2 It is expressed as:

[0125]

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

[0127]

[0128] Where LM0 and LM e They are the mutual inductance without eccentricity and the change of mutual inductance caused by eccentricity when the pulsation of inductance with rotor position is ignored respectively;

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

[0130]

[0131] Where LL0 and LL e They are the unbiased self-inductance value and the change in self-inductance caused by eccentricity, respectively.

[0132] Through the T6 transformation matrix, the armature flux in the torque plane, suspension plane and zero-sequence plane can be obtained as:

[0133]

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

[0135]

[0136] In the formula, when the air gap circular angle θ in the k-phase winding inductance points to the corresponding winding axial direction,

[0137]

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

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

[0140]

[0141] (3) Permanent magnet flux: According to formula (10), it can be deduced that the permanent magnet flux of the i-th phase winding when the rotor is not eccentric is expressed as:

[0142]

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

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

[0145] Where n p_pm =6 is the number of permanent magnet poles, F m is the magnetomotive force amplitude, a m are Fourier series coefficients.

[0146] Substituting equations (12)-(13) into equation (21), combined with equation (9), the permanent magnet flux of the i-th phase winding of the single-winding BFSPMM can be obtained as:

[0147]

[0148] In the formula, ψ fe is the change in permanent magnet flux amplitude caused by eccentricity.

[0149] When the air gap circular angle θ in the i-phase winding inductance points to the corresponding winding axial direction, the permanent magnet flux linkage of the suspension plane can be obtained through the T6 transformation matrix:

[0150]

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

[0152]

[0153] In the formula,

[0154]

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

[0156]

[0157] Therefore, in the flux, the torque current component and the suspension flux caused by the permanent magnet magnetomotive force are linearly related to the radial displacement of the rotor, and the suspension current component can regulate the suspension flux, thereby constructing a suspension flux control, as shown below.

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

[0159] (1) Suspension flux control: According to formula (28), when When , the desired suspension plane flux can be expressed as:

[0160]

[0161] Among them, the air gap magnetic field is used to adjust the controllable suspension force. and Available from ADR,

[0162]

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

[0164]

[0165] The expected voltage of the floating plane is:

[0166]

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

[0168] The motor suspension can be realized by obtaining the inverter switching signal according to the expected voltage vector. The phase voltage control equation is:

[0169]

[0170] Where U DC is the DC bus voltage, u NO is the center point voltage, the upper bridge arm of phase k is open and the lower bridge arm is closed, then S k =1, otherwise S k =0.

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

[0172]

[0173] in,

[0174]

[0175] In order to keep the switching frequency constant, the switching device of each phase bridge arm is switched only once in one control cycle. For a six-phase inverter, there are at most five effective voltage vectors in one control cycle, defined as V a (a=1-5). a The action time is set to τ a In addition, the action time of the zero voltage vector V0 is t0. The expected equivalent voltage vector It is composed of 5 effective voltage vectors. According to the "volt-second" balance principle, The relationship with duty cycle can be written as:

[0176]

[0177] In the formula, S ia τ a The 6×1 matrix D represents the product of the switching state of the 6-phase inverter and its action time. i The 6×1 matrix representing the duty cycle of the i-th phase bridge arm, i=AF,

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

[0179]

[0180] In the formula,

[0181]

[0182] Therefore, when D A When the duty cycle of V0 is expressed in a control cycle, D A = 0, we can solve for D B -D F The duty cycle of the six-phase inverter that meets the control requirements can be obtained by only limiting the duty cycle.

[0183] (2) Flux observer: In formula (31), the actual flux ψ is accurately obtained. αS , βS In the traditional flux observation method, the direct integration method has the problems of DC bias and integration drift. The low-pass filter flux observer can effectively filter the DC component, but the amplitude and phase of the observed flux will change with the different cutoff frequencies of the observer, which is not suitable for high-speed working conditions. The present invention considers the orthogonality of the flux vector and the back electromotive force vector to compensate the observation result. Figure 3 As is known to all, the magnetic flux angle and back EMF angle The angle between them should always be 90°, that is, Control is zero. Its expression is:

[0184]

[0185] Among them, e S and are the suspension plane back electromotive force vector and suspension flux vector, e αS 、e βSis the back electromotive force of the αS and βS axes of the suspension plane, and the superscript “^” indicates the observed value. According to the low-pass filter flux observer, the suspension flux in equation (39) can be obtained as:

[0186]

[0187] Among them, ω c is the cut-off frequency, and γ is the adjustment coefficient, which can be obtained by the angle adjuster (AAR) according to formula (39). αS and e βS are the back EMFs of the αS and βS axes of the suspension plane, respectively; and is the observed actual magnetic flux ψ αS , βS ; That is e S and are the back electromotive force vector of the suspension plane and the suspension flux vector respectively. s is the differential of the complex domain expression of the transfer function.

