Bearingless permanent magnet motor prediction voltage control method based on flux linkage coupling

Abstract

The invention relates to a bearingless permanent magnet motor predictive voltage control method based on flux linkage coupling, which considers coupling influence and eccentric displacement factors, adopts model predictive voltage control, and respectively establishes a suspension force / torque predictive control system based on voltage prediction. Firstly, the current value of a suspension / torque winding at the next moment is predicted based on a coupling flux linkage equation and a motor voltage equation, and then the flux linkage value of the suspension / torque winding at the next moment and the torque value at the next moment are predicted. Next, a torque winding air gap flux linkage value at the next moment and a radial suspension force value at the next moment are predicted in sequence; and finally, calculating to obtain a suspension winding voltage vector which enables the value function value of the suspension system to be minimum and a torque winding voltage vector which enables the value function value of the torque system to be minimum, and respectively outputting the suspension winding voltage vector and the torque winding voltage vector to an inverter of the suspension / torque system to complete control of suspension and torque. Compared with the prior art, the coupling influence and the eccentric displacement are considered, the flux linkage prediction model is improved, and the system control precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of bearingless motor control, and in particular to a predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling. Background Art

[0002] Compared with traditional bearingless motors, bearingless permanent magnet synchronous motors have a simpler structure, higher operating efficiency and larger power density, and are applied in fields such as life science, chemical industry, and semiconductor industry. With the further development of the economy, in many special electrical drive fields, the traditional drive and transmission methods will surely be changed, which will play an important role in improving product quality, reducing costs, and reducing pollution. Therefore, actively carrying out the research and application of bearingless permanent magnet synchronous motors has practical and profound significance. However, the multi-variable, non-linear, and strong coupling characteristics of bearingless motors themselves make the analysis and calculation of the motor magnetic levitation force relatively complex, seriously restricting the application and development of permanent magnet type bearingless motors.

[0003] The literature of Chinese patent application CN110995096A discloses a suspension force prediction control system for a bearingless coreless permanent magnet motor, which synthesizes the air-gap flux linkage by using the initially observed flux linkage of the suspension force winding and the torque winding, and calculates the magnitude of the motor radial suspension force corresponding to each switching state in the next sampling period through a prediction algorithm. The literature with Chinese patent publication number CN115001329A constructs a model predictor for a bearingless permanent magnet thin-film motor, establishes a suspension force prediction controller, directly controls it, and adds a control period as a delay compensation. In the above patents, when establishing the suspension prediction model and the torque prediction model, the influence of coupling factors and eccentric displacement is not considered, which will lead to inaccurate prediction models, resulting in problems such as a decrease in the steady-state accuracy of the suspension system and a slowdown in the dynamic response speed, making the anti-interference ability of the system weak.

[0004] In summary, it has high practical significance to propose a predictive voltage control method for a bearingless permanent magnet motor that considers the coupling factors of suspension and torque and the influence of eccentric displacement on the model. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling, taking into account the coupling influence and eccentric displacement, improving the flux linkage prediction model, and improving the system control accuracy.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling, the method includes:

[0008] Obtain the suspension force given value and the torque given value according to the displacement difference between the actual displacement value and the preset displacement value of the motor at the current moment and the speed difference between the actual speed value and the preset speed value of the motor, and calculate and obtain the flux linkage given value of the suspension winding in combination with the preset flux linkage given value of the torque winding air gap;

[0009] Using the actual displacement value, actual speed value, voltage values and current values of the suspension winding and the torque winding of the motor at the current moment, based on the coupled flux linkage equation and the motor voltage equation, predict the current prediction values and flux linkage prediction values of the torque winding and the suspension winding at the next moment, and the coupled flux linkage equation considers the eccentric displacement and the flux linkage interaction between the suspension winding and the torque winding;

[0010] Using the predicted flux linkage value of the torque winding at the next moment, predict the predicted value of the air gap flux linkage of the suspension winding at the next moment, and combine the predicted current value of the suspension winding to predict the predicted value of the suspension force at the next moment; use the predicted current values of the suspension winding and the torque winding at the next moment to predict the predicted value of the torque at the next moment;

[0011] Using the predicted suspension force value and torque value, obtain the suspension reference voltage vector for controlling the radial suspension force generated by the suspension winding and the torque reference voltage vector for controlling the electromagnetic torque generated by the torque winding through the direct voltage vector selection strategy, and complete the control of the bearingless permanent magnet motor;

[0012] Wherein, the current moment is the k moment, and the next moment is the k + 2 moment after one-beat delay compensation processing.

[0013] Further, after obtaining the voltage value and current value of the suspension winding and the voltage value and current value of the torque winding, convert the voltage value and current value of the suspension winding and the voltage value and current value of the torque winding into the voltage value and current value of the suspension winding and the voltage value and current value of the torque winding in the d-q coordinate system through Clark transformation.

[0014] Further, obtain the suspension force given value by processing the displacement difference between the actual displacement value and the given displacement value through a PID controller, and obtain the torque given value by processing the speed difference between the actual speed value and the given speed value through a PI controller.

