Synchronous motor sensorless control method based on newton-raphson predictive phase-locked loop

Abstract

The application relates to a synchronous motor position sensorless control method based on a Newton-Raphson prediction phase-locked loop and relates to the technical field of motor control.The application is aimed at solving the problems of the existing position sensorless control method, i.e., the additional loss and noise caused by the high-frequency signal injection in extracting the position signal and the poor dynamic performance caused by the traditional phase-locked loop technology, and the problem of a large number of iterative operations required for solving the cost function of the prediction phase-locked loop technology.The application observes the alpha-beta coordinate system flux linkage estimation value, reconstructs the filtered alpha-beta coordinate system flux linkage estimation value, and further constructs a cost function; when the number of iterations in the current motor control period does not reach the maximum, the rotor position angle is updated by using the Newton method, and the cost function is further updated; when the number of iterations in the current motor control period reaches the maximum, the improved Newton method is used to calculate the convergence angle in the current motor control period and to calculate the angular velocity estimation value, so that the position sensorless control of the synchronous motor is realized.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology. Background Technology

[0002] Synchronous reluctance motors (SynRMs) are characterized by their simple structure, low cost, and suitability for high-temperature and high-speed applications, making them an ideal replacement for mainstream induction motors in industrial drives and electric vehicles. Obtaining accurate rotor position information is crucial for achieving high-performance synchronous reluctance motor control. However, the use of position sensors increases costs and the complexity of the control system; therefore, researching sensorless control methods for synchronous reluctance motors is of practical significance.

[0003] Currently, sensorless control methods mainly fall into two categories: high-frequency injection-based methods and basic model-based methods. High-frequency injection-based methods instantaneously excite the motor by injecting an additional high-frequency (HF) signal and estimate the rotor position by detecting the spatial orientation of the induced HF current. However, HF signal injection inevitably introduces additional losses and noise. Furthermore, saliency-based methods are only applicable to zero-speed and low-speed ranges.

[0004] To extend the operating range of sensorless motors, a basic model-based approach suitable for medium to high speeds has been proposed. This approach estimates the stator flux linkage of the motor and then uses a phase-locked loop (PLL)-based position observer to detect position and velocity. Among these observers, the proportional-integral (PI-PLL) based PLL is widely used due to its simple structure. However, PI-PLLs use a fixed controller gain, requiring iterative experimental adjustments to achieve satisfactory performance. Furthermore, fixed-gain PI-PLLs exhibit poor dynamic performance due to their inherent linearity and limited bandwidth.

[0005] In recent years, the idea of ​​predicting cost functions using finite control set models has been applied to sensorless systems to improve dynamic performance, leading to the development of Predictive Phase-Locked Loop (PPLL) technology. PPLLs offer advantages such as good dynamic performance and no need for parameter tuning. However, PPLLs require numerous iterations to search for the optimal position that minimizes the cost function, and this increased computational cost limits their application in low-cost controllers. Therefore, researching sensorless PLL technology that ensures convergence and speed is of practical significance.

[0006] Based on the introduction of the above background art, it can be known that the current position sensorless control method is limited in extracting position signal by extra loss and noise caused by high frequency signal injection and poor dynamic performance caused by traditional phase-locked loop technology. The predictive phase-locked loop technology avoids complex parameter setting and improves the dynamic performance of the system, but a large number of iterative operations are required to solve the cost function. SUMMARY

[0007] The present application is to solve the problem that the current position sensorless control method is limited in extracting position signal by extra loss and noise caused by high frequency signal injection and poor dynamic performance caused by traditional phase-locked loop technology, and a large number of iterative operations are required to solve the cost function of the predictive phase-locked loop technology, and the present application provides a synchronous motor position sensorless control method based on Newton-Raphson predictive phase-locked loop.

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

[0009] The flux observer is used to observe the αβ coordinate system flux estimation value, the αβ coordinate system flux estimation value after high-pass filtering is reconstructed to obtain the αβ coordinate system effective flux, and the cost function is constructed based on the αβ coordinate system effective flux;

[0010] When the iteration number j in the current motor control period does not reach the maximum iteration number N, the rotor position angle is updated based on the cost function by using Newton method, the cost function is updated by using the updated rotor position angle, then j is set to j+1, and whether j reaches N is re-judged;

[0011] When the iteration number j in the current motor control period reaches the maximum iteration number N, the convergence angle in the current motor control period is calculated by using the improved Newton method, and then the convergence angle is differentiated and averaged to obtain the angular velocity estimation value The low-pass filtered speed estimation value is used to realize the position sensorless control of the synchronous motor.

