Phase-locked loop control method of permanent magnet auxiliary synchronous reluctance motor
The finite position set phase-locked loop control method designed by inverse quadratic interpolation reduces the number of iterations and computational burden of permanent magnet assisted synchronous reluctance motors, achieves high-precision position and speed estimation, and solves the problems of computational complexity and poor dynamic response of traditional methods. It is applicable to fields such as electric vehicles and aerospace.
Patent Information
- Application Number
- CN202511939878.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-22
- Publication Date
- 2026-03-17
AI Technical Summary
Existing phase-locked loop control methods for permanent magnet assisted synchronous reluctance motors have a heavy computational burden, require many iterations, and are difficult to reduce computational complexity while maintaining high accuracy, and also have poor dynamic response.
A finite position set phase-locked loop (IQI-FPS-PLL) is designed using the inverse quadratic interpolation (IQI) method. By constructing a nonlinear flux observer and iteratively solving the problem using the inverse quadratic interpolation method, high-precision position estimation can be achieved in just 4 iterations. Combined with a low-pass filter to process speed estimation, it is integrated into the motor vector control system.
It significantly reduces the computational burden, improves dynamic response speed and steady-state accuracy, overcomes the trade-off between computational complexity and accuracy in traditional methods, and achieves sub-millisecond response speed and anti-interference capability.
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Figure CN121689949A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application relates to the technical field of motor control, in particular to a phase-locked loop control method for a permanent magnet assisted synchronous reluctance motor. BACKGROUND
[0002] The permanent magnet assisted synchronous reluctance motor (PMaSynRM) is widely used in electric vehicles and aerospace fields due to its wide speed range, low cost and high fault tolerance. To achieve high-performance vector control, the rotor position and speed information need to be obtained in real time. The traditional method relies on mechanical position sensors, but such sensors increase system cost, occupy space, need frequent maintenance and are susceptible to electromagnetic interference, which reduces system reliability. The position sensorless control technology can effectively avoid the above problems.
[0003] The flux linkage observer estimates the flux linkage by integrating the back electromotive force, but there is a problem of DC bias and integral drift. The nonlinear flux linkage observer can suppress the adverse effects of integration through error compensation. When extracting the rotor position from the flux linkage, the traditional phase-locked loop (PLL) uses a PI regulator, which has the problems of complex parameter tuning, limited bandwidth and poor dynamic response. In recent years, finite control set model predictive control (FCS-MPC) has been applied to position estimation due to its good dynamic performance, and finite position set phase-locked loop (FPS-PLL) has been derived. However, the existing FPS-PLL method requires multiple iterations to achieve high accuracy, which increases the computational burden, and there is a trade-off between accuracy and computational complexity. Therefore, a position sensorless phase-locked loop control method is needed that can significantly reduce the number of iterations and computational burden while maintaining high accuracy. SUMMARY
[0004] The purpose of the application is to provide a phase-locked loop control method for a permanent magnet assisted synchronous reluctance motor, which significantly reduces the number of iterations and computational burden through inverse quadratic interpolation (IQI), limits the position error to a very low level with only 4 iterations, and does not require parameter adjustment, with excellent dynamic performance and steady-state accuracy.
[0005] To achieve the above purpose, the application provides a phase-locked loop control method for a permanent magnet assisted synchronous reluctance motor, comprising the following steps: S1, constructing a nonlinear flux linkage observer based on the mathematical model of the permanent magnet assisted synchronous reluctance motor, obtaining the estimated value of the flux linkage of the axis; S2, designing a limited position set phase-locked loop based on inverse quadratic interpolation method, including constructing a cost function for rotor position estimation based on the estimated flux linkage, iteratively solving the cost function by inverse quadratic interpolation method, and outputting the estimated value of the rotor position after a fixed number of iterations; S3, performing differential operation on the estimated value of the rotor position, and obtaining the estimated value of the rotor speed by processing the differential result through a low-pass filter; S4, integrating the nonlinear flux linkage observer and the limited position set phase-locked loop based on the inverse quadratic interpolation method into the motor vector control system to realize sensorless control.