[0015] Further, the coupled flux linkage equation is:

[0016]

[0017] Wherein, ψ 1d is the d-axis flux linkage of the torque winding, ψ 1q is the q-axis flux linkage of the torque winding, ψ 2d is the d-axis flux linkage of the suspension winding, ψ 2qis the q-axis magnetic flux of the levitation winding, L1 is the self-inductance of the torque winding, L2 is the self-inductance of the levitation winding, M′ is the mutual inductance coefficient between the levitation winding and the torque winding, i 1d is the d-axis current of the torque winding, i 1q is the q-axis current of the torque winding, i 2d is the d-axis current of the levitation winding, i 2q is the q-axis current of the levitation winding, i f is the equivalent excitation current of the rotor permanent magnet, x is the actual displacement value of the x-axis of the bearingless permanent magnet motor, y is the actual displacement value of the y-axis of the bearingless permanent magnet motor,

[0018]

[0019]

[0020]

[0021] where μ0 is the vacuum permeability, l is the axial length of the motor, r is the rotor radius, N1 is the number of turns of the torque winding, N2 is the number of turns of the levitation winding, and δ0 is the nominal air-gap length;

[0022] The voltage equation of the motor is:

[0023]

[0024] where, u 1d is the d-axis voltage of the torque winding, u 1q is the q-axis voltage of the torque winding, u 2d is the d-axis voltage of the levitation winding, u 2q is the q-axis voltage of the levitation winding, R1 is the resistance of the torque winding, R2 is the resistance of the levitation winding, and ω is the rotational speed of the motor.

[0025] Furthermore, the process of predicting the current prediction values and magnetic flux prediction values of the torque winding and the levitation winding at the next moment includes:

[0026] Substitute the coupled magnetic flux equation into the discretized motor voltage equation, and obtain the current prediction expression and magnetic flux prediction expression through calculation;

[0027] Based on the actual displacement value, actual rotational speed value, voltage value and current value of the levitation winding, and voltage value and current value of the torque winding of the bearingless permanent magnet motor at the current moment, respectively use the current prediction expression and magnetic flux prediction expression to obtain the current prediction values and magnetic flux prediction values of the torque winding and the levitation winding at the next moment.

[0028] Further, the calculation expression of the given value of the magnetic flux of the levitation winding is:

[0029]

[0030] Among them, F x * is the x - direction component of the suspension force given value, F y * is the y - direction component of the suspension force given value, k M is the magnetic coupling coefficient, ψ 1m * is the given value of the combined air - gap magnetic flux of the torque winding.

[0031] Furthermore, the process of the direct voltage vector selection strategy includes:

[0032] Using the suspension force given value, the predicted value of the suspension force at the next moment, and the given value of the suspension winding magnetic flux, obtain the suspension winding voltage vector, and the suspension winding voltage vector is the suspension reference voltage vector that minimizes the value of the suspension system cost function;

[0033] Using the torque given value, the predicted value of the torque, the preset given value of the stator magnetic flux of the torque winding, the predicted value of the suspension winding magnetic flux, the given value of the torque winding magnetic flux, and the given value of the suspension winding magnetic flux, obtain the torque winding voltage vector, and the torque winding voltage vector is the torque reference voltage vector that minimizes the value of the torque system cost function;

[0034] Using the suspension winding voltage vector to control the suspension winding to generate a radial suspension force to maintain the stable suspension of the rotor of the bearingless permanent - magnet motor, and using the torque winding voltage vector to control the torque winding to generate an electromagnetic torque to drive the rotation of the rotor of the bearingless permanent - magnet motor, thus completing the control of the bearingless permanent - magnet motor.

[0035] Even further, the prediction process of the predicted value of the suspension force at the next moment includes:

[0036] Obtain the leakage inductance of the torque winding, and use the predicted value of the magnetic flux of the torque winding and the leakage inductance to obtain the predicted value of the air - gap magnetic flux of the suspension winding;

[0037] Using the predicted value of the air - gap magnetic flux of the suspension winding and the predicted value of the current, based on the suspension force mathematical model, obtain the predicted value of the suspension force at the next moment;

[0038] Among them, the expression for obtaining the predicted value of the air - gap magnetic flux is:

[0039]

[0040] Among them, ψ 1md (k + 2) is the d - axis component of the air - gap magnetic flux of the torque winding at the (k + 2) moment, ψ 1mq (k + 2) is the q - axis component of the air - gap magnetic flux of the torque winding at the (k + 2) moment, L 1δd is the d - axis leakage inductance of the torque winding, L1δq is the q-axis leakage inductance of the torque winding, k 1d (k + 2) is the predicted value of the d-axis current of the torque winding at time (k + 2), i 1q (k + 2) is the predicted value of the q-axis current of the torque winding at time (k + 2);

[0041] The expression of the suspension force mathematical model is:

[0042]

[0043] F x is the x-axis component of the radial suspension force on the rotor, F y is the y-axis component of the radial suspension force on the rotor, k M is the magnetic coupling coefficient, k L is the leakage magnetic influence coefficient, k ecc is the eccentricity stiffness coefficient, i 2d is the d-axis component of the suspension winding current, i 2q is the q-axis component of the suspension winding current, x is the actual displacement value of the rotor in the x-axis direction, and y is the actual displacement value of the rotor in the y-axis direction;

[0044]

[0045]

[0046]

[0047] Among them, p1 is the number of pole pairs of the torque winding, p2 is the number of pole pairs of the suspension winding, ψ 1d is the d-axis component of the stator magnetic flux linkage of the torque winding, ψ 1m is the resultant air-gap magnetic flux linkage of the torque winding, ψ ds is the stator magnetic flux linkage of the suspension winding, L m2 is the mutual inductance of the suspension winding, l is the axial length of the motor, r is the radius of the rotor, N1 is the number of turns of the torque winding, N2 is the number of turns of the suspension winding, δ0 is the nominal air-gap length, μ0 is the permeability of free space, m p is the number of phases of the motor.

[0048] Furthermore, the torque prediction model is:

[0049] T e (k + 2) = A k+2 ·ψ 1d (k + 2) + B k+2 ·ψ 1q (k + 2) + C k+2 ·ψ 2d (k + 2)

[0050] + D k+2 ·ψ2q (k + 2)

[0051] Among them, T e (k + 2) is the torque at time (k + 2), ψ 1d (k + 2) is the d-axis magnetic flux linkage of the torque winding at time (k + 2), ψ 1q is the q-axis magnetic flux linkage of the torque winding at time (k + 2), ψ 2d (k + 2) is the d-axis magnetic flux linkage of the suspension winding at time (k + 2), ψ 2q is the q-axis magnetic flux linkage of the suspension winding at time (k + 2), A k+2 、B k+2 、C k+2 and D k+2 are the predicted parameters derived at time k + 2.