[0012] Further, the construction method of the flux observer comprises:

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

[0014]

[0015] Wherein, is the αβ axis flux vector estimation value, s is the Laplace operator, u αβ is the αβ axis stator voltage vector, R s is the resistance, i αβis the stator current vector of the αβ axis, is the DC bias of the stator flux linkage.

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

[0017]

[0018] wherein, is the flux linkage vector of the αβ axis, L αβ is the inductance matrix of the αβ axis.

[0019] Further, the inductance matrix L αβ of the αβ axis is expressed as:

[0020] L αβ = T -1 (θ) L dq T(θ),

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

[0022] Further, the effective flux linkage in the αβ coordinate system is obtained by reconstructing the high-pass filtered flux linkage estimation value in the αβ coordinate system, including:

[0023] The reconstruction equation is:

[0024]

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

[0026] Further, the cost function is constructed based on the effective flux linkage in the αβ coordinate system, including:

[0027] The predefined cost function ε(·) is constructed with the angle as the control set:

[0028]

[0029] where ||·|| denotes the Euclidean norm, θ i is the i-th angle of the control set, is the estimated value of is the γδ-axis flux linkage vector, is the γδ-axis current vector estimate, is the γδ-axis inductance vector estimate, T(·) is a coordinate transformation matrix, and has is the reconstructed flux linkage vector estimate, i αβ is the αβ-axis stator current vector.

[0030] Further, the above updating the rotor position angle based on the cost function using Newton method comprises:

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

[0032]

[0033] where θ j is the rotor position angle obtained in the j-th iteration in the current motor control period, θ j+1 is the updated rotor position angle, and ε'(·) and ε"(·) are the first and second order derivatives of the cost function, respectively.

[0034] Further, the above updating the cost function using the updated rotor position angle comprises:

[0035] The updated rotor position angle θ j+1 is used to update the γδ-axis inductance vector estimate and further update the cost function.

[0036] Further, the above calculating the convergence angle in the current motor control period using the improved Newton method comprises:

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

[0038]

[0039] where θ is the corrected convergence angle in the current motor control period using the improved Newton method, θ N is the position angle obtained in the N-th iteration in the current motor control period, and ε"(·) is the second order derivative of the cost function.

[0040] Further, the above obtaining the angular velocity estimate by differentiating the convergence angle comprises: including:

[0041]

[0042] wherein, 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 application proposes a Newton-Raphson prediction phase-locked loop synchronous reluctance motor position sensorless control method, which has the following beneficial effects:

[0044] 1. The application estimates the flux linkage by using a flux linkage observer and uses HPF to filter the direct current bias of the flux linkage. In view of the phase delay and amplitude attenuation problems caused by HPF, the lagging phase angle corresponding to the fundamental frequency is calculated, and the method of rotation transformation is used to reconstruct the flux linkage estimation value. The proposed method does not increase the complexity of the control system and improves the accuracy of flux linkage observation.

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

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

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

[0048] Figure 2 is the principle diagram of PPLL when i s = 0.5 p.u, θ = 30°;

[0049] Figure 3 is the schematic diagram of the convergence angle and the selected initial angle when i s = 0.5 p.u, θ = 30°;

[0050] Figure 4 is the NR-PPLL flowchart with position correction;

[0051] Figure 5 is the sensorless control principle diagram using NR-PPLL;

[0052] Figure 6 Fig. 2 is a schematic diagram of experimental results under load variation conditions, wherein (a) represents a conventional PI-PLL, and (b) represents the proposed NR-PPLL;

[0053] Figure 7 Fig. 3 is a schematic diagram of experimental results under variable speed conditions, wherein (a) represents a conventional PI-PLL, and (b) represents the proposed NR-PPLL. DETAILED DESCRIPTION

[0054] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application. It should be noted that, in the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0055] Referring to the drawings Figures 1 to 4 To specifically describe the present embodiment, the synchronization motor sensorless control method based on Newton-Raphson predictive phase-locked loop in the present embodiment comprises:

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

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

[0058]

[0059] wherein, is the stator voltage vector of the αβ axis, u α and u β are the stator voltages of the α and β axes respectively, R s is the resistance; is the stator current vector of the αβ axis, i α and i β are the stator currents of the α and β axes respectively; is the flux linkage vector of the αβ axis, and are the flux linkages of the α and β axes respectively, t is time.

