Newton iteration method-based finite set phase-locked loop control method

Abstract

The invention belongs to the technical field of motor control, and particularly relates to a finite set phase-locked loop control method based on a Newton iteration method, which is suitable for permanent magnet synchronous motor sensorless control. The finite set phase-locked loop control method based on the Newton iteration method comprises the following steps: sampling back electromotive force, and finding out the amplitude of the back electromotive force; the # imgabs0 # is calculated; and obtaining a rotor position based on a finite set phase-locked loop rotor position estimation strategy of a Newton iteration method. Due to the rapidness of solving of the Newton iteration method, the estimated position of the rotor is rapidly solved through the Newton iteration method, and the finite set phase-locked loop can obtain the estimated value of the rotor position more rapidly than a phase-locked loop in the related technology. Compared with a phase-locked loop in the related technology, the control method of the finite set phase-locked loop based on the Newton iteration method has higher robustness and quicker dynamic performance, and meanwhile, the steady-state performance is further improved.

Description

Technical Field

[0001] This application belongs to the technical field of motor control, and particularly relates to a control method for a finite set phase-locked loop based on the Newton iteration method, which is applicable to sensorless control of permanent magnet synchronous motors. Background Art

[0002] Permanent magnet synchronous motors are widely used in transportation, industrial manufacturing, aerospace and other fields due to their high torque density and excellent dynamic and steady-state performance. Precise control of these motors requires accurate rotor position information. However, traditional mechanical sensors are prone to failure in harsh environments (such as humid or dusty environments), affecting system stability and reliability and increasing maintenance costs. Therefore, sensorless control technology has received attention as an effective method to improve system reliability and reduce costs. In particular, sensorless control technology based on the back electromotive force model, which determines the rotor position by estimating the fundamental frequency back electromotive force, has become a research hotspot due to its practicality and high efficiency.

[0003] However, the traditional phase-locked loop algorithm contains a PI controller. The inherent linear characteristics and limited bandwidth are the main disadvantages of the PI controller, and the fixed parameters of the PI controller cannot achieve satisfactory performance due to frequent changes in operating conditions. In addition, the tuning of parameters is mainly achieved through repeated experiments, which is a time-consuming process. Therefore, there is an urgent need for a phase-locked loop algorithm with high robustness and high precision to improve the sensorless control performance of PMSMs. Summary of the Invention

[0004] This 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 existing in the phase-locked loop in the prior art, and realizes the estimation of the rotor position by constructing a cost function and using the Newton iteration method.

[0005] This application provides a control method for a finite set phase-locked loop based on the Newton iteration method, including: The control method includes: Sampling the back electromotive force to find the amplitude of the back electromotive force; Calculate ; Based on the rotor position estimation strategy of the finite set phase-locked loop using the Newton iteration method, obtain the rotor position.

[0006] According to the control method for a finite set phase-locked loop based on the Newton iteration method provided by this application, in the step of sampling the back electromotive force to find the amplitude of the back electromotive force, it specifically includes: Using an extended state observer to estimate the back electromotive force, then The back electromotive force on the ; Wherein, is the rotor position, is the amplitude of the back electromotive force, which is expressed as: ; Wherein, and are respectively the inductance of the axis and the axis, and are respectively the current of the axis and the axis, is the electrical angular velocity,

[0007] According to a control method of a finite set phase-locked loop based on the Newton iteration method provided by the present application, when the motor is running, the rotor position continuously changes between 0 - 2π rad, and a coordinate system is established and defined as the estimated rotating reference frame; The position estimation error is defined as ; Wherein, is the estimated rotor position, is the rotor position estimation error; The orthogonal projections of the back electromotive force on the d-q axes are denoted as and , the estimated back electromotive force is aligned with the axis and becomes smaller as decreases, and is used to determine whether the d axis is aligned with the axis; The equivalent position error of the axis and the axis is calculated as: The equivalent position error of the axis and the axis is calculated as:

[0008] According to a control method of a finite set phase-locked loop based on the Newton iteration method provided by the present application, in the step of obtaining the rotor position in the rotor position estimation strategy of the finite set phase-locked loop based on the Newton iteration method, the cost function is: ; Among them, .

