A control method for finite set phase-locked loop based on Newton iteration method

Abstract

The present application belongs to the field of motor control technology, and specifically relates to a control method of a finite set phase-locked loop based on the Newton iteration method, which is suitable for position sensorless control of a permanent magnet synchronous motor. According to the control method of the finite set phase-locked loop based on the Newton iteration method of the present application, it includes: sampling the back electromotive force to find the amplitude of the back electromotive force; calculating; obtaining the rotor position based on the finite set phase-locked loop rotor position estimation strategy of the Newton iteration method. Due to the rapid solution of the Newton iteration method, the estimated position of the rotor is quickly solved by the Newton iteration method, and the finite set phase-locked loop can obtain the estimated value of the rotor position faster than the phase-locked loop in the related art. Compared with the phase-locked loop in the related art, the control method of the finite set phase-locked loop based on the Newton iteration method of the present application has stronger robustness and faster dynamic performance, and the steady-state performance is also further improved.

Description

Technical Field

[0001] The present application belongs to the field of motor control technology, and specifically relates to a control method for a finite set phase-locked loop based on the Newton iteration method, which is suitable for position sensorless control of a permanent magnet synchronous motor. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in transportation, industrial manufacturing, aerospace, and other fields due to their high torque density and excellent dynamic and steady-state performance. Accurate control of these motors requires precise rotor position information, but traditional mechanical sensors are prone to failure in harsh environments (such as humid or dusty ones), affecting system stability and reliability and increasing maintenance costs. Consequently, sensorless control technology has attracted attention as an effective method to improve system reliability and reduce costs. In particular, sensorless control techniques based on back-EMF models, which determine rotor position by estimating the fundamental back-EMF, have become a research hotspot due to their practicality and efficiency.

[0003] However, traditional phase-locked loop (PLL) algorithms incorporate PI controllers. Their inherent linearity and limited bandwidth are major drawbacks. Furthermore, the fixed parameters of PI controllers cannot achieve satisfactory performance due to the frequent changes in operating conditions. Furthermore, parameter tuning is primarily achieved through trial and error, a time-consuming process. Therefore, a highly robust and accurate PLL algorithm is urgently needed to improve the sensorless control performance of PMSMs. Summary of the Invention

[0004] The present application provides a control method for a finite set phase-locked loop based on the Newton iteration method, which is used to solve the defects of slow dynamic performance and weak anti-interference ability of the phase-locked loop in the prior art, and realizes the estimated position of the rotor by constructing a cost function and using the Newton iteration method.

[0005] The present application provides a control method for a finite set phase-locked loop based on the Newton iteration method, comprising:

[0006] The control method includes:

[0007] Sampling the back EMF to find out the amplitude of the back EMF;

[0008] calculate ;

[0009] A finite set phase-locked loop rotor position estimation strategy based on Newton iteration method is used to obtain the rotor position.

[0010] According to a control method of a finite set phase-locked loop based on the Newton iteration method provided by the present application, the step of sampling the back electromotive force and finding the amplitude of the back electromotive force specifically includes:

[0011] Using the extended state observer to estimate the back EMF, The back EMF of the shaft is expressed as:

[0012] ;

[0013] in, is the rotor position, is the magnitude of the back EMF,

[0014] Expressed as:

[0015] ;

[0016] in, and They are Axis and The inductance of the shaft, and They are Axis and The shaft current, is the electrical angular velocity, is the permanent magnet flux linkage, is a differential operator.

[0017] According to a control method of a finite set phase-locked loop based on Newton iteration method provided by the present application, when the motor is running, the rotor position changes continuously between 0-2π rad, and a coordinate system and define it as the estimated rotation reference system;

[0018] The position estimation error is defined as ;

[0019] in, is the estimated rotor position, is the rotor position estimation error;

[0020] The back EMF The orthogonal projection on the dq axis is denoted as and , the estimated back EMF is related to Axis alignment and along with The decrease of To determine the d-axis and Whether the axes are aligned;

[0021] Axis and The equivalent position error of the axis is calculated as:

[0022] ;

[0023] Axis and The equivalent position error of the axis is calculated as:

[0024] .

[0025] According to a control method of a finite set phase-locked loop based on Newton iteration method provided by the present application, in the step of obtaining the rotor position in the finite set phase-locked loop rotor position estimation strategy based on Newton iteration method, the cost function is:

[0026] ;

[0027] in, .

[0028] According to a control method for a finite set phase-locked loop based on the Newton iteration method provided in this application, based on the cost function, the Newton iteration formula is:

[0029] ;

[0030] when hour, ;

[0031] when hour, ;

[0032] Where j represents the number of iterations.

