Synchronous motor sensorless control method based on Newton-Raphson predictive phase-locked loop

Abstract

The invention discloses a synchronous motor sensorless control method based on a Newton-Raphson predictive phase-locked loop, and relates to the technical field of motor control. The invention aims to solve the problems that an existing position-sensorless control method is limited by extra loss and noise caused by high-frequency signal injection in the aspect of position signal extraction and poor dynamic performance caused by a traditional phase-locked loop technology, and a prediction phase-locked loop technology needs a large amount of iterative operation for solving a cost function. According to the method, the flux linkage estimation value of the alpha-beta coordinate system is observed, the filtered flux linkage estimation value of the alpha-beta coordinate system is reconstructed, and then a cost function is constructed; when the number of iterations in the current motor control period does not reach the maximum, updating a rotor position angle by using a Newton method, and further updating a cost function; and when the number of iterations in the current motor control period reaches the maximum, calculating a convergence angle in the current motor control period by using an improved Newton method, and calculating an angular velocity estimated value, thereby realizing position-sensorless control of the synchronous motor.

Description

Technical Field

[0001] The invention belongs to the technical field of motor control. Background Art

[0002] Synchronous reluctance motor (SynRM) has the characteristics of simple structure, low cost, and suitability for high temperature and high speed applications, making it an ideal replacement for mainstream induction motors in the field of industrial drives and electric vehicles. Obtaining accurate rotor position information is the key to achieving high-performance synchronous reluctance motor control. However, the application of position sensors increases the cost and complexity of the control system, so it is of practical significance to study the position sensorless control method of synchronous reluctance motors.

[0003] At present, the control methods without position sensors are mainly based on high-frequency injection and basic model. The high-frequency injection-based method injects an additional high-frequency (HF) signal to instantaneously excite the motor and estimates the rotor position by detecting the spatial orientation of the induced HF current. However, HF signal injection inevitably generates additional losses and noise. In addition, the significance-based method is only applicable to zero speed and low speed ranges.

[0004] In order to extend the operating range of position sensorless motors, a basic model-based approach suitable for medium and high speeds has been proposed. The basic model-based approach estimates the stator flux of the motor and then detects the position and speed using a position observer based on a phase-locked loop (PLL). Among these observers, the proportional-integral controller-based phase-locked loop (PI-PLL) is widely used due to its simple structure. However, the PI-PLL uses fixed controller gains, which need to be modified repeatedly through experiments to obtain satisfactory performance. In addition, the fixed gain PI-PLL has poor dynamic performance due to its inherent linear characteristics and limited bandwidth.

[0005] In recent years, the idea of ​​predicting the cost function of the finite control set model has been applied to position sensorless controllers to improve dynamic performance, and the predictive phase-locked loop (PPLL) technology has been proposed. PPLL has the advantages of good dynamic performance and no need for parameter tuning. However, PPLL requires a large number of iterations to search for the optimal position that minimizes the cost function. The increase in the amount of calculation limits its application in low-cost controllers. Therefore, it is of practical significance to study the predictive phase-locked loop position sensorless technology that ensures convergence and rapidity.

[0006] Based on the introduction of the above background technology, it can be seen that the current position sensorless control method is limited in extracting position signals due to the additional loss and noise caused by high-frequency signal injection and the poor dynamic performance caused by traditional phase-locked loop technology. Although the predictive phase-locked loop technology avoids complex parameter setting and improves the dynamic performance of the system, it requires a large number of iterative operations to solve the cost function. Summary of the invention

[0007] The present invention aims to solve the problem that the existing position sensorless control method is limited in extracting position signals due to the additional loss and noise caused by high-frequency signal injection and the poor dynamic performance caused by traditional phase-locked loop technology, and the predictive phase-locked loop technology requires a large number of iterative operations to solve the cost function. A position sensorless control method for a synchronous motor based on a Newton-Raphson predictive phase-locked loop is provided.

[0008] A synchronous motor position sensorless control method based on a Newton-Raphson predictive phase-locked loop comprises:

[0009] Observe the estimated value of the magnetic flux in the αβ coordinate system by using a magnetic flux observer, reconstruct the estimated value of the magnetic flux in the αβ coordinate system after high-pass filtering, obtain the effective magnetic flux in the αβ coordinate system, and construct a cost function based on the effective magnetic flux in the αβ coordinate system;

[0010] When the number of iterations j does not reach the maximum number of iterations N in the current motor control cycle, the rotor position angle is updated using the Newton method based on the cost function, the cost function is updated using the updated rotor position angle, and then j=j+1 is set, and whether j reaches N is re-determined;

[0011] When the number of iterations j in the current motor control cycle reaches the maximum number of iterations N, the convergence angle in the current motor control cycle is calculated using the improved Newton method, and then the convergence angle is differentially averaged to obtain the angular velocity estimate The speed estimate after low-pass filtering is used to realize the position sensorless control of synchronous motor.