[0006] Preferably, the mathematical model of the permanent magnet assisted synchronous reluctance motor in S1 includes: the voltage equation of the permanent magnet assisted synchronous reluctance motor in the stationary coordinate system: ; the flux linkage equation in the stationary coordinate system: ; the flux linkage equation in the rotating coordinate system: ; wherein, , , , , , are respectively the motor voltage, current and flux linkage of the axis and axis, , , , are respectively the current and flux linkage of the axis and axis, is the stator resistance, is the motor electrical angular velocity, is the motor rotor position, is the active flux linkage; ; wherein, is the permanent magnet flux linkage, and are respectively the inductance of the axis and axis.
[0007] Preferably, the specific process of constructing the nonlinear flux observer in S1 is as follows: a. Based on The flux linkage equation of the axis defines the state variables. And on Perform differentiation; ; ; in, for Axial magnetic flux, for Axial magnetic flux, for The derivative; b. Define output variables ; ; in, for The actual value of the rate of change of the shaft flux linkage. for The actual value of the rate of change of the shaft flux linkage; c. Constructing intermediate variables for a nonlinear flux observer ; ; in, for Rotor flux linkage component of shaft, for Rotor flux linkage component of shaft, for Estimated value of shaft flux linkage, for Estimated value of shaft flux linkage; d. Establish the physical constraints for the nonlinear flux observer; ; e. Construct the nonlinear flux observer equations and expand them to obtain... Axial components; ; ; in, For observer gain, for The axis estimates the rate of change of flux linkage. for The axis is used to estimate the rate of change of magnetic flux; f. Discretize the nonlinear flux observer equations to obtain shaft and Estimated value of shaft flux linkage and .
[0008] Preferably, the cost function constructed in S2 includes: Theoretically, the cost function is constructed based on the rotor position error: ; wherein, is the output value of the cost function for rotor position estimation, is the position estimation error, is the actual rotor position, is the estimated rotor position; In actual implementation, the cost function is specifically implemented as: ; wherein, is the candidate rotor position angle, when the value of obtains the estimated rotor position .
[0009] Preferably, the specific steps of iteratively solving the cost function in S2 by using the inverse quadratic interpolation method are as follows: S21, select three different initial angle values , , as the iteration starting point; S22, calculate the cost function , , corresponding to the three angle values to obtain , , ; S23, calculate the new angle estimation value by using the inverse quadratic interpolation method, and the specific formula is as follows: ; S24, update the iteration point, replace one of the current three iteration points with , and keep the latest three points as the starting point for the next round of iteration; S25, repeat the above steps S22-S24 for a fixed number of iterations.
[0010] Preferably, the fixed number of iterations in S25 is 4 times.
[0011] Preferably, the motor vector control system in S4 includes a speed loop, a current loop, a coordinate transformation, and a space vector pulse width modulation module.
[0012] Therefore, the application adopts the phase-locked loop control method of the permanent magnet auxiliary synchronous reluctance motor, and has the following beneficial effects. (1) The IQI-FPS-PLL based on the inverse quadratic interpolation method can limit the position estimation error to a very low level only by 4 iterations, significantly reduces the calculation burden, solves the trade-off problem between accuracy and calculation complexity of the traditional FPS-PLL method, and still maintains sub-millisecond response speed when the speed suddenly changes and the load changes, overcoming the problem of poor dynamic response of the traditional phase-locked loop due to limited bandwidth.
[0013] (2) The nonlinear flux linkage observer constructed in the application effectively suppresses the DC bias and integral drift by introducing physical constraint conditions and feedback correction mechanism, improves the accuracy of flux linkage estimation and system robustness; the position estimation process based on the inverse quadratic interpolation method does not depend on the PI regulator, avoids the complex parameter setting process in the traditional phase-locked loop, simplifies the system debugging, and improves the engineering applicability.
[0014] (3) The application fixes the number of iterations to 4 times under the premise of ensuring high estimation accuracy, greatly reduces the processor calculation load, and is conducive to realizing high-frequency control cycle in high dynamic application scenarios; the method has clear structure and good portability, and can be extended for full-speed range position sensorless control of other types of alternating current motors (such as permanent magnet synchronous motor and induction motor).