[0033] According to a control method of a finite set phase-locked loop based on Newton iteration method provided by the present application, after the step of obtaining the rotor position in the finite set phase-locked loop rotor position estimation strategy based on Newton iteration method,

[0034] The convergence of Newton iteration is verified, and the convergence domain is , the sufficient conditions for local convergence of Newton iteration are as follows:

[0035] Convergence condition 1: The derivative of the estimated position is not 0;

[0036] ;

[0037] Right now, Established;

[0038] Convergence condition 2: The first and second derivatives of exist in the convergence region;

[0039] ;

[0040] Convergence condition three: the iteration is in the convergence domain The absolute value of the first derivative is less than 1;

[0041] ;

[0042] In the convergence region , meeting the above conditions.

[0043] According to a control method of a finite set phase-locked loop based on the Newton iteration method provided in the present application, in the rotor position estimation strategy of the finite set phase-locked loop based on the Newton iteration method, in the step of obtaining the rotor position, the Newton iteration is performed three times, and the result of the third iteration is used as the final rotor position estimation.

[0044] According to a control method of a finite set phase-locked loop based on Newton iteration method provided by the present application, in the step of sampling the back electromotive force and finding the amplitude of the back electromotive force, the rotor position estimation of the previous control cycle is selected. As the rotor position estimate The initial value of .

[0045] The control method for a finite set phase-locked loop (PLL) based on the Newton iteration method provided in this application, due to the rapid solution of the Newton iteration method, can quickly solve the estimated rotor position by using the Newton iteration method. This finite set PLL can obtain an estimated value of the rotor position more quickly than PLLs in related technologies. Compared to PLLs in related technologies, the control method for a finite set PLL based on the Newton iteration method provided in this application has stronger robustness and faster dynamic performance, while also further improving steady-state performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the present application or the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0047] Figure 1 It is a space vector reference system of the control method of the finite set phase-locked loop based on the Newton iteration method provided by the present application;

[0048] Figure 2 This is a finite set phase-locked loop flow chart of a finite set phase-locked loop control method based on Newton iteration method provided by the present application;

[0049] Figure 3 The invention provides a sensorless control structure diagram of a finite set phase-locked loop control method based on Newton iteration method;

[0050] Figure 4The curve in FIG is a simulation result of an angle estimation error curve of a phase-locked loop method in the related art;

[0051] Figure 5 The curve in is a simulation result of an angle estimation error curve of a control method for a finite set phase-locked loop based on Newton iteration method provided in this application;

[0052] Figure 6 The curve in is the simulation result of the speed estimation curve of the phase-locked loop method in the related art;

[0053] Figure 7 The curve in is a simulation result of a speed estimation curve of a control method of a finite set phase-locked loop based on Newton iteration method provided in this application;

[0054] Figure 8 The curve in FIG is a simulation result of an angle estimation error curve when the reference speed changes in the phase-locked loop method in the related art;

[0055] Figure 9 The curve in is a simulation result of an angle estimation error curve when the reference speed changes in the control method of a finite set phase-locked loop based on the Newton iteration method provided by the present application;

[0056] Figure 10 The curve in FIG is a phase-locked loop method in the related art, in which the estimated speed curve is compared with the simulation result when the reference speed changes;

[0057] Figure 11 The curve in FIG. 1 is a comparison of the estimated speed curve and the simulation result when the reference speed changes in the control method of the finite set phase-locked loop based on the Newton iteration method provided in the present application. DETAILED DESCRIPTION

[0058] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions of this application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments of this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application.

[0059] The following combination Figures 1-11 The control method of the finite set phase-locked loop based on the Newton iteration method of the present application is described. It is worth noting that the following description is only for illustrative purposes and is not intended to limit the present application.

[0060] The control method of the finite set phase-locked loop based on the Newton iteration method specifically includes:

[0061] S10: Sample the back electromotive force and find the amplitude of the back electromotive force. Furthermore, since the rotor position is a slowly changing mechanical variable, the rotor position estimation of the previous control cycle is selected. As the rotor position estimate The initial value of .

[0062] S20: Calculation In this step, It can prepare for the calculation of subsequent iterative formulas.

[0063] S30: Obtain the rotor position using a finite set phase-locked loop rotor position estimation strategy based on the Newton iteration method. Further, according to the Newton iteration formula, perform three Newton iterations and use the result of the third iteration as the final rotor position estimation.