[0012] Furthermore, the method for constructing the above-mentioned flux observer includes:

[0013] The synchronous motor stator voltage and flux equations in the αβ coordinate system are constructed, and the flux observer is constructed using the synchronous motor stator voltage and flux equations. The expression of the flux observer is:

[0014]

[0015] in, is the estimated value of the magnetic flux vector along the αβ axis, s is the Laplace operator, u αβ is the αβ axis stator voltage vector, R s is the resistance, i αβis the αβ axis stator current vector, To estimate the DC bias of the stator flux.

[0016] Furthermore, the stator voltage and flux equations of the synchronous motor in the above αβ coordinate system are as follows:

[0017]

[0018] in, is the magnetic flux vector of αβ axis, L αβ is the αβ axis inductance matrix.

[0019] Furthermore, the above αβ axis inductance matrix L αβ The expression is:

[0020] L αβ =T -1 (θ)L dq T(θ),

[0021] Among them, T(·) is the coordinate transformation matrix, and there is θ is the rotor position angle, L dq is the dq axis inductance matrix, and L dq =[L d 0;0L q ], L d and L q They are the d-axis and q-axis inductances respectively.

[0022] Furthermore, the above-mentioned high-pass filtered αβ coordinate system magnetic flux estimation value is reconstructed to obtain the αβ coordinate system effective magnetic flux, including:

[0023] The reconstructed equation is:

[0024]

[0025] in, is the estimated value of the reconstructed magnetic flux vector, is the estimated angular frequency, is the amplitude attenuation caused by the high-pass filter, and ω HPF is the corner frequency of the high-pass filter, T(·) is the coordinate transformation matrix, and is the estimated value of the magnetic flux vector on the αβ axis.

[0026] Furthermore, the cost function is constructed based on the effective magnetic flux of the αβ coordinate system, including:

[0027] Taking the angle as the control set, construct a predefined cost function ε(·):

[0028]

[0029] Among them, ||·|| represents the Euclidean norm, θ i is the i-th angle in the control set, for The estimated value of is the magnetic flux vector of γδ axis, is the estimated value of the γδ axis current vector, is the estimated value of the inductance vector of the γδ axis, T(·) is the coordinate transformation matrix, and is the estimated value of the reconstructed magnetic flux vector, i αβ is the αβ-axis stator current vector.

[0030] Furthermore, the above-mentioned updating of the rotor position angle by using Newton's method based on the cost function includes:

[0031] The expression for updating the rotor position angle is:

[0032]

[0033] Among them, θ j is the rotor position angle obtained in the jth iteration of the current motor control cycle, θ j+1 is the updated rotor position angle, ε′(·) and ε″(·) are the first and second order derivatives of the cost function, respectively.

[0034] Furthermore, the above-mentioned updating cost function using the updated rotor position angle includes:

[0035] Using the updated rotor position angle θ j+1 Update the estimated value of the γδ axis inductance vector according to the table lookup method Then update the cost function.

[0036] Furthermore, the above-mentioned calculation of the convergence angle in the current motor control cycle using the improved Newton method includes:

[0037] The expression for calculating the convergence angle in the current motor control cycle is:

[0038]

[0039] in, is the convergence angle corrected by the improved Newton method in the current motor control cycle, θ N is the position angle obtained in the Nth iteration of the current motor control cycle, and ε″(·) is the second-order derivative of the cost function.

[0040] Furthermore, the above-mentioned convergence angle is differentiated and averaged to obtain the angular velocity estimate value include:

[0041]

[0042] Among them, T c is the length of a motor control cycle, k is the current motor control cycle number, and n is the total number of motor control cycles.

[0043] In order to ensure accurate estimation of the position signal and improve the motor operation performance, the present invention proposes a position sensorless control method for a synchronous reluctance motor based on a Newton-Raphson predictive phase-locked loop. The beneficial effects of the method are as follows:

[0044] 1. The present invention uses a flux observer method to estimate flux and uses HPF to filter out flux DC bias. In order to solve the phase delay and amplitude attenuation problems caused by HPF, the lagging phase angle corresponding to the fundamental frequency is calculated, and the flux estimation value is reconstructed using the rotation transformation method. The proposed method does not increase the complexity of the control system and improves the accuracy of flux observation.