[0009] According to a control method of a finite-set phase-locked loop based on the Newton iteration method provided by the present application, based on the cost function, the Newton iteration formula is: ; When , ; When , ; where j represents the number of iterations.

[0010] According to a control method of a finite-set phase-locked loop based on the Newton iteration method provided by the present application, after the step of obtaining the rotor position in the rotor position estimation strategy of the finite-set phase-locked loop based on the Newton iteration method, Verify the convergence of the Newton iteration, and the convergence domain is , and the sufficient conditions for the local convergence of the Newton iteration are as follows: Convergence condition 1: The derivative of the estimated position is not 0; ; That is, holds; Convergence condition 2: The first-order and second-order derivatives of exist within the convergence domain; Convergence condition 3: The absolute value of the first-order derivative of the iterative formula with respect to in the convergence domain is less than 1; ; Within the convergence domain , the above conditions are satisfied.

[0011] According to a control method of a finite-set phase-locked loop based on the Newton iteration method provided by the present application, in the step of obtaining the rotor position in the rotor position estimation strategy of the finite-set phase-locked loop based on the Newton iteration method, the Newton iteration is performed three times, and the result of the third iteration is used as the final rotor position estimate.

[0012] According to a control method of a finite-set phase-locked loop based on the 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, select the rotor position estimate of the previous control period as the initial value of the rotor position estimate .

[0013] The control method of the finite set phase-locked loop based on the Newton iteration method provided by this application can quickly solve the estimated position of the rotor through the Newton iteration method due to the fast solution of the Newton iteration method. The finite set phase-locked loop can obtain the estimated value of the rotor position faster than the phase-locked loop in the related technology. Compared with the phase-locked loop in the related technology, the control method of the finite set phase-locked loop based on the Newton iteration method in this application has stronger robustness and faster dynamic performance, and at the same time, the steady-state performance is further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in this application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of this application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0015] Figure 1 is the space vector reference system of the control method of the finite set phase-locked loop based on the Newton iteration method provided by this application; Figure 2 is the flowchart of the finite set phase-locked loop of the control method of the finite set phase-locked loop based on the Newton iteration method provided by this application; Figure 3 is the sensorless control structure diagram of the control method of the finite set phase-locked loop based on the Newton iteration method provided by the application; Figure 4 The curve in is the simulation result of the angle estimation error curve of the phase-locked loop method in the related technology; Figure 5 The curve in is the simulation result of the angle estimation error curve of the control method of the finite set phase-locked loop based on the Newton iteration method provided by this application; Figure 6 The curve in is the simulation result of the speed estimation curve of the phase-locked loop method in the related technology; Figure 7 The curve in is the simulation result of the speed estimation curve of the control method of the finite set phase-locked loop based on the Newton iteration method provided by this application; Figure 8 The curve in is the simulation result of the angle estimation error curve when the reference speed changes in the phase-locked loop method in the related technology; Figure 9 The curve in is the simulation result of the angle estimation error curve when the reference speed changes in the control method of the finite set phase-locked loop based on the Newton iteration method provided by this application; Figure 10The curve in [reference] shows the comparison between the estimated speed curve and the simulation result when the reference speed changes in the phase-locked loop method in the related art. Figure 11 The curve in [reference] shows the comparison between 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 by the present application. Detailed implementation manners

[0016] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be clearly and completely described below with reference to the accompanying drawings in the present application. Apparently, the described embodiments are some but not all of the embodiments of the present application. All other embodiments obtained by those of ordinary skill in the art without making creative efforts based on the embodiments in the present application belong to the scope of protection of the present application.

[0017] The following combines Figures 1-11 to describe the control method of the finite set phase-locked loop based on the Newton iteration method of the present application. It should be understood that the following description is only an exemplary illustration and not a specific limitation to the present application.