[0064] According to the control method of the finite set phase-locked loop based on the Newton iteration method of the present application, due to the rapid solution of the Newton iteration method, the estimated rotor position is quickly solved by the Newton iteration method. The finite set phase-locked loop can obtain the estimated value of the rotor position more quickly than the phase-locked loop in the related art. Compared with the phase-locked loop in the related art, the control method of the finite set phase-locked loop based on the Newton iteration method of the present application has stronger robustness and faster dynamic performance, while also further improving steady-state performance.

[0065] The motor's back electromotive force (BEMF) is the voltage generated by the rotor cutting through the stator's magnetic field during rotation. This voltage not only contains information about the rotor's angle but also about its speed. Therefore, accurate BEMF must be acquired to estimate the rotor's position.

[0066] According to some embodiments of the present application, the finite set phase-locked loop rotor position estimation strategy based on the Newton iteration method, in the step of sampling the back electromotive force and finding the amplitude of the back electromotive force, specifically includes:

[0067] Using the extended state observer to estimate the back EMF, The back EMF of the shaft is expressed as:

[0068] ;

[0069] in, is the rotor position, is the magnitude of the back EMF,

[0070] Expressed as:

[0071] ;

[0072] in, and They are Axis and The inductance of the shaft, and They are Axis and The shaft current, is the electrical angular velocity, is the permanent magnet flux linkage, is a differential operator.

[0073] The estimated back electromotive force is processed using a phase-locked loop (PLL) in the related art to extract the rotor position. The transfer function of the PLL in the related art can be expressed as:

[0074] ;

[0075] in, is an estimate of the rotor position, and are the proportional and integral gains of the PI controller respectively.

[0076] Due to the frequent changes in operating conditions, the bandwidth of the PI controller using fixed parameters is fixed, making it impossible to achieve ideal control results. In addition, the bandwidth of the phase-locked loop in related art is usually set very small to resist the harmonics in the estimated BEMFs, which leads to poor dynamic performance. Moreover, adjusting the PI parameters is also a complex task. The above problems mean that when the operating conditions of permanent magnet synchronous motors change frequently, the performance of the phase-locked loop in related art still needs to be improved.

[0077] When the motor is running, the rotor position changes continuously between 0-2π rad. Figure 1 As shown, establish coordinate system and define it as the estimated rotation reference system.

[0078] The position estimation error is defined as ;

[0079] in, is the estimated rotor position, is the rotor position estimation error;

[0080] The back EMF The orthogonal projection on the dq axis is denoted as and , the estimated back EMF is related to Axis alignment and along with The decrease of To determine the d-axis and Whether the axes are aligned;

[0081] Axis and The equivalent position error of the axis is calculated as:

[0082] ;

[0083] Axis and The equivalent position error of the axis is calculated as:

[0084] .

[0085] In the finite set phase-locked loop in the related art, its cost function is set as:

[0086] ;

[0087] The above formula is to minimize the cost function. The estimated position error not only converges to 0 rad, but also converges to ±πrad, so it may cause At the same time, the finite set phase-locked loop in the related art requires 64 iterations to obtain the optimal rotor position, which is very computationally intensive.

[0088] To solve the above problem, according to some embodiments of the present application, in the step of obtaining the rotor position in the finite set phase-locked loop rotor position estimation strategy based on the Newton iteration method, the cost function is:

[0089] ;

[0090] in, .

[0091] The Newton iteration method is an extremely fast convergence method for solving nonlinear equations. The Newton iteration method can be used to obtain the final position of the rotor with as few iterations as possible.

[0092] In the control method of the finite set phase-locked loop based on the Newton iteration method of the present application, based on the above cost function, the Newton iteration formula is:

[0093] ;

[0094] when hour, ;

[0095] when hour, ;

[0096] Where j represents the number of iterations.

[0097] According to some embodiments of the present application, after the step of obtaining the rotor position in the finite set phase-locked loop rotor position estimation strategy based on the Newton iteration method,

[0098] The convergence of Newton iteration is verified, and the convergence domain is , the sufficient conditions for local convergence of Newton iteration are as follows:

[0099] Convergence condition 1: The derivative of the estimated position is not 0;

[0100] ;

[0101] Right now, Established;

[0102] Convergence condition 2: The first and second derivatives of exist in the convergence region;

[0103] ;

[0104] Convergence condition three: the iteration is in the convergence domain The absolute value of the first derivative is less than 1;

[0105] ;

[0106] In the convergence region , meeting the above conditions.

[0107] Therefore, the convergence condition of the Newton iteration method is satisfied.