[0045] 2. The predictive phase-locked loop synchronous reluctance motor position sensorless control method of the present invention has the advantages of no parameter setting and good dynamic performance. In view of the problem of many iterations and large amount of calculation in traditional PPLL, a Newton-Raphson based PPLL (NR-PPLL) method is proposed, which only needs three iterations to obtain the accurate angle position, reducing the amount of calculation. The proposed NR-PPLL method estimates the angle within one cycle, avoids the position coupling problem of the traditional observer, and improves the dynamic performance of the system.

[0046] 3. The present invention proposes a method with convergence angle correction, which solves the problem of incorrect convergence caused by inappropriate initial point selection in Newton's method. The proposed correction method is simple and does not increase the control complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is the flux linkage vector diagram of synchronous reluctance motor;

[0048] Figure 2 For PPLL in i s =0.5pu, θ=30°;

[0049] Figure 3 For s =0.5pu, θ=30°, schematic diagram of convergence angle and selected initial angle;

[0050] Figure 4 is a flow chart of NR-PPLL with position correction;

[0051] Figure 5 The schematic diagram of sensorless control using NR-PPLL;

[0052] Figure 6 Schematic diagram of experimental results under load variation conditions, where (a) represents the traditional PI-PLL and (b) represents the proposed NR-PPLL;

[0053] Figure 7 Schematic diagram of experimental results under variable speed conditions, where (a) represents the traditional PI-PLL and (b) represents the proposed NR-PPLL. DETAILED DESCRIPTION

[0054] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0055] Refer to the figure Figures 1 to 4 Specifically describing this embodiment, the synchronous motor position sensorless control method based on the Newton-Raphson predictive phase-locked loop described in this embodiment includes:

[0056] Step 1: Construct the stator voltage and flux equations of the synchronous reluctance motor in the αβ coordinate system.

[0057] The stator voltage equation of the synchronous reluctance motor in the αβ coordinate system is expressed as:

[0058]

[0059] in, is the αβ axis stator voltage vector, u α and u β α and β axis stator voltages respectively; R s is the resistor; is the αβ axis stator current vector, i α and i β α and β axis stator currents respectively; is the magnetic flux vector of αβ axis, and are the α and β axis flux respectively, and t is the time.

[0060] The magnetic flux equation of the synchronous reluctance motor in the αβ coordinate system is expressed as:

[0061]

[0062] Among them, L αβis the αβ axis inductance matrix, expressed as:

[0063] L αβ =T -1 (θ)L dq T(θ),

[0064] Among them, T(·) is the coordinate transformation matrix, and there is θ is the rotor position angle;

[0065] L dq =[L d 0;0L q ] is the dq axis inductance matrix, L d and L q They are the d-axis and q-axis inductances respectively.

[0066] Step 2: Based on the stator voltage and flux equations obtained in step 1, a flux observer is constructed to estimate the flux in the αβ coordinate system. A high-pass filter (HPF) is used to filter the DC bias of the flux estimate. The filtered flux estimate is reconstructed using phase lag to eliminate the flux estimation error caused by the HPF and obtain the effective flux.

[0067] The expression of the flux observer is:

[0068]

[0069] in, is the estimated value of the αβ axis magnetic flux vector, s is the Laplace operator, To estimate the DC bias of the stator flux.

[0070] HPF function G HPF The expression is:

[0071]

[0072] Among them, ω HPF is the corner frequency of the HPF.

[0073] The rotor position estimation error φ(ω) caused by phase lag is expressed as:

[0074]

[0075] in, is the angular frequency.

[0076] The equation for reconstructing the filtered flux estimation is:

[0077]

[0078] in, is the estimated value of angular frequency; is the estimated value of the reconstructed magnetic flux vector, and are the estimated values ​​of magnetic linkage after reconstruction for α and β axes, respectively; is the amplitude attenuation caused by the HPF, and

[0079] Step 3: Construct a predefined cost function using the angle as the control set 。

[0080] The cost function ε(θ i ) is expressed as:

[0081]

[0082] where ||·|| represents the Euclidean norm; θ i is the i-th angle in the control set; for The estimated value of is the magnetic flux vector of γδ axis; is the estimated value of the γδ axis current vector, and are the estimated values ​​of γ- and δ-axis currents, respectively; is the estimated value of the γδ axis inductance vector,

[0083] Step 4: Select the angle that minimizes the cost function as the estimated rotor position angle, expressed as: ε′(θ i )=0.