[0018] The control method of the finite set phase-locked loop based on the Newton iteration method specifically includes: S10: Sample the back electromotive force to find the amplitude of the back electromotive force. Further, since the rotor position is a slowly changing mechanical variable, the rotor position estimate of the previous control period is selected as the initial value of the rotor position estimate .

[0019] S20: Calculate . In this step, can prepare for the calculation of the subsequent iteration formula.

[0020] S30: Based on the rotor position estimation strategy of the finite set phase-locked loop based on the Newton iteration method, obtain the rotor position. Further, according to the Newton iteration formula, perform Newton iteration three times and use the result of the third iteration as the final rotor position estimate.

[0021] 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 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 at the same time, the steady-state performance is further improved.

[0022] The back electromotive force (BEMF) of the motor is the voltage generated by the rotor cutting the stator magnetic field during rotation, which not only contains information about the rotor angle but also carries speed information. Therefore, it is first necessary to obtain accurate BEMF to prepare for estimating the rotor position.

[0023] According to some embodiments of the present application, in the step of sampling the BEMF and finding the amplitude of the BEMF in the rotor position estimation strategy of the finite set phase-locked loop based on the Newton iteration method, it specifically includes: Using an extended state observer to estimate the BEMF, then The BEMF of the axis is expressed as: ; Wherein, is the rotor position, is the amplitude of the BEMF, is expressed as: ; Wherein, and are respectively the inductance of the axis and the inductance of the axis, and are respectively the current of the axis and the current of the axis, is the electrical angular velocity, is the permanent magnet flux linkage, is the differential operator.

[0024] Using the phase-locked loop in the related technology to process the estimated BEMF, the rotor position can be extracted. The transfer function of the phase-locked loop in the related technology can be expressed as: ; Wherein, is the estimated value of the rotor position, and are respectively the proportional and integral gains of the PI controller.

[0025] Due to the frequent change of working conditions, the bandwidth of the PI controller with fixed parameters is fixed, so the ideal control effect cannot be achieved. In addition, the bandwidth of the phase-locked loop in the related technology is usually set very small to resist the harmonics in the estimated BEMFs, which results in poor dynamic performance. And adjusting the parameters of the PI is also a complex task. The above problems mean that when the working conditions of the permanent magnet synchronous motor change frequently, the performance of the phase-locked loop in the related technology still needs to be improved.

[0026] When the motor is running, the rotor position continuously changes between 0 - 2π rad. AsFigure 1 As shown, establish a coordinate system and define it as the estimated rotation reference frame.

[0027] Define the position estimation error as ; where is the estimated rotor position, is the rotor position estimation error; Denote the orthogonal projections of the back electromotive force on the d-q axes as and , the estimated back electromotive force is aligned with the axis and becomes smaller as decreases. Use to determine whether the d-axis is aligned with the axis; The equivalent position error between the axis and the axis is calculated as: The equivalent position error between the axis and the .

[0028] In the finite set phase-locked loop in the related art, its cost function is set as: ; The above formula minimizes the cost function, and the estimated position error not only converges to 0 rad, but also converges to ±π rad. Therefore, it may cause estimation error. At the same time, the finite set phase-locked loop in the related art requires 64 iterations to obtain the optimal rotor position, and the computational amount is very large.

[0029] To solve the above problems, 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: ; where .

[0030] The Newton iteration method is a very fast convergence method for solving non-linear equations. Using the Newton iteration method can obtain the final position of the rotor with as few iterations as possible.

[0031] 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: ; When is the case, ; When is the case, ; wherein, j represents the number of iterations.

[0032] 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, Verify the convergence of the Newton iteration, and the convergence domain is , and the sufficient conditions for the local convergence of the Newton iteration are as follows: Convergence condition 1: The derivative of the estimated position is not 0; ; That is, holds; Convergence condition 2: The first-order and second-order derivatives of exist within the convergence domain; Convergence condition 3: The absolute value of the first-order derivative of the iterative formula with respect to in the convergence domain is less than 1; ; Within the convergence domain , the above conditions are satisfied.