[0052] Furthermore, the process of obtaining the voltage vector of the suspension winding includes:

[0053] Using the given value of the suspension force, the predicted value of the suspension force at the next moment, and the given value of the magnetic flux linkage of the suspension winding, obtain the reference voltage vector of the suspension in the d-q coordinate system;

[0054] Convert the reference voltage vector of the suspension in the d-q coordinate system into polar coordinate form, and determine the sector where the reference voltage vector of the suspension is located according to its angle, and select the reference voltage vector of the suspension that minimizes the value of the suspension system cost function as the voltage vector of the suspension winding;

[0055] The expression of the suspension system cost function is:

[0056]

[0057] Among them, is the reference voltage vector of the suspension, u 2i are the two basic vectors of the sector where the reference voltage vector of the suspension is located;

[0058] The process of obtaining the voltage vector of the torque winding includes:

[0059] Using the given value of the torque, the predicted value of the torque, the preset given value of the stator magnetic flux linkage of the torque winding, the predicted value of the magnetic flux linkage of the suspension winding, the given value of the magnetic flux linkage of the torque winding, and the given value of the magnetic flux linkage of the suspension winding, obtain the reference voltage vector of the torque in the d-q coordinate system;

[0060] Convert the reference voltage vector of the torque in the d-q coordinate system into polar coordinate form, and determine the sector where the reference voltage vector of the torque is located according to its angle, and select the reference voltage vector of the torque that minimizes the value of the torque system cost function as the voltage vector of the torque winding;

[0061] The expression of the torque system cost function is:

[0062]

[0063] Among them, is the torque reference voltage vector, and u 1i are two basic vectors in the sector where the torque reference voltage vector is located.

[0064] Compared with the prior art, the beneficial effects of the present invention include:

[0065] 1. In the process of controlling by predicting voltage, the present invention takes into account the interaction (coupling effect) between the suspension flux linkage and the torque flux linkage and the eccentric displacement, solves the inaccuracy problem caused by the traditional control not considering the coupling effect and the eccentric displacement, improves the steady-state control accuracy of the suspension system, reduces the influence brought by the suspension force pulsation, and further improves the anti-interference ability of the system.

[0066] 2. In the present invention, all predictions are compensated by one beat delay plus one beat. This approach can eliminate the influence of the control cycle delay on the suspension force and torque tracking, and reduce the amplitude of the suspension force pulsation of the motor.

[0067] 3. The present invention uses continuous sector division and value function optimization to select the voltage vector. In the past, model predictive current control and model predictive torque control indirectly achieved the optimal vector selection through intermediate variables, while this method is a direct voltage selection, bypassing the traditional intermediate variables and directly optimizing the voltage vector through the value function. The dynamic response speed can be greatly improved without restricting the number of motor switching states.

[0068] 4. In the present invention, the suspension force control and the torque control are adjusted in real time through flux linkage interaction, which can suppress sudden load changes or external disturbances, and the system has strong anti-interference ability. Description of the Drawings

[0069] Figure 1 is the flowchart of the method of the present invention;

[0070] Figure 2 is the system structure diagram of the present invention. Detailed Embodiments

[0071] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0072] Embodiment 1

[0073] This embodiment aims to disclose a predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling. The method steps are as follows: Figure 1 As shown, its specific step process includes:

[0074] Step S1: Obtain the motor parameters and acquisition data of the bearingless permanent magnet motor at the current moment;

[0075] Step S2: Obtain the suspension force given value and torque given value, and combine with the torque winding air-gap flux linkage given value to calculate and obtain the suspension winding flux linkage given value;

[0076] Step S3: Based on the coupled flux linkage equation and the motor voltage equation, predict the current prediction values and flux linkage prediction values of the torque winding and suspension winding at the next moment;

[0077] Step S4: Predict the air-gap flux linkage prediction value of the suspension winding at the next moment, and combine with the current prediction values of the suspension winding and torque winding to predict the suspension force prediction value at the next moment and the torque prediction value at the next moment;

[0078] Step S5: Calculate and obtain the suspension winding voltage vector that minimizes the value of the suspension system cost function and the torque winding voltage vector that minimizes the value of the torque system cost function;

[0079] Step S6: Use the suspension winding voltage vector to control the suspension winding to generate a radial suspension force to maintain the stable suspension of the bearingless permanent magnet motor rotor, and use the torque winding voltage vector to control the torque winding to generate an electromagnetic torque to drive the rotation of the bearingless permanent magnet motor rotor to complete the control of the bearingless permanent magnet motor;

[0080] Among them, the current moment is the k moment, and the next moment should originally be the k + 1 moment. However, due to the delay problem, the k + 1 moment is processed with a one-beat delay compensation to become the k + 2 moment.

[0081] The one-beat delay compensation is to eliminate the negative impact brought by the control delay and eliminate the influence of the control cycle delay on the suspension force and torque tracking.

[0082] In step S1, the motor parameters and acquisition data of the bearingless permanent magnet motor at the current moment include: the actual displacement value, preset displacement value, actual speed value, preset speed value, torque winding stator flux linkage given value, torque winding air-gap flux linkage given value, voltage value and current value of the suspension winding, and voltage value and current value of the torque winding.