[0188] Therefore, according to the output of the flux observer, equation (31) is rewritten as:

[0189]

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

[0191]

[0192] In the formula, l m and l s are the rotor mass center length and shaft length, l g is the length of the center of gravity, m a and g a are the rotor mass and gravitational acceleration, J xy is the rotor equatorial moment of inertia. mpx and F mpy are the unbalanced magnetic pulls in the x and y directions, respectively, ux and f uy Unmodeled dynamics in the x and y directions, respectively.

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

[0194]

[0195] Substituting equation (9) into equation (43), it can be deduced that the unbalanced magnetic pull of the single-winding BFSPMM rotor when it is dynamically eccentric is:

[0196]

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

[0198] According to formula (44), the rotor radial displacement contains the same-frequency pulsation signal of the speed. If the inverse characteristics of the phase-frequency characteristics of the controlled object can be obtained, phase compensation and amplitude compensation can be provided to the ADR to a certain extent. Since the actual system model cannot be very accurate and the model parameters cannot be fixed, the present invention constructs an ADR based on the repetitive control principle to reduce the same-frequency pulsation of the speed with unmodeled dynamics. Model-compensated repetitive controller, such as Figure 4 shown.

[0199] exist Figure 4 In the figure, the first part is a repetitive signal generator, which is an integration link with the signal fundamental wave period as the step length. In order to improve the stability, a low-pass filter Q(z) is set to weaken the integration effect:

[0200] The second part is the model compensator, which derives the suspension current i according to equation (42): ds 、i qS The inverse function between the radial displacement of the rotor and the repetitive signal generator is:

[0201]

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

[0203] In order to reduce the same frequency pulsation of the speed, the Least Mean Square (LMS) notch filter H(z) is used to enhance ω rm The control signal strength of the frequency band. Since the displacement is very small, the square term of the displacement in equation (44) is ignored, and the control quantity of the speed same-frequency pulsation suppression control in the unbalanced magnetic pull is obtained by combining equation (5) as follows:

[0204]

[0205] In the formula,

[0206]

[0207] Since the above control link does not include an integral link, there is still a steady-state error caused by the DC component of the unbalanced magnetic pull caused by factors such as rotor gravity and mass imbalance. Eliminate steady-state errors:

[0208]

[0209] Where p0 is the proportionality coefficient.

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

[0211]

[0212] When using i dT =0 control strategy, the expected flux in the suspension flux control proposed by the present invention is:

[0213]

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

[0215] The present invention adopts the above technical scheme, and sets a model compensation repetitive controller with an integral link, a model compensator and a same-frequency phase-shift notch filter in a magnetic suspension rotor system; the integral link is used to eliminate steady-state errors, the model compensator is used to obtain the inverse system output signal so as to obtain an accurate displacement control signal, and the notch filter is used to reduce the same-frequency pulsation of the radial displacement of the rotor; further, voltage information is collected by a voltage sensor to calculate and obtain the generated electromotive force of the suspension plane, and at the same time, the observed flux signal is obtained according to the observer, the displacement sensor collects the displacement information to calculate and obtain the expected displacement for comparison, and at the same time, the model compensation repetitive controller is used to calculate and obtain the expected suspension flux, and the expected suspension flux is compared with the actual flux obtained by the flux observer to obtain the flux error, and the expected voltage is calculated by the flux error, and the encoder collects angle information to obtain the expected voltage of the torque plane based on traditional direct torque control; the expected voltage is combined with the expected voltage of the torque plane to calculate the duty cycle of each phase bridge arm, and the inverter switching signal is obtained based on the duty cycle of each phase bridge arm.

[0216] The present invention effectively handles the radial displacement pulsation of the rotor under steady-state conditions and the displacement mutation phenomenon under dynamic conditions, thereby achieving good control.

[0217] Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. In the absence of conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians of the art without making creative work are within the scope of protection of the present application.

Claims

1. A method for repeatedly controlling the suspended flux of a single-winding bearingless flux switching motor, characterized in that: According to the magnetic suspension rotor system of the single-winding bearingless flux switching motor, a suspension flux model of the rotor dynamic eccentricity is established; according to the suspension flux model of the rotor dynamic eccentricity, a model compensation repetitive controller with an integral link, a model compensator and a same-frequency phase-shift notch filter is set in the magnetic suspension rotor system; the integral link is used to eliminate steady-state errors, the model compensator is used to obtain the inverse system output signal 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 expected suspension flux is calculated by the model compensation repetitive controller, and the expected suspension flux is compared with the actual flux obtained by the flux observer to obtain the flux error. The expected voltage is calculated through the flux error, thereby obtaining the inverter switching signal.

2. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 1, characterized in that: The control method specifically includes the following steps: Step 1: Decompose the six-phase current of the single-winding bearingless flux switching motor (BFSPMM) into the torque plane current i αT i βT , suspension plane current i αS i βS and zero sequence current i o1 i o2 ; Step 2: Calculate the torque current component i in the synchronous rotating coordinate system through the torque equation and the suspension force equation dT i qT and the suspension current component i dS i qS ; Step 3, based on the torque current component, respectively transform the suspension plane armature flux and the suspension plane flux in the synchronous rotating coordinate system, Step 4, set up a repetitive controller with an integral link, model compensation and notch filter; obtain the desired suspension current through the repetitive controller; calculate the desired suspension flux from the desired suspension current, Step 5, comparing the expected suspension flux with the flux obtained by the flux observer to obtain the flux error; Step 6, obtain the expected voltage through the flux error calculation, obtain the expected voltage of the torque plane based on the expected voltage of the suspension plane combined with traditional direct torque control, calculate the duty cycle of each phase bridge arm, control the inverter based on the duty cycle of each phase bridge arm, and obtain the inverter switching signal.

3. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2, characterized in that: Torque plane current i in step 1 αT i βT , suspension plane current i αS i βS and zero sequence current i o1 i o2 The expression is as follows: In the formula, 4. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2, characterized in that: The torque current component i in the synchronous rotating coordinate system in step 2 dT i qT and the suspension current component i dS i qS The current has the following relationship: In the formula, θ re is the angle between the torque plane αT axis and dT axis, θ sus is the angle between the αS axis and the dS axis of the suspension plane; That is, when the αT axis coincides with the αS axis, θ sus It is expressed as: In the formula, k d for i qT The amplitude of the suspension force generated by the interaction of the current and the unit suspension current, k q for i qT The amplitude of the suspension force generated by the interaction of the current and the unit suspension current, k PM The amplitude of the suspension force generated by the magnetic field established by the permanent magnet and the unit suspension current.

5. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2, characterized in that: The expression of the armature flux of the suspended plane in the synchronous rotating coordinate system in step 3 is as follows: Among them, θ re is the angle between the αT axis and the dT axis of the torque plane; The expression of the suspension plane magnetic flux in the synchronously rotating coordinate system is as follows: Among them, when the air gap circular angle θ in the k-th phase winding inductance points to the corresponding winding axial direction, Among them, v1 and v2 are constants; LL0 and LL e are the self-inductance without eccentricity and the change of self-inductance caused by eccentricity; e is the initial eccentricity distance, is the initial eccentricity angle.

6. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2, characterized in that: Step 4 specifically includes the following steps: Step 4-1, respectively collecting and acquiring DC bus voltage information, rotor displacement information and angle information of the single-winding bearingless flux switching circuit; Step 4-2, calculating and obtaining the comparison expected displacement based on the rotor displacement information; Step 4-3, the expected suspension current signal is calculated based on the model-compensated repetitive controller; the expected suspension current based on the model-compensated repetitive controller is: in, and is the model compensator output; and It is the speed same frequency pulsation suppression control quantity; and Eliminate the component for steady-state error; Step 4-4, when using i dT = 0 control strategy, the expected magnetic flux in the suspension magnetic flux control is calculated as: Among them, Δx and Δy are the displacement distances of the rotor in the x direction and y direction respectively; LL0 and LL e are the self-inductance without eccentricity and the change of self-inductance caused by eccentricity; e is the initial eccentricity distance, is the angle between the rotating coordinate system of the suspension plane and the stationary coordinate system; step 4-5, compare the expected suspension flux with the actual flux obtained by the flux observer to obtain the flux error, and calculate the expected voltage through the flux error, thereby obtaining the inverter switching signal.

7. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2 or 6, characterized in that: The output of the model compensator in the model compensation repetitive controller in step 4 is: Among them, Δe x and Δe y are the displacement errors in the x-direction and y-direction respectively; the low-pass filter Q(z) in the model compensator is used to suppress the high-frequency noise caused by the differential action; The control quantity for suppressing the pulsation of the same frequency in the unbalanced magnetic pull is as follows: In the formula, θ rm is the mechanical angle; H(z) is the notch filter; The steady-state error elimination component in the unbalanced magnetic pull is as follows: Where p0 is the proportionality coefficient.

8. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2, characterized in that: Step 5 specifically includes the following steps: Step 5-1, calculating and obtaining the back electromotive force of the suspension plane based on the DC bus voltage information; Step 5-2, the observation result of the low-pass filter flux observer is compensated by the orthogonality of the flux vector and the back electromotive force vector to obtain the suspension flux observed by the link observer; the suspension flux observed by the low-pass filter flux observer is: Among them, ω c is the cut-off frequency, γ is the adjustment coefficient; e αS and e βS are the back EMFs of the αS and βS axes of the suspension plane, respectively; and and is the observed actual magnetic flux ψ αS , βS ; That is e S and are the suspension plane back electromotive force vector and the suspension flux vector respectively; Step 5-3, according to the output of the flux observer, the flux error between the expected flux and the actual flux in the αS and βS axes is transformed into: in, It represents the flux error between the expected flux in the αS axis and the observed actual flux; It represents the flux error between the expected flux in the βS axis and the observed actual flux.

9. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 2, characterized in that: The expected voltage of the floating plane in step 6 is: In the formula, R s is the stator resistance, T K To control the cycle.

10. The method for repeatedly controlling the suspended flux linkage of a single-winding bearingless flux switching motor according to claim 9, characterized in that: The general solution of the duty cycle of each phase bridge arm in step 6 is: In the formula,

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