[0060] The expression of the flux linkage equation of the synchronous reluctance motor in the αβ coordinate system is:

[0061]

[0062] wherein, L αβis the inductance matrix in αβ axis, which is denoted as:

[0063] L αβ = T -1 (θ) L dq T(θ),

[0064] where T(·) is the coordinate transformation matrix, and has θ is the rotor position angle;

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

[0066] Step 2, according to the stator voltage and flux linkage equations obtained in step 1, construct a flux linkage observer, and then estimate the αβ coordinate system flux linkage. Use a high-pass filter (HPF) to filter the direct current bias of the flux linkage estimation value. Use phase lag to reconstruct the filtered flux linkage estimation value to eliminate the flux linkage estimation error caused by HPF, and obtain the effective flux linkage.

[0067] The expression of the flux linkage observer is:

[0068]

[0069] where, is the αβ axis flux linkage vector estimation value, s is the Laplace operator, is the direct current bias of the estimated stator flux linkage.

[0070] The expression of the HPF function G HPF is:

[0071]

[0072] where ω HPF is the turning frequency of the HPF.

[0073] The expression of the rotor position estimation error φ(ω) caused by phase lag is:

[0074]

[0075] where, is the angular frequency.

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

[0077]

[0078] where, is the angular frequency estimation value; are the reconstructed flux estimates for the α and β axes respectively; are the reconstructed flux estimates for the α and β axes respectively; is the amplitude attenuation caused by the HPF, and has

[0079] Step 3, construct a predefined cost function with the angle as the control set 。

[0080] The PPLL-pre-designed 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; is the estimate of , is the flux vector of the γδ axis; is the current vector estimate of the γδ axis, are the current estimates of the γ and δ axes respectively;

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

[0084] However, the angles in the control set cannot fully meet the requirement of minimizing the cost function. In order to meet the requirement 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 meet the requirement of minimizing the cost function. As shown in Figure 2 , with the increase of the estimated angle, the flux estimated by the integral voltage model rotates clockwise, while the flux calculated by the current model rotates counterclockwise. The difference between the two vectors is equal to When the two vectors coincide at θ i = 30° or θ i = 210°, the cost function is minimized. As shown in Figure 3 , the convergence angle is related to the initial angle of iteration, so the relationship between the flux, the cost function value and the convergence angle under different initial angles is given.

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

[0086] Let the iteration number be j, in each motor control period, when j = 0, the initial angle θ0 of the iteration in the current motor control period is selected as the convergence angle in the last motor control period

[0087] Judge whether the iteration number j in the current motor control period reaches the maximum iteration number N of Newton method.

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

[0089]

[0090] Where, θj is the rotor position angle obtained in the jth iteration in the current motor control period, θj+1 is the updated rotor position angle, and ε"(·) is the second derivative of the cost function. j j+1

[0091] The inductance surface is obtained by current injection method, and the inductance table (LUT) is generated by fitting, and the updated position angle θj+1 is used to update j+1 and then make j = j + 1, and judge whether j reaches N.

[0092] If j reaches N, the improved Newton method with convergence angle correction effect is used to calculate the convergence angle:

[0093]

[0094] Where, θk is the corrected convergence angle in the current motor control period by using the improved Newton method, and θN is the position angle obtained in the Nth iteration in the current motor control period. N

[0095] Step 5, differential average the convergence angle to obtain the speed estimation value, add a low-pass filter (LPF) to filter the speed estimation value, and use the filtered speed estimation value to realize the position sensorless control of the synchronous motor.

[0096] The expression of the smooth angular velocity estimation value is as follows:

[0097]

[0098] Where, T is the length of one motor control period, k is the current motor control period number, and n is the total number of motor control periods. c

[0099] The expression of the LPF filtering the speed estimation value is as follows: ​​​​​​

[0100]

[0101] where ω LPF is the cut-off frequency of the LPF.

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

[0103] Figure 5 The sensorless control principle diagram using the NR-PPLL is shown, and the control strategy uses MTPA. The flux linkage is estimated according to the αβ-axis reference voltage, and the estimated angular frequency is used to compensate for the distortion caused by the HPF. The proposed NR-PPLL estimates the position and speed in one period, avoiding the position coupling problem of the traditional observer and improving the dynamic performance of the system. Figure 6 and Figure 7 The experimental comparison of the proposed NR-PPLL method and the traditional PI-PLL method is shown.

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

[0105] In Figure 7 , the load is 0.5 p.u, and the speed increases from 1500 rpm to 3000 rpm. It can be seen that the position and speed estimation errors of the PI-PLL are larger, and the speed estimation error remains constant during acceleration. This is because the 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 application is described herein with reference to particular embodiments thereof, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present application. It is therefore to be understood that numerous modifications can be made to the illustrative embodiments and that other arrangements can be devised without departing from the spirit and scope of the present application as defined by the appended claims. It is to be understood that the features of the dependent claims can be combined with those of the parent application in any way without departing from the spirit and scope of the present application. It is also to be understood that features described in relation to one embodiment can be used in other embodiments.