[0083] After obtaining the voltage and current values of the suspension winding and the voltage and current values of the torque winding, the voltage and current values of the suspension winding and the three-phase voltage and current values of the torque winding are converted into the voltage and current values of the suspension winding and the voltage and current values of the torque winding in the d-q coordinate system through the Clark transformation. Converting the three-phase voltage into the voltage and current in the d-q coordinate system is beneficial to simplify the calculation process and accelerate the prediction speed.

[0084] In step S2, according to the displacement difference between the actual displacement value and the preset displacement value and the speed difference between the actual speed value and the preset speed value, the suspension force reference value and the torque reference value are obtained through calculation, and combined with the given value of the air-gap magnetic flux of the torque winding, the given value of the magnetic flux of the suspension winding is calculated.

[0085] The suspension force reference value can be obtained by processing the displacement difference between the actual displacement value and the preset displacement value through a PID controller, and the torque reference value can be obtained by processing the speed difference between the actual speed value and the preset speed value through a PI controller. Among them, the specific inputs of the PID controller are the x-axis displacement difference and the y-axis displacement difference between the actual displacement value and the preset displacement value.

[0086] The specific calculation expression of the given value of the magnetic flux of the suspension winding is:

[0087]

[0088] F x is the x-axis component of the radial suspension force on the rotor, F y is the y-axis component of the radial suspension force on the rotor, k M is the magnetic coupling coefficient, ψ 1m * is the given value of the synthetic air-gap magnetic flux of the torque winding.

[0089] In step S3, using the actual displacement value, actual speed value, voltage and current values of the suspension winding, and voltage and current values of the torque winding of the bearingless permanent magnet motor at the current moment, based on the coupled magnetic flux equation and the motor voltage equation, the predicted current values and magnetic flux predicted values of the torque winding and the suspension winding at the next moment are predicted.

[0090] In this embodiment, the coupled magnetic flux matrix of the bearingless permanent magnet synchronous motor takes into account the eccentric displacement (that is, there is a difference between the actual displacement value and the ideal preset displacement value). The coupled magnetic flux matrix established considering eccentricity in the synchronous rotating d-q coordinate system is:

[0091]

[0092] From this matrix, the coupled magnetic flux equation can be obtained as:

[0093]

[0094] where ψ 1d is the d-axis component of the stator flux linkage of the torque winding, ψ 1q is the q-axis component of the stator flux linkage of the torque winding, ψ 2d is the d-axis component of the stator flux linkage of the suspension winding, ψ 2q is the q-axis component of the stator flux linkage of the suspension winding, L1 is the self-inductance of the torque winding, L2 is the self-inductance of the suspension winding, M′ is the mutual inductance coefficient between the suspension winding and the torque winding, i 1d is the d-axis component of the current of the torque winding, i 1q is the q-axis component of the current of the torque winding, i 2d is the d-axis component of the current of the suspension winding, i 2q is the q-axis component of the current of the suspension winding, i f is the equivalent excitation current of the rotor permanent magnet, x is the actual displacement value in the x-axis direction of the rotor, y is the actual displacement value in the y-axis direction of the rotor;

[0095]

[0096]

[0097]

[0098] where μ0 is the permeability of free space, l is the axial length of the motor, r is the radius of the rotor, N1 is the number of turns of the torque winding, N2 is the number of turns of the suspension winding, and δ0 is the nominal air-gap length;

[0099] The motor voltage equation is:

[0100]

[0101] where i 1d , u 1q are the components of the voltage of the torque winding in the d-q coordinate system, u 2d , u 2q are the components of the voltage of the suspension winding in the d-q coordinate system, R1 is the stator resistance of the torque winding, R2 is the stator resistance of the suspension winding, and ω is the rotational speed of the motor.

[0102] The process of predicting the current prediction values and flux linkage prediction values of the torque winding and the suspension winding at the next moment includes:

[0103] Substitute the coupled flux linkage equation into the discretized motor voltage equation, and the current prediction expression and flux linkage prediction expression can be obtained through calculation. Here, the discretization adopts the forward difference approximation;

[0104] Based on the actual displacement value, actual rotational speed value, voltage value and current value of the suspension winding, and voltage value and current value of the torque winding of the bearingless permanent magnet motor at the current moment, the current prediction values and flux linkage prediction values of the torque winding and suspension winding at the next moment are obtained by using the current prediction expression and flux linkage prediction expression respectively.

[0105] In the discretized motor voltage equation, the forward difference approximation is adopted to convert the continuous time derivatives in the motor voltage equation and into the discrete form, and the converted form of the time derivative is as follows:

[0106]

[0107] where, T s is the sampling period.

[0108] In step S4, the air-gap flux linkage prediction value of the suspension winding at the next moment is predicted by using the flux linkage prediction value of the torque winding at the next moment, and the suspension force prediction value at the next moment is predicted in combination with the current prediction value of the suspension winding.

[0109] The prediction process of the suspension force prediction value at the next moment includes:

[0110] Obtain the leakage inductance of the torque winding, and use the flux linkage prediction value of the torque winding and the leakage inductance to obtain the air-gap flux linkage prediction value of the suspension winding;

[0111] Based on the suspension force mathematical model, use the air-gap flux linkage prediction value and current prediction value of the suspension winding to obtain the suspension force prediction value at the next moment;

[0112] Among them, the expression for obtaining the air-gap flux linkage prediction value is:

[0113]

[0114] where, ψ 1md (k + 2) is the d-axis air-gap flux linkage of the torque winding at the (k + 2) moment, ψ 1mq (k + 2) is the q-axis air-gap flux linkage of the torque winding at the (k + 2) moment, L 1δd is the d-axis leakage inductance of the torque winding, L 1δq is the q-axis leakage inductance of the torque winding, i 1d (k + 2) is the d-axis current prediction value of the torque winding at the (k + 2) moment, i 1q (k + 2) is the q-axis current prediction value of the torque winding at the (k + 2) moment;