[0084] However, the angle of control concentration cannot fully meet the requirements of minimizing the cost function. In order to meet the requirements of minimizing the cost function as much as possible, the Newton-Raphson algorithm is used to improve the PPLL, and then find the rotor position angle that can be close to the requirements of minimizing the cost function. Figure 2 As shown in Figure 1, as the estimated angle increases, the flux estimated by the integrated voltage model rotates clockwise, while the flux calculated by the current model rotates counterclockwise. The difference between these two vectors is equal to When these two vectors are at θ i =30° or θ i =210°, the cost function is minimized. Figure 3 As shown, the convergence angle is related to the initial angle of iteration, so the relationship between the flux, cost function value and convergence angle at different initial angles is given.

[0085] Figure 4 The flow chart of NR-PPLL with position correction is given, specifically:

[0086] Assume that the number of iterations is j. In each motor control cycle, when j=0, the initial angle θ of the iteration in the current motor control cycle is 0 Select the convergence angle of the previous motor control cycle

[0087] Determine whether the number of iterations j in the current motor control cycle reaches the maximum number of iterations N of the Newton method.

[0088] If j does not reach N, the rotor position angle is updated using Newton's method:

[0089]

[0090] Among them, θ j is the rotor position angle obtained in the jth iteration of the current motor control cycle, θ j+1 is the updated rotor position angle, and ε″(·) is the second-order derivative of the cost function.

[0091] The inductance surface is obtained by current injection method, and the inductance table (LUTs) is generated by fitting. j+1 Update by table lookup Then update the cost function, set j=j+1, and re-judge whether j reaches N.

[0092] If j reaches N, the convergence angle is calculated using the modified Newton method with convergence angle correction effect:

[0093]

[0094] in, is the convergence angle corrected by the improved Newton method in the current motor control cycle, θ N It is the position angle obtained in the Nth iteration of the current motor control cycle.

[0095] Step 5, differentially averaging the convergence angle to obtain a speed estimate, and adding a low-pass filter (LPF) to filter the speed estimate, and using the filtered speed estimate to implement position sensorless control of the synchronous motor.

[0096] The convergence angle is differentiated and averaged to obtain a smoothed angular velocity estimate The expression is:

[0097]

[0098] Among them, T c is the length of a motor control cycle, k is the current motor control cycle number, and n is the total number of motor control cycles.

[0099] The LPF expression for the filtered velocity estimate is:

[0100]

[0101] Among them, ω LPF is the corner frequency of LPF.

[0102] To further illustrate the effectiveness of the method of the present invention and its specific implementation process, a specific implementation case of the method of the present invention is given. A 3-kW, two-pole synchronous reluctance motor is used as the experimental object, the control frequency is 10 kHz, and the number of Newton method iterations N is set to 3.

[0103] Figure 5 The sensorless control principle diagram using NR-PPLL is shown in Figure 2. The control strategy uses MTPA. The flux linkage is estimated based on the αβ axis reference voltage, and the estimated angular frequency is used to compensate for the distortion caused by HPF. The proposed NR-PPLL estimates the It avoids the position coupling problem of traditional observers and improves the dynamic performance of the system. Figure 6 and Figure 7 Experimental comparison of the proposed NR-PPLL method and the traditional PI-PLL method.

[0104] exist Figure 6 In the figure, the motor runs at 1500rpm and the load ranges from 0.5pu to 1p.u. Compared with PI-PLL, NR-PPLL has smaller transient speed and position estimation errors. The results show that the proposed NR-PPLL method can follow the speed reference faster.

[0105] exist Figure 7 In the figure, the load is 0.5pu and the speed increases from 1500rpm to 3000rpm. It can be seen that the position and speed estimation errors of PI-PLL are larger, and the speed estimation error remains constant during acceleration. This is because PI-PLL has a steady-state error when tracking the ramp speed, which in turn leads to a position estimation error. In contrast, the speed estimation error of the proposed method is zero except at the beginning and end of acceleration.

[0106] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the present invention. It should therefore be understood that many modifications may be made to the exemplary embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in a manner different from that described in the original claims. It should also be understood that the features described in conjunction with a single embodiment may be used in other described embodiments.