[0108] Refer to the following Figure 2 Detailed description of the embodiment of the present application

[0109] See also Figure 2 As shown, according to some embodiments of the present application, the control method of the finite set phase-locked loop based on the Newton iteration method specifically includes the following steps:

[0110] S10: Sample the back electromotive force and find the amplitude of the back electromotive force. Since the rotor position is a slowly changing mechanical variable, the rotor position estimate of the previous control cycle is selected as the initial value of the rotor position estimate.

[0111] S20: Calculation , prepare for the calculation of subsequent iterative formula;

[0112] S30: According to the Newton iteration formula, perform Newton iteration three times and use the result of the third iteration as the final rotor position estimation.

[0113] Compared with the phase-locked loop in the related art, the method proposed in this application does not require parameter adjustment and can adapt to different working conditions. Compared with the phase-locked loop method in the related art, its dynamic performance and robustness have been greatly improved, and the steady-state performance has also been enhanced to a certain extent.

[0114] Compared to finite-set phase-locked loops (PLLs) in related art, the method proposed in this application significantly reduces the amount of computation, reducing the number of iterations from 64 to 3, and significantly improving computational accuracy. Furthermore, the improved finite-set phase-locked loop strategy proposed in this application has only one cost function and does not rely on other methods to maintain convergence, thus significantly reducing the complexity of the algorithm.

[0115] Finally, the sensorless control structure diagram of the control method of the finite set phase-locked loop based on the Newton iteration method is as follows: Figure 3 shown.

[0116] The following combination Figure 3 、 Figure 4-11 The effectiveness of the control method of the finite set phase-locked loop based on the Newton iteration method proposed in this application is verified, and the performance of the method is analyzed in combination with simulation results.

[0117] like Figure 3 As shown, Figure 3 It is a simulation model of permanent magnet synchronous motor servo control system.

[0118] exist Figure 3 In the simulation model shown, PI controllers are used for both the speed loop and the current loop.

[0119] First, the angular velocity reference input of the permanent magnet synchronous motor is given as After obtaining the voltage and current output by the inverter, the coordinate transformation is performed and then input into the expanded observer; the back electromotive force is estimated. , which is then input into the improved finite set phase-locked loop proposed in this application to obtain an estimated value of the angular position ; Then obtain the estimated value of electrical angular velocity by difference method , and then use it for speed closed-loop control after low-pass filtering to obtain the q-axis reference current Used for current loop control;

[0120] Secondly, use the current sensor to obtain the motor's phase a, phase b and phase c currents 、 and , and then obtain the actual current of the motor d (q) axis through coordinate transformation Used for current control to obtain current loop control input ;

[0121] Furthermore, the switching signal state vector of the inverter is obtained by coordinate transformation and SVPWM pulse modulation method. ; Finally, the inverter is based on the DC bus voltage And the switching signal outputs three-phase current to drive the permanent magnet synchronous motor to operate.

[0122] Again, based on Figure 3 The simulation model of the permanent magnet synchronous motor servo control system is given, and the comparative simulation results of the finite set phase-locked loop method in the related art and the finite set phase-locked loop control method based on Newton iteration method proposed in this application are given.

[0123] The speed reference is rpm and 6 seconds when suddenly adding 15 Under the condition of step disturbance, Figure 4 、 Figure 5 、 Figure 6 and Figure 7 The simulation results of angle estimation error curve and speed estimation curve of the phase-locked loop method using related technology and the improved finite set phase-locked loop method are given respectively.

[0124] from Figure 4 It can be seen that when the phase-locked loop in the related art is used, when a sudden load is applied, the estimated angle will have an estimation error of 3.4°, and it takes 0.37s to adjust to the normal estimation error level;

[0125] And in Figure 5 In the paper, after adopting the control method of finite set phase-locked loop based on Newton iteration method, when the load is suddenly added, the estimated angle error is 0.1°, which greatly improves the anti-disturbance performance of the algorithm.

[0126] from Figure 6 and Figure 7 The comparison in Figure 2 shows that when a sudden load is applied, the speed drop of the control method using the finite set phase-locked loop based on the Newton iteration method is significantly smaller than that of the phase-locked loop method in the related art. This further verifies its improvement in the dynamic performance and anti-interference performance of the algorithm. At the same time, after reaching steady state, the speed fluctuation of the control method using the finite set phase-locked loop based on the Newton iteration method is slightly greater than that of the phase-locked loop method in the related art. This is because the finite set phase-locked loop directly extracts phase information from the estimated back EMF and then calculates the estimated speed through the differential method. The differential method will lead to error amplification. This disadvantage can be eliminated by averaging and filtering the estimated angle before performing the differential.