[0115] The expression of the suspension force mathematical model is:

[0116]

[0117] Among them, F x is the x - component of the radial suspension force, F y is the y - component of the radial suspension force, k M is the magnetic coupling coefficient, k L is the leakage magnetic influence coefficient, k ecc is the eccentricity stiffness coefficient, i 2d is the d - axis component of the current in the suspension winding, i 2q is the q - axis component of the current in the suspension winding, x is the actual displacement value of the rotor in the x - axis direction, and y is the actual displacement value of the rotor in the y - axis direction;

[0118]

[0119]

[0120]

[0121] Among them, p1 is the number of pole pairs of the torque winding, p2 is the number of pole pairs of the suspension winding, ψ 1d is the d - axis component of the stator magnetic flux linkage of the torque winding, ψ 1m is the resultant air - gap magnetic flux linkage of the torque winding, ψ 2s is the stator magnetic flux linkage of the suspension winding, L m2 is the mutual inductance of the suspension winding, l is the axial length of the motor, r is the rotor radius, N1 is the number of turns of the torque winding, N2 is the number of turns of the suspension winding, δ0 is the nominal air - gap length, μ0 is the permeability of free space, m p is the number of phases of the motor.

[0122] In step S4, using the predicted values of the currents in the suspension winding and the torque winding at the next moment, predict the predicted value of the torque at the next moment.

[0123] The prediction formula for the predicted value of the torque at the next moment is:

[0124] T e (k + 2)=A k+2 ·ψ 1d (k + 2)+B k+2 ·ψ 1q (k + 2)+C k+2 ·ψ 2d (k + 2)

[0125] +D k+2 ·ψ 2q (k + 2)

[0126] Among them, T e (k + 2) is the torque at the (k + 2) moment, ψ 1d (k + 2) is the d - axis component of the stator magnetic flux linkage of the torque winding at the (k + 2) moment, ψ 1q(k + 2) is the q-axis component of the stator flux linkage of the torque winding at time (k + 2), ψ 2d (k + 2) is the d-axis component of the stator flux linkage of the suspension winding at time (k + 2), ψ 2q (k + 2) is the q-axis component of the stator flux linkage of the suspension winding at time (k + 2), A k+2 、B k+2 、C k+2 and d k+2 are the predicted parameters derived at time k + 2.

[0127] The specific derivation process of this prediction formula is as follows:

[0128] Substituting the above coupling flux linkage matrix into the co-energy formula, the co-energy formula of the bearingless permanent magnet synchronous motor can be obtained as follows:

[0129]

[0130] where L1 is the self-inductance of the torque winding, L2 is the self-inductance of the suspension winding, M′ is the mutual inductance coefficient between the suspension winding and the torque winding, i 1d is the d-axis component of the current in the torque winding, i 1q is the q-axis component of the current in the torque winding, i 2d is the d-axis component of the current in the suspension winding, i 2q is the q-axis component of the current in the suspension winding, i f is the equivalent excitation current of the rotor permanent magnet;

[0131] According to the principle of electromechanical energy conversion, the electromagnetic torque T e is the partial derivative of the co-energy with respect to the mechanical angle , and the expression is:

[0132]

[0133] Substituting the above coupling flux linkage equation into this expression of the electromagnetic torque T e , the formula can be transformed into:

[0134] T e =A·ψ 1d +B·ψ 1q +C·ψ 2d +D·ψ 2q

[0135] Thus, during this transformation process, the values of A k 、B k 、C k and D k at time k can be obtained

[0136] The prediction formula for the predicted value of the torque at the next moment is:

[0137] T e (k + 2) = A k+2 ·ψ 1d (k + 2) + B k+2 ·ψ 1q (k + 2) + C k+2 ·ψ 2d (k + 2)

[0138] +D k+2 ·ψ 2q (k + 2).

[0139] In step S5, using the suspension force set value, the predicted suspension force value at the next moment, and the set value of the suspension winding magnetic flux linkage, the suspension winding voltage vector is obtained, and the suspension winding voltage vector is the suspension reference voltage vector that minimizes the value function of the suspension system.

[0140] The process of obtaining the suspension winding voltage vector includes:

[0141] Using the suspension force set value, the predicted suspension force value at the next moment, and the set value of the suspension winding magnetic flux linkage, the suspension reference voltage vector in the d-q coordinate system is obtained;

[0142] The suspension reference voltage vector in the d-q coordinate system is converted into polar coordinate form, and the sector where the suspension reference voltage vector is located is judged according to its angle.

[0143] The process of obtaining the suspension reference voltage vector in the d-q coordinate system includes:

[0144] According to the flux linkage deadbeat principle, let the predicted value of the suspension winding magnetic flux linkage at the (k + 2) moment be equal to the set value of the suspension winding magnetic flux linkage. Based on the flux linkage prediction expression, the coupled magnetic flux equation, and the motor voltage equation obtained in step S3, the suspension reference voltage vector in the d-q coordinate system can be solved.

[0145] The expression of the value function of the suspension system is:

[0146]

[0147] Where, is the suspension reference voltage vector, u 2i are the two basic vectors of the sector where the suspension reference voltage vector is located.

[0148] In step S5, using the torque set value, the predicted torque value, the set value of the stator magnetic flux linkage of the torque winding, the predicted value of the suspension winding magnetic flux linkage, the set value of the torque winding magnetic flux linkage, and the set value of the suspension winding magnetic flux linkage, the torque winding voltage vector is obtained, and the torque winding voltage vector is the torque reference voltage vector that minimizes the value function of the torque system;

[0149] The process of obtaining the torque winding voltage vector includes:

[0150] Using the torque given value, torque predicted value, torque winding stator flux linkage given value, suspension winding flux linkage predicted value, torque winding flux linkage given value, and suspension winding flux linkage given value, obtain the torque reference voltage vector in the d-q coordinate system;

[0151] Convert the torque reference voltage vector in the d-q coordinate system into polar coordinate form, and determine the sector where the torque reference voltage vector is located according to its angle.