[0015] The technical solutions of the application will be further described in detail below with the help of the drawings and examples. DESCRIPTION OF DRAWINGS
[0016] Figure 1 The application is a phase-locked loop control method of a permanent magnet auxiliary synchronous reluctance motor. Figure 2 The application is a phase-locked loop control method of a permanent magnet auxiliary synchronous reluctance motor. Figure 3 The application is a phase-locked loop control method of a permanent magnet auxiliary synchronous reluctance motor, and the traditional PI-PLL speed change dynamic performance simulation comparison diagram, wherein (a) is the traditional PI-PLL, and (b) is the IQI-FPS-PLL of the application. Figure 4 The application is a phase-locked loop control method of a permanent magnet auxiliary synchronous reluctance motor, and the traditional PI-PLL load mutation dynamic performance simulation comparison diagram, wherein (a) is the traditional PI-PLL, and (b) is the IQI-FPS-PLL of the application. DETAILED DESCRIPTION
[0017] The following detailed description of embodiments of the application provided in the accompanying drawings is not intended to limit the scope of the application as claimed, but merely to provide selected embodiments of the application. Based upon the embodiments in the present application, all other embodiments that a person of ordinary skill in the art obtains without creative work under the premise that the scope of the present application is obtained.
[0018] Embodiments As shown in the drawings, the present application provides a phase-locked loop control method of a permanent magnet auxiliary synchronous reluctance motor, comprising the following steps: Figure 1 In each control cycle, the current of the motor is collected by a current sensor, and the voltage is reconstructed by measuring the DC bus voltage and the inverter switch state. Then, the current and voltage are converted to the stationary two-phase coordinate system by Clark transformation, obtaining the voltage signal and current signal required by the algorithm directly, and providing input for subsequent algorithms.
[0019] S1, a nonlinear flux linkage observer is constructed based on the mathematical model of the permanent magnet auxiliary synchronous reluctance motor, and the estimated values of the axis and axis flux linkage are obtained; A simulation model of the permanent magnet auxiliary synchronous reluctance motor is built based on MATLAB / Simulink, and the mathematical model of the permanent magnet auxiliary synchronous reluctance motor includes: The voltage equation of the permanent magnet auxiliary synchronous reluctance motor in the stationary coordinate system: ; The flux linkage equation in the stationary coordinate system: ; The flux linkage equation in the rotating coordinate system: ; Wherein, , , , , , are the motor voltage, current and flux linkage of the axis and axis, , , , are the current and flux linkage of the axis and axis, is the stator resistance, is the motor electrical angular velocity, For the rotor position of the motor, For the active flux linkage; ; Where, For the permanent magnet flux linkage, And Respectively, Inductance of the axis and axis.
[0020] Construct a nonlinear flux linkage observer to estimate the flux linkage through state variables and output variables, and avoid the problem of integral drift, the specific process is: a. Based on the flux linkage equation of the axis, define the state variable and take the derivative of ; ; Where, For the axis flux linkage, For the axis flux linkage, For the derivative of ; b. Define the output variable ; ; Where, For the actual value of the axis flux linkage rate of change, For the actual value of the axis flux linkage rate of change; c. Construct the intermediate variable of the nonlinear flux linkage observer ; ; Where, For the axis rotor flux linkage component, For the axis rotor flux linkage component, For the estimated value of the axis flux linkage, For the estimated value of the axis flux linkage; d. Establish the physical constraint condition of the nonlinear flux linkage observer; ; e. Construct the nonlinear flux linkage observer equation, and expand to get axis component; ; ; where, is the observer gain, is the estimated rate of change of flux in the d-axis, is the estimated rate of change of flux in the d-axis; f. Discretize the nonlinear flux observer equation to get the estimated value of flux in the d-axis and the estimated value of flux in the q-axis and .
[0021] The nonlinear flux observer estimates the flux in the d-axis from the voltage equation and the flux equation, compensating for the integral error.
[0022] S2, design a finite set of position phase-locked loop based on inverse quadratic interpolation method, including constructing a cost function for rotor position estimation based on the estimated flux, using inverse quadratic interpolation method to iteratively solve the cost function, after a fixed number of iterations, output the estimated value of the rotor position .