[0033] Therefore, the convergence condition of the Newton iteration method is satisfied.

[0034] Next, refer to Figure 2 to describe in detail the See Figure 2 As shown in S10: Sample the back electromotive force to find the amplitude of the back electromotive force. Since the rotor position is a slowly changing mechanical variable, the rotor position estimation of the previous control cycle is selected as the initial value of the rotor position estimation.

[0035] S20: Calculate , to prepare for the calculation of the subsequent iterative formula; S30: According to the Newton iteration formula, perform the Newton iteration three times and use the result of the third iteration as the final rotor position estimation.

[0036] Compared with the phase-locked loop in the related art, the method proposed in this application does not require parameter adjustment, can adapt to different working conditions, and 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.

[0037] Compared with the finite set phase-locked loop in the related art, the method proposed in this application greatly reduces the computational complexity, reduces the number of iterations from 64 times to 3 times, and the computational accuracy has been greatly improved. At the same time, in the improved finite set phase-locked loop strategy proposed in this application, there is only one cost function and it does not rely on other methods to maintain convergence, so the complexity of the algorithm is greatly reduced.

[0038] Finally, the sensorless control structure diagram of the finite set phase-locked loop control method based on the Newton iteration method is as Figure 3 shown.

[0039] Next, combined with Figure 3 and Figures 4-11 to verify the effectiveness of the finite set phase-locked loop control method based on the Newton iteration method proposed in this application, and analyze the performance of this method in combination with the simulation results.

[0040] As Figure 3 shown, Figure 3 it is the simulation model of the permanent magnet synchronous motor servo control system.

[0041] In Figure 3 the shown simulation model, both the speed loop and the current loop adopt PI controllers.

[0042] First, given the angular velocity reference input of the permanent magnet synchronous motor as , after obtaining the voltage and current output via the inverter and performing coordinate transformation, they are input into the extended observer; the back electromotive force is estimated, and then it is input into the improved finite set phase-locked loop proposed in this application to obtain the estimated value of the angular position; then the estimated value of the electrical angular velocity is obtained through the difference method, and then after low-pass filtering, it is used for speed closed-loop control to obtain the q-axis reference current for current loop control; Secondly, the a-phase, b-phase, and c-phase currents , and of the motor are obtained by using current sensors, and then the actual currents of the d(q)-axis of the motor are obtained through coordinate transformation for current control to obtain the current loop control input ; Further, the switching signal state vector of the inverter is obtained through coordinate transformation and SVPWM pulse modulation method ; Finally, the inverter outputs three-phase currents according to the DC bus voltage and the switching signals to drive the permanent magnet synchronous motor to operate.

[0043] Again, based on Figure 3 the simulation model of the permanent magnet synchronous motor servo control system, the comparative simulation results of the finite set phase-locked loop method in the related technology and the control method of the finite set phase-locked loop based on the Newton iteration method proposed in this application are given.

[0044] When the speed reference is rpm and a 15 step disturbance is suddenly added at 6 seconds, Figure 4 、 Figure 5 、 Figure 6 and Figure 7 respectively give the simulation results of the angle estimation error curve and the speed estimation curve of the phase-locked loop method using the related technology and the improved finite set phase-locked loop method; From Figure 4 it can be seen that when using the phase-locked loop in the related technology, when a sudden load is applied, the estimated angle will have an estimation error of 3.4°, and it takes 0.37 s of adjustment time to return to the normal estimation error level; While in Figure 5 after adopting the control method of the finite set phase-locked loop based on the Newton iteration method, when a sudden load is applied, the estimated angle error is 0.1°, which greatly improves the anti-disturbance performance of the algorithm.