[0152] The process of obtaining the torque reference voltage vector in the d-q coordinate system includes:

[0153] According to the torque deadbeat principle, make the torque predicted value at the (k + 2) moment equal to the torque given value. According to the flux linkage deadbeat principle, make the torque winding flux linkage predicted value at the (k + 2) moment equal to the torque winding flux linkage given value. Based on the prediction formula of the torque predicted value, the coupled flux linkage equation, and the motor voltage equation obtained in step S3, the torque reference voltage vector in the d-q coordinate system can be solved.

[0154] The expression of the torque system value function is:

[0155]

[0156] Where is the torque reference voltage vector, u 1i are the two basic vectors of the sector where the torque reference voltage vector is located.

[0157] In the control method disclosed in this embodiment, through a double closed-loop predictive control architecture, a PID controller is introduced in the suspension force control to generate a given value, the current and flux linkage are predicted by combining the flux linkage coupling model, and the voltage vector is optimized using the value function to achieve stable rotor suspension; in the torque control, a PI controller is used to generate the torque given value, the flux linkage and torque prediction results are integrated, and the voltage vector is optimized to improve the dynamic response speed. During the control process, the influence of magnetic coupling between windings and eccentric displacement is considered, and the control lag is eliminated through delay compensation to ensure the efficient and stable operation of the system in a multi-variable strong coupling environment, solving the problems of low steady-state accuracy and slow dynamic response caused by inaccurate models in traditional control, improving the anti-interference ability and control accuracy of the system, and being applicable to the control of bearingless permanent magnet synchronous motors with multi-variable strong coupling.

[0158] Embodiment 2

[0159] Based on the above Embodiment 1, this embodiment aims to disclose a predictive voltage control system for a bearingless permanent magnet motor based on flux linkage coupling. The overall system is as Figure 2 shown, including:

[0160] The first PID controller 4, the second PID controller 5, the suspension winding voltage prediction module 6, the suspension winding polar coordinate transformation module 7, the suspension winding sector determination module 8, the suspension winding value function module 9, the suspension winding inverter module 10, the BPMSM bearingless permanent magnet synchronous motor 11, the displacement sensor 12, the position sensor 13, the Clark transformation module 14, the suspension and torque winding current prediction module 15, the suspension and torque winding flux linkage prediction module 16, the torque winding air-gap flux linkage prediction module 17, the radial suspension force prediction module 18, the flux linkage reference calculation module 19, the torque prediction module 20, the PI controller 21, the torque winding reference voltage prediction module 22, the torque polar coordinate transformation module 23, the torque winding sector determination module 24, the torque winding value function module 25, the torque winding inverter module 26, the speed sensor 27.

[0161] The specific control process of the bearingless permanent magnet motor voltage prediction control system based on flux linkage coupling for the bearingless permanent magnet motor is as follows:

[0162] Suspension force prediction control: The displacement sensor 12 and the position sensor 13 are used to obtain the actual displacement value and the preset displacement value of the bearingless permanent magnet motor at the current moment, and the difference between the two is obtained by subtraction. According to the displacement difference, the suspension force reference value is obtained through the first PID controller 4 and the second PID controller 5;

[0163] Obtain the voltage value and current value of the suspension winding and the voltage value and current value of the torque winding of the bearingless permanent magnet motor at the current moment, and obtain the voltage value and current value of the suspension winding and the voltage value and current value of the torque winding in the d-q coordinate system through the Clark transformation module 14;

[0164] Using the actual displacement value of the bearingless permanent magnet motor at the current moment, the voltage value and current value of the suspension winding and the voltage value and current value of the torque winding in the d-q coordinate system, the predicted current value of the suspension winding and the predicted current value of the torque winding at the next moment are obtained based on the suspension and torque winding current prediction module 15;

[0165] Using the actual displacement value of the bearingless permanent magnet motor at the current moment, the predicted current value of the suspension winding and the predicted current value of the torque winding at the next moment, the predicted flux linkage value of the suspension winding and the predicted flux linkage value of the torque winding at the next moment are obtained based on the suspension and torque winding flux linkage prediction module 16;

[0166] Using the predicted flux linkage value of the torque winding at the next moment, the predicted air-gap flux linkage value of the suspension winding at the next moment is obtained based on the torque winding air-gap flux linkage prediction module 17;

[0167] Using the predicted air-gap flux linkage value of the suspension winding and the predicted current value of the suspension winding at the next moment, the predicted suspension force value at the next moment is obtained based on the radial suspension force prediction module 18;

[0168] Obtain the given value of the stator flux linkage of the torque winding. Using the given value of the suspension force, the predicted value of the suspension force at the next moment, and the given value of the air-gap flux linkage of the torque winding, based on the suspension winding voltage prediction module 6, obtain the predicted reference voltage vector and calculate its position angle through the suspension winding polar coordinate transformation module 7;

[0169] The suspension winding inverter module 10 uses the suspension winding sector determination module 8 to determine the sector where the predicted reference voltage vector is located according to the position angle, and then uses the suspension winding cost function module 9 to construct a cost function and obtain the switching signal that minimizes the cost function value;

[0170] Using the switching signal, obtain the three-phase voltage based on the suspension winding inverter module 10, and control the bearingless permanent magnet motor through the three-phase voltage to achieve stable suspension of the rotor of the bearingless permanent magnet motor.