Claims

1. A synchronous motor position sensorless control method based on a Newton-Raphson predictive phase-locked loop, characterized in that: include: Observe the estimated value of the magnetic flux in the αβ coordinate system by using a magnetic flux observer, reconstruct the estimated value of the magnetic flux in the αβ coordinate system after high-pass filtering, obtain the effective magnetic flux in the αβ coordinate system, and construct a cost function based on the effective magnetic flux in the αβ coordinate system; When the number of iterations j does not reach the maximum number of iterations N in the current motor control cycle, the rotor position angle is updated using the Newton method based on the cost function, the cost function is updated using the updated rotor position angle, and then j=j+1 is set, and whether j reaches N is re-determined; When the number of iterations j in the current motor control cycle reaches the maximum number of iterations N, the convergence angle in the current motor control cycle is calculated using the improved Newton method, and then the convergence angle is differentially averaged to obtain the angular velocity estimate The speed estimate after low-pass filtering is used to realize the position sensorless control of synchronous motor.

2. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 1, characterized in that: The method for constructing the flux observer includes: The synchronous motor stator voltage and flux equations in the αβ coordinate system are constructed, and the flux observer is constructed using the synchronous motor stator voltage and flux equations. The expression of the flux observer is: in, is the estimated value of the magnetic flux vector along the αβ axis, s is the Laplace operator, u αβ is the αβ axis stator voltage vector, R s is the resistance, i αβ is the αβ axis stator current vector, To estimate the DC bias of the stator flux.

3. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 2, characterized in that: The stator voltage and flux equations of the synchronous motor in the αβ coordinate system are as follows: in, is the magnetic flux vector of αβ axis, L αβ is the αβ axis inductance matrix.

4. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 3, characterized in that: The αβ axis inductance matrix L αβ The expression is: L αβ =T -1 (i)L dq T(θ), Among them, T(·) is the coordinate transformation matrix, and there is θ is the rotor position angle, L dq is the dq axis inductance matrix, and L dq =[L d 0;0L q ], L d and L q They are the d-axis and q-axis inductances respectively.

5. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 1, characterized in that: The reconstructing the estimated magnetic flux of the αβ coordinate system after high-pass filtering to obtain the effective magnetic flux of the αβ coordinate system includes: The reconstructed equation is: in, is the estimated value of the reconstructed magnetic flux vector, is the estimated angular frequency, is the amplitude attenuation caused by the high-pass filter, and ω HPF is the corner frequency of the high-pass filter, T(·) is the coordinate transformation matrix, and is the estimated value of the magnetic flux vector on the αβ axis.

6. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 1, characterized in that: The cost function is constructed based on the effective magnetic flux of the αβ coordinate system, including: Taking the angle as the control set, construct a predefined cost function ε(·): Among them, ‖·‖ represents the Euclidean norm, θ i is the i-th angle in the control set, for The estimated value of is the magnetic flux vector of γδ axis, is the estimated value of the γδ axis current vector, is the estimated value of the inductance vector of the γδ axis, T(·) is the coordinate transformation matrix, and is the estimated value of the reconstructed magnetic flux vector, i αβ is the αβ-axis stator current vector.

7. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 6, characterized in that: The updating of the rotor position angle by using Newton's method based on the cost function comprises: The expression for updating the rotor position angle is: Among them, θ j is the rotor position angle obtained in the jth iteration of the current motor control cycle, θ j+1 is the updated rotor position angle, ε′(·) and ε″(·) are the first and second order derivatives of the cost function, respectively.

8. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 7, characterized in that: The updating of the cost function using the updated rotor position angle comprises: Using the updated rotor position angle θ j+1 Update the estimated value of the γδ axis inductance vector according to the table lookup method Then update the cost function.

9. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 6, characterized in that: The method of calculating the convergence angle in the current motor control cycle by using the improved Newton method includes: The expression for calculating the convergence angle in the current motor control cycle is: in, is the convergence angle corrected by the improved Newton method in the current motor control cycle, θ N is the position angle obtained in the Nth iteration of the current motor control cycle, and ε″(·) is the second-order derivative of the cost function.

10. The method for controlling a synchronous motor without position sensor based on a Newton-Raphson predictive phase-locked loop according to claim 9, characterized in that: The convergence angle is differentiated and averaged to obtain an angular velocity estimate include: Among them, T c is the length of a motor control cycle, k is the current motor control cycle number, and n is the total number of motor control cycles.

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