Claims

1. A method of sensorless control of a synchronous machine based on a Newton-Raphson predicted phase-locked loop, characterized in that, Comprise: Observe flux linkage by using flux linkage observer Coordinate system flux linkage estimation value, high-pass filtered Coordinate system flux linkage estimation value is reconstructed, and Coordinate system effective flux linkage, based on the Coordinate system effective flux linkage to construct cost function; number of iterations in the current motor control cycle maximum number of iterations is not reached the rotor position angle is updated using Newton method based on the cost function, the cost function is updated using the updated rotor position angle, and then it is determined again whether the maximum number of iterations is reached ; number of iterations in the current motor control cycle reaches a maximum number of iterations , the improved Newton method is used to calculate the convergence angle under the current motor control cycle, and then the convergence angle is differentially averaged to obtain an angular velocity estimation value , and the low-pass filtered speed estimation value is used to realize the position sensorless control of the synchronous motor; The method comprises the following steps: The coordinate system effective flux linkage construction cost function comprises: constructing a predefined cost function with angles as control set : ， wherein denotes the Euclidean norm, is the i-th element of the control set, is the i-th angle, is the estimate of is the estimate of is the estimate of is the estimate of is the estimate of is the estimate of is the estimate of is the estimate of is the coordinate transformation matrix and has , is the estimate of the reconstructed flux vector, is the estimate of is the estimate of the stator current vector; The cost function is updated by using the updated rotor position angle, comprising: Updating a rotor position angle updating according to a look-up table axial inductance vector estimate and updating the cost function The convergence angle in the current motor control period is calculated by using the improved Newton method, comprising: The expression for calculating the convergence angle in the current motor control period is: ， wherein, is the converged angle corrected by the improved Newton method in the current motor control cycle, is the position angle obtained in the first iteration in the current motor control cycle, is the position angle obtained in the first iteration in the current motor control cycle, is the second derivative of the cost function.

2. The Newton-Raphson prediction-based phase-locked loop based synchronous motor sensorless control method according to claim 1, characterized in that, The construction method of the flux observer comprises: Construction The synchronous motor stator voltage and flux linkage equations in the coordinate system are constructed, and a flux linkage observer is constructed using the synchronous motor stator voltage and flux linkage equations. The expression of the flux linkage observer is: ， wherein is axis flux linkage vector estimate, is the Laplacian operator, is axis stator voltage vector, is the resistance, is axis stator current vector, is the DC offset of the estimated stator flux linkage.

3. The Newton-Raphson prediction PLL based sensorless control method of synchronous machines according to claim 2, characterized in that, The The equations of stator voltage and flux linkage of synchronous machine in the coordinate system are as follows: ， ， wherein is the axis flux linkage vector, is the axis inductance matrix.

4. The Newton-Raphson prediction PLL based sensorless control method of synchronous machines according to claim 3, characterized in that, Axial inductance matrix The expression for the axial inductance matrix is ， wherein is the coordinate transformation matrix and has , is the rotor position angle, is the axis inductance matrix and has , and are the axis and axis inductance.

5. The Newton-Raphson prediction PLL based sensorless control method of synchronous machines according to claim 1, characterized in that, The high-pass filtered reconstructing the coordinate system flux linkage estimate to obtain a coordinate system effective flux linkage, comprising: The equation is reconstructed as: ， wherein is the reconstructed flux vector estimate, is the angular frequency estimate, is the amplitude attenuation caused by the high-pass filter, and has , is the cut-off frequency of the high-pass filter, is the coordinate transformation matrix, and has , , is the axis flux vector estimate.

6. The Newton-Raphson prediction PLL based sensorless control method of synchronous machines according to claim 1, characterized in that, The rotor position angle is updated by using the Newton method based on the cost function, comprising: The expression for updating the rotor position angle is: ， wherein, is the rotor position angle obtained at the ith iteration for the current motor control cycle, is the updated rotor position angle, and are the first and second derivatives of the cost function, respectively.

7. The Newton-Raphson prediction PLL based sensorless control method of synchronous machines according to claim 1, characterized in that, differential averaging of the convergence angle yields an angular velocity estimate comprising: ， wherein, is the length of one motor control cycle, is the current motor control cycle number, is the total number of motor control cycles.

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