[0171] Torque predictive control: Use the speed sensor 27 to obtain the actual speed value and the preset speed value of the bearingless permanent magnet motor at the current moment, and subtract the two to obtain the speed difference. According to the speed difference, obtain the given value of the torque through the PI controller 21;

[0172] Using the predicted value of the current of the suspension winding at the next moment and the predicted value of the current of the torque winding, based on the torque prediction module 20, obtain the predicted value of the torque of the bearingless permanent magnet motor at the next moment;

[0173] Obtain the given value of the air-gap flux linkage of the torque winding. Using the given value of the air-gap flux linkage of the torque winding and the given value of the suspension force, calculate and obtain the given value of the flux linkage of the suspension winding based on the flux linkage given calculation module 19;

[0174] Using the given value of the torque, the predicted value of the torque, the given value of the stator flux linkage of the torque winding, the predicted value of the flux linkage of the suspension winding, the given value of the flux linkage of the torque winding, and the given value of the flux linkage of the suspension winding, based on the torque winding reference voltage prediction module 22, predict the reference voltage vector and calculate its position angle through the torque polar coordinate transformation module 23;

[0175] According to the position angle, use the torque winding sector determination module 24 to determine the sector where the predicted reference voltage vector is located, construct a cost function through the torque winding cost function module 25, and obtain the switching signal that minimizes the cost function value;

[0176] Using the switching signal, obtain the three-phase voltage based on the torque winding inverter module 26, and control the bearingless permanent magnet motor through the three-phase voltage to achieve torque control of the rotor of the bearingless permanent magnet motor.

[0177] As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling, characterized in that, The method includes: Obtain the suspension force reference value and the torque reference value according to the displacement difference between the actual displacement value and the preset displacement value of the motor at the current moment and the speed difference between the actual speed value and the preset speed value of the motor, and calculate and obtain the flux linkage reference value of the suspension winding in combination with the preset flux linkage reference value of the torque winding air gap; Utilize the actual displacement value, actual speed value, voltage values and current values of the suspension winding and torque winding of the motor at the current moment, and based on the coupled flux linkage equation and the motor voltage equation, predict the current prediction values and flux linkage prediction values of the torque winding and suspension winding at the next moment, where the coupled flux linkage equation considers the eccentric displacement and the flux linkage interaction between the suspension winding and the torque winding; Utilize the predicted flux linkage value of the torque winding at the next moment to predict the predicted air gap flux linkage value of the suspension winding at the next moment, and in combination with the predicted current value of the suspension winding, predict the predicted suspension force value at the next moment; utilize the predicted current values of the suspension winding and torque winding at the next moment to predict the predicted torque value at the next moment; Utilize the predicted suspension force value and predicted torque value to obtain the suspension reference voltage vector for controlling the radial suspension force generated by the suspension winding and the torque reference voltage vector for controlling the electromagnetic torque generated by the torque winding through the direct voltage vector selection strategy, and complete the control of the bearingless permanent magnet motor; Among them, the current moment is the k moment, and the next moment is the k + 2 moment after one-beat delay compensation processing.

2. The predictive voltage control method of a bearingless permanent magnet motor based on flux linkage coupling according to claim 1, characterized in that After obtaining the voltage values and current values of the suspension winding and the voltage values and current values of the torque winding, convert the voltage values and current values of the suspension winding and the voltage values and current values of the torque winding into the voltage values and current values of the suspension winding and the voltage values and current values of the torque winding in the d-q coordinate system through the Clark transformation.

3. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 1, characterized in that, Obtain the suspension force reference value by processing the displacement difference between the actual displacement value and the preset displacement value through a PID controller, and obtain the torque reference value by processing the speed difference between the actual speed value and the preset speed value through a PI controller.

4. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 1, characterized in that, The coupled flux linkage equation is: Among them, ψ 1d is the d-axis magnetic flux linkage of the torque winding, ψ 1q is the q-axis magnetic flux linkage of the torque winding, ψ 2d is the d-axis magnetic flux linkage of the suspension winding, ψ 2q is the q-axis magnetic flux linkage of the suspension winding, L1 is the self-inductance of the torque winding, L2 is the self-inductance of the suspension winding, M′ is the mutual inductance coefficient between the suspension winding and the torque winding, i 1d is the d-axis current of the torque winding, i 1q is the q-axis current of the torque winding, i 2d is the d-axis current of the suspension winding, i 2q is the q-axis current of the suspension winding, i f is the equivalent excitation current of the rotor permanent magnet, x is the actual displacement value of the x-axis of the bearingless permanent magnet motor, y is the actual displacement value of the y-axis of the bearingless permanent magnet motor, Among them, μ0 is the vacuum permeability, l is the axial length of the motor, r is the rotor radius, N1 is the number of turns of the torque winding, N2 is the number of turns of the suspension winding, and δ0 is the nominal air gap length; The motor voltage equation is: where, u 1d is the d-axis voltage of the torque winding, u 1q is the q-axis voltage of the torque winding, u 2d is the d-axis voltage of the suspension winding, u 2q is the q-axis voltage of the suspension winding, R1 is the resistance of the torque winding, R2 is the resistance of the suspension winding, and ω is the rotational speed of the motor.

5. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 4, characterized in that The process of predicting the current prediction values and flux linkage prediction values of the torque winding and suspension winding at the next moment includes: Substitute the coupled flux linkage equation into the discretized motor voltage equation, and obtain the current prediction expression and flux linkage prediction expression through calculation; Based on the actual displacement value, actual speed value, voltage values and current values of the suspension winding and torque winding of the bearingless permanent magnet motor at the current moment, respectively utilize the current prediction expression and flux linkage prediction expression to obtain the current prediction values and flux linkage prediction values of the torque winding and suspension winding at the next moment.

6. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 1, characterized in that The calculation expression of the flux linkage reference value of the suspension winding is: Among them, F x * is the given value of the suspension force on the x-axis, F y * is the given value of the suspension force on the y-axis, k M is the magnetic coupling coefficient, ψ 1m * is the given value of the air-gap magnetic flux of the torque winding.

7. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 1, characterized in that The process of the direct voltage vector selection strategy includes: Utilize the suspension force reference value, the predicted suspension force value at the next moment and the flux linkage reference value of the suspension winding to obtain the suspension winding voltage vector, and the suspension winding voltage vector is the suspension reference voltage vector that minimizes the value of the suspension system cost function; Obtain a torque winding voltage vector by using the torque given value, torque predicted value, preset torque winding stator flux linkage given value, levitation winding flux linkage predicted value, torque winding flux linkage given value, and levitation winding flux linkage given value. The torque winding voltage vector is a torque reference voltage vector that minimizes the value of the torque system cost function; Use the levitation winding voltage vector to control the levitation winding to generate a radial levitation force and maintain the stable levitation of the rotor of the bearingless permanent magnet motor. Use the torque winding voltage vector to control the torque winding to generate an electromagnetic torque and drive the rotation of the rotor of the bearingless permanent magnet motor to complete the control of the bearingless permanent magnet motor.

8. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 7, characterized in that The prediction process of the predicted value of the levitation force at the next moment includes: Obtain the leakage inductance of the torque winding, and use the predicted value of the flux linkage of the torque winding and the leakage inductance to obtain the predicted value of the air-gap flux linkage of the levitation winding; Based on the levitation force mathematical model, use the predicted value of the air-gap flux linkage of the levitation winding and the predicted value of the current to obtain the predicted value of the levitation force at the next moment; Among them, the expression for obtaining the predicted value of the air-gap flux linkage is: Among them, ψ 1md (k + 2) is the d-axis air-gap magnetic flux linkage of the torque winding at time (k + 2), ψ 1mq (k + 2) is the q-axis air-gap magnetic flux linkage of the torque winding at time (k + 2), L 1δd is the d-axis leakage inductance of the torque winding, L 1δq is the q-axis leakage inductance of the torque winding, i 1d (k + 2) is the predicted value of the d-axis current of the torque winding at time (k + 2), i 1q (k + 2) is the predicted value of the q-axis current of the torque winding at time (k + 2); The expression of the levitation force mathematical model is: Among them, F x is the radial suspension force of the x-axis, F y is the radial suspension force of the y-axis, k M is the magnetic coupling coefficient, k L is the leakage magnetic influence coefficient, k ecc is the eccentricity stiffness coefficient, i 2d is the d-axis current of the suspension winding, i 2q is the q-axis current of the suspension winding, x is the actual displacement value of the x-axis of the bearingless permanent magnet motor, y is the actual displacement value of the y-axis of the bearingless permanent magnet motor, where p1 is the number of pole pairs of the torque winding, p2 is the number of pole pairs of the suspension winding, ψ 1d is the d-axis magnetic flux linkage of the torque winding, ψ 1m is the total air-gap magnetic flux linkage of the torque winding, ψ 2s is the total magnetic flux linkage of the suspension winding, L m2 is the mutual inductance of the suspension winding, l is the axial length of the motor, r is the rotor radius, N1 is the number of turns of the torque winding, N2 is the number of turns of the suspension winding, δ0 is the nominal air-gap length, μ0 is the permeability of free space, m p is the number of phases of the motor.

9. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 7, characterized in that The prediction formula for the predicted value of the torque at the next moment is: T e (k + 2)= A k+2 ·ψ 1d (k + 2)+ B k+2 ·ψ 1q (k + 2)+ C k+2 ·ψ 2d (k + 2)+ D k+2 ·ψ 2q (k + 2) Among them, T e (k + 2) is the torque at the (k + 2)th moment, ψ 1d (k + 2) is the d-axis magnetic flux linkage of the torque winding at the (k + 2)th moment, ψ 1q is the q-axis magnetic flux linkage of the torque winding at the (k + 2)th moment, ψ 2d (k + 2) is the d-axis magnetic flux linkage of the suspension winding at the (k + 2)th moment, ψ 2q is the q-axis magnetic flux linkage of the suspension winding at the (k + 2)th moment, A k+2 、B k+2 、C k+2 and D k+2 are the predicted parameters derived at the (k + 2)th moment.

10. A predictive voltage control method for a bearingless permanent magnet motor based on flux linkage coupling according to claim 7, characterized in that, The process of obtaining the levitation winding voltage vector includes: Use the levitation force given value, the predicted value of the levitation force at the next moment, and the levitation winding flux linkage given value to obtain a levitation reference voltage vector in the d-q coordinate system; Convert the levitation reference voltage vector in the d-q coordinate system into polar coordinate form, and judge the sector where the levitation reference voltage vector is located according to its angle. Select the levitation reference voltage vector that minimizes the value of the levitation system cost function as the levitation winding voltage vector; The expression of the levitation system cost function is: Among them, is the floating reference voltage vector, u 2i are the two basic vectors of the sector where the floating reference voltage vector is located; The process of obtaining the torque winding voltage vector includes: Use the torque given value, torque predicted value, preset torque winding stator flux linkage given value, levitation winding flux linkage predicted value, torque winding flux linkage given value, and levitation winding flux linkage given value to obtain a torque reference voltage vector in the d-q coordinate system; Convert the torque reference voltage vector in the d-q coordinate system into polar coordinate form, and judge the sector where the torque reference voltage vector is located according to its angle. Select the torque reference voltage vector that minimizes the value of the torque system cost function as the torque winding voltage vector; The expression of the torque system cost function is: Among them, is the torque reference voltage vector, u 1i are two basic vectors of the sector where the torque reference voltage vector is located.

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