[0023] The constructed cost function includes: Theoretically defined, based on the rotor position error to construct the cost function: ; where, is the output value of the cost function for rotor position estimation, is the position estimation error, is the actual rotor position, is the estimated rotor position; Actually implemented, in the algorithm execution, the cost function is specifically implemented by the estimated flux: ; where, is the candidate rotor position angle, when the value of the cost function is obtained .
[0024] As shown in Figure 2 , the specific steps of using inverse quadratic interpolation method to iteratively solve the cost function are as follows: S21, select three different initial angle values , , as the starting point of iteration; S22, calculate the cost function , , corresponding to the three angle values 、 、 ; S23, calculate a new angle estimation value by using inverse quadratic interpolation method, and the specific formula is as follows: ; S24, update the iteration points, replace one of the current three iteration points with , and keep the latest three points as the starting point of the next iteration; S25, repeat the above steps S22-S24 for a fixed number of iterations, and the fixed number of iterations is 4 times.
[0025] S3, perform a differential operation on the rotor position estimation value , and obtain a rotor speed estimation value by processing the differential result through a low-pass filter, and the low-pass filter is used to suppress differential noise.
[0026] S4, integrate the nonlinear flux observer and the IQI-FPS-PLL based on the inverse quadratic interpolation method as a "position sensorless module" into the motor vector control system, and the motor vector control system is a double closed-loop structure, including a speed loop, a current loop, a coordinate transformation and a space vector pulse width modulation (SVPWM) module, to realize position sensorless control.
[0027] In this embodiment, the rotor position estimation value and the speed estimation value obtained by the position sensorless module are used as the angle input of the coordinate transformation and the feedback signal of the speed loop, respectively, so as to replace the physical sensor, so that the motor vector control system realizes closed-loop control through the speed loop, the current loop, the coordinate transformation and the SVPWM module without the need of a mechanical position sensor. This embodiment can be applied to the motor control related fields such as electric vehicle driving system, industrial frequency converter and aerospace, and realizes efficient and reliable position sensorless control.
[0028] To verify the effectiveness and superiority of the method of this embodiment, system simulation is carried out in the MATLAB / Simulink environment, and this embodiment is compared and analyzed with the traditional PI-PLL based on PI regulator.
[0029] To prove the fast convergence property of the inverse quadratic interpolation method (IQI), tests are carried out under different actual rotor positions, the position estimation errors after 4 iterations from the same set of initial values are recorded, and the results are shown in the following table: Table 1 Theoretical error after 4 iterations under different initial values
[0030] As can be seen from the above table, only 4 iterations are needed, and the position estimation error of the method of the application can be reduced to 10 -8 rad level or even lower, achieving extremely high steady-state estimation accuracy. This fully proves the significant advantages of the application in convergence speed and calculation efficiency, and solves the trade-off between accuracy and calculation complexity of the traditional FPS-PLL method with fixed and extremely small number of iterations.
[0031] In order to evaluate the performance of the embodiment under dynamic conditions, simulation tests of speed mutation and load mutation are carried out.
[0032] As shown in Figure 3 When the motor speed occurs step change, the response speed of the method of the embodiment is obviously faster than that of the traditional PI-PLL, the overshoot is smaller, and the speed command can be tracked faster, showing better dynamic response performance.
[0033] As shown in Figure 4 When the motor load changes suddenly, the position estimation of the traditional PI-PLL method will have obvious fluctuations and long recovery time, while the position estimation curve of the method of the embodiment fluctuates less and can quickly recover to stable, showing stronger anti-interference ability and robustness.
[0034] Therefore, the application adopts the above-mentioned phase-locked loop control method of the permanent magnet auxiliary synchronous reluctance motor, realizes high-precision position estimation in 4 iterations through inverse quadratic interpolation, and solves the problem of heavy calculation burden and slow dynamic response of the traditional method; the method does not need parameter tuning and has strong robustness, providing an innovative solution for high-performance motor drive.
[0035] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the application but not to limit it, although the application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the application can still be modified or replaced by equivalents, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the application.