[0127] Figures 8-11 The simulation results of the angle estimation error curve and speed estimation curve using the phase-locked loop method in related technology and the control method using a finite set phase-locked loop based on Newton iteration method when the reference speed changes are given respectively.

[0128] from Figure 8It can be seen from the figure that when the reference speed changes from 500 rpm to 1000 rpm at a rate of 3000, the angle error estimated by the phase-locked loop in the related art will produce an error of 13.2°; at the same time, when the speed is increased to 1000 rpm, its estimation error increases significantly;

[0129] from Figure 9 It can be seen that in the control method of the finite set phase-locked loop based on the Newton iteration method, when the reference speed changes, the angle error estimated by the finite set phase-locked loop is almost unaffected and always maintains in a small range; when the speed reaches 1000rpm, the estimated error will increase slightly, but it is similar to Figure 8 Compared with the phase-locked loop in related technologies, it can be almost ignored.

[0130] from Figure 10 and Figure 11 It can be seen that when the reference speed changes to 1000 rpm, the speed fluctuation estimated by the phase-locked loop method in the relevant technology increases significantly, while the speed fluctuation estimated by the control method of the finite set phase-locked loop based on the Newton iteration method remains within a very small range, and the change in speed has almost no effect on it.

[0131] This is because the control method for the finite set phase-locked loop based on the Newton iteration method in the embodiment of the present application directly extracts the angular position information from the phase of the back electromotive force, so changes in speed have almost no effect on it. This shows that the control method for the finite set phase-locked loop based on the Newton iteration method in the present application has better dynamic performance and steady-state performance.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A control method for a finite set phase-locked loop based on Newton iteration method, characterized in that: The control method includes: Sample the back EMF and find the amplitude of the back EMF ; calculate ; The rotor position estimation strategy of the finite set phase-locked loop based on the Newton iteration method is used to obtain the rotor position. The cost function is: ； in, , is the position estimation error, and for Orthogonal projection on the dq axis.

2. The control method of a finite set phase-locked loop based on Newton iteration method according to claim 1, characterized in that: The step of sampling the back electromotive force and finding the amplitude of the back electromotive force specifically includes: Using the extended state observer to estimate the back EMF, The back EMF of the shaft is expressed as: ； in, is the rotor position, Expressed as: ； in, and They are Axis and The inductance of the shaft, and They are Axis and The shaft current, is the electrical angular velocity, is the permanent magnet flux linkage.

3. The control method of a finite set phase-locked loop based on Newton iteration method according to claim 2, characterized in that: When the motor is running, the rotor position changes continuously between 0 - 2π rad, establishing coordinate system and define it as the estimated rotation reference system; The position estimation error is defined as ; in, is the estimated rotor position, is the rotor position estimation error; The estimated back EMF is Axis alignment and along with The decrease of To determine the d-axis and Whether the axes are aligned; Axis and The equivalent position error of the axis is calculated as: ； Axis and The equivalent position error of the axis is calculated as: 。 4. The control method of a finite set phase-locked loop based on Newton iteration method according to claim 1, characterized in that: Based on the cost function, the Newton iteration formula is: ； when hour, ; when hour, ; Where j represents the number of iterations, is the differential operator.

5. The control method of a finite set phase-locked loop based on Newton iteration method according to claim 4, characterized in that: After the step of obtaining the rotor position in the finite set phase-locked loop rotor position estimation strategy based on Newton iteration method, The convergence of Newton iteration is verified, and the convergence domain is , the sufficient conditions for local convergence of Newton iteration are as follows: Convergence condition 1: The derivative of the estimated position is not 0; ； Right now, Established; Convergence condition 2: The first and second derivatives of exist in the convergence region; ； Convergence condition three: the iteration is in the convergence domain The absolute value of the first derivative is less than 1; ； In the convergence region , meeting the above conditions.

6. The control method of a finite set phase-locked loop based on Newton iteration method according to claim 1, characterized in that: In the finite set phase-locked loop rotor position estimation strategy based on Newton iteration method, in the step of obtaining the rotor position, Newton iteration is performed three times, and the result of the third iteration is used as the final rotor position estimation.

7. The control method of a finite set phase-locked loop based on Newton iteration method according to claim 1, characterized in that: In the step of sampling the back electromotive force and finding the amplitude of the back electromotive force, the rotor position estimation of the previous control cycle is selected. As the rotor position estimate The initial value of .

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