Claims
1. A phase-locked loop control method of a permanent magnet assisted synchronous reluctance machine, characterized by, The method comprises the following steps: S1, a nonlinear flux linkage observer is constructed based on the mathematical model of the permanent magnet auxiliary synchronous reluctance motor, and the axis and estimated value of the axis flux linkage; S2, designing a limited position set phase-locked loop based on inverse quadratic interpolation method, comprising constructing a cost function for rotor position estimation based on estimated flux linkage, iteratively solving the cost function by using inverse quadratic interpolation method, and outputting the estimated value of rotor position after a fixed number of iterations; S3, performing differential operation on the estimated value of rotor position, processing the differential result through a low-pass filter to obtain the estimated value of rotor speed; S4, integrating the nonlinear flux linkage observer and the limited position set phase-locked loop based on inverse quadratic interpolation method into a motor vector control system to realize position sensorless control.
2. The phase-locked loop control method of a permanent magnet assisted synchronous reluctance motor according to claim 1, characterized in that, The mathematical model of the permanent magnet auxiliary synchronous reluctance motor in S1 comprises: In the stationary Voltage equation of PMSynRM in stationary coordinate system: ； In the stationary Equation of flux linkage in the stationary coordinate system: ； In rotation Equation of flux linkage in the rotating coordinate system: ； wherein , , , , , are the motor voltages, currents and fluxes of the axis and axis, respectively, , , , are the currents and fluxes of the axis and axis, respectively, is the stator resistance, is the motor electrical angular velocity, is the motor rotor position, is the active flux; ； wherein, is the permanent magnet flux linkage, and are the inductances of the axis and axis, respectively.
3. The phase-locked loop control method of a permanent magnet assisted synchronous reluctance motor according to claim 2, characterized in that, The specific process of constructing the nonlinear flux linkage observer in S1 is as follows: a. based on Equation of flux linkage of the shaft defines the state variable and to derivation; ； ； wherein is axial flux, is axial flux, is derivative; b. define output variables ; ； wherein is the actual value of the rate of change of the shaft flux linkage, is the actual value of the rate of change of the shaft flux linkage; c. constructing intermediate variables for a nonlinear flux linkage observer ; ； wherein is a rotor flux component, is a rotor flux component, is an estimate of the shaft flux, is an estimate of the shaft flux; d. Establishing the physical constraint condition of the nonlinear flux linkage observer; ； e. Constructing the nonlinear flux linkage observer equation, which is expanded to axial component; ； ； wherein, is an observer gain, is is a rate of change of the flux linkage estimated by the axis, is is a rate of change of the flux linkage estimated by the axis; f.The nonlinear flux linkage observer equation is discretized to obtain the shaft and the estimated value of the shaft flux linkage and .
4. The phase-locked loop control method of a permanent magnet assisted synchronous reluctance motor according to claim 2, characterized by, The cost function constructed in S2 comprises: Theoretically, the cost function is constructed based on rotor position error: ； wherein is an output value of a cost function for rotor position estimation, is a position estimation error, is an actual rotor position, is an estimated rotor position; In actual implementation, the cost function is specifically implemented by using estimated flux linkage in algorithm execution: ； wherein, is the candidate rotor position angle, when is the value obtains the estimated rotor position .
5. The phase-locked loop control method of a permanent magnet assisted synchronous reluctance motor according to claim 4, characterized in that, The specific steps of iteratively solving the cost function by using inverse quadratic interpolation method in S2 are as follows: S21, selecting three different initial angle values , , as iteration starting points; S22, calculate the cost function corresponding to the three angle values , , get , , ; S23, calculating a new angle estimated value by using inverse quadratic interpolation method, and the specific formula is as follows: ； S24, Update the iteration point, using... Replace one of the current three iteration points, and keep the latest three points as the starting point for the next iteration; S25, repeating the above steps S22-S24 for a fixed number of iterations.
6. The phase-locked loop control method of a permanent magnet assisted synchronous reluctance machine according to claim 5, characterized in that: The fixed number of iterations in S25 is 4 times.
7. The phase-locked loop control method of a permanent magnet assisted synchronous reluctance machine according to claim 1, characterized in that: The motor vector control system in S4 comprises a speed loop, a current loop, a coordinate transformation and a space vector pulse width modulation module.