[0045] From Figure 6 and Figure 7 in the comparison, it can be seen that when a sudden load is applied, the speed drop of the control method of the finite set phase-locked loop based on the Newton iteration method is significantly less than that of the phase-locked loop method in the related technology. This further verifies the improvement of its dynamic performance and anti-disturbance performance of the algorithm; at the same time, after reaching the steady state, the speed fluctuation of the control method of the finite set phase-locked loop based on the Newton iteration method is slightly larger than that of the phase-locked loop method in the related technology. This is because the finite set phase-locked loop directly extracts the phase information from the estimated back electromotive force and then calculates the estimated speed by the difference method. The difference method will cause the amplification of errors. This shortcoming can be eliminated by averaging and filtering the estimated angle and then taking the difference.

[0046] Figures 8-11 respectively give the simulation results of the angle estimation error curve and the speed estimation curve of the phase-locked loop method using the related technology and the control method of the finite set phase-locked loop based on the Newton iteration method when the reference speed changes.

[0047] From Figure 8 It can be seen that when the reference speed changes from 500 rpm to 1000 rpm at a change rate of 3000, the angle error estimated by the phase-locked loop in the related art will generate an error of 13.2°; at the same time, when the speed increases to 1000 rpm, its estimated error increases significantly; 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 hardly affected and always remains within a small range; when the speed reaches 1000 rpm, the estimated error will increase slightly, but compared with Figure 8 the phase-locked loop in the related art in

[0048] From Figure 10 and Figure 11 It can be seen that when the reference speed changes to 1000 rpm, the speed fluctuation estimated by using the phase-locked loop method in the related art increases significantly, while the speed fluctuation estimated by using the control method of the finite set phase-locked loop based on the Newton iteration method still remains within a very small range, and the change of speed hardly has an impact on it.

[0049] This is because according to the control method of the finite set phase-locked loop based on the Newton iteration method in the embodiments of the present application, the angle position information is directly extracted from the phase of the back electromotive force, so the change of speed hardly has an impact on it. This shows that the control method of the finite set phase-locked loop based on the Newton iteration method in the present application has better dynamic performance and steady-state performance.

[0050] 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 foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate 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 the Newton iteration method, characterized in that the control method includes: sampling the back electromotive force to find the amplitude of the back electromotive force; Calculation ; acquiring the rotor position based on the rotor position estimation strategy of the finite set phase-locked loop using the Newton iteration method.

2. The control method of the finite set phase-locked loop based on the Newton iteration method according to claim 1, characterized in that In the step of sampling the back electromotive force to find the amplitude of the back electromotive force, it specifically includes: The back electromotive force is estimated by using an extended state observer, then The back electromotive force of the [axis] is expressed as: ； Among them, is the rotor position, is the amplitude of the back electromotive force, Expressed as: ； Among them, and are respectively the inductance of the axis and the and are respectively the current of the axis, is the electrical angular velocity, is the permanent magnet flux linkage, is the differential operator.

3. The control method of the finite set phase-locked loop based on the Newton iteration method according to claim 2, characterized in that, When the motor is running, the rotor position continuously changes between 0 - 2π rad, and a coordinate system is established and defined as the estimated rotating reference frame; Define the position estimation error as ; wherein, is the estimated rotor position, is the rotor position estimation error; Denote the orthogonal projection of the back electromotive force on the d-q axes as and . The estimated back electromotive force is aligned with the axis and decreases as decreases. Use to determine whether the d-axis is aligned with the axis; The shaft and The equivalent position error of the shaft is calculated as: ； Axis and The equivalent position error of the axis is calculated as follows: 。 4. The control method of the finite set phase-locked loop based on the Newton iteration method according to claim 1, characterized in that, In the step of acquiring the rotor position based on the rotor position estimation strategy of the finite set phase-locked loop using the Newton iteration method, the cost function is: ； Among them, .

5. The control method of the finite set phase-locked loop based on the Newton iteration method according to claim 4, characterized in that, Based on the cost function, the Newton iteration formula is: ； When , ; When then ; where j represents the number of iterations.

6. The control method of the finite set phase-locked loop based on the Newton iteration method according to claim 5, characterized in that After the step of acquiring the rotor position based on the rotor position estimation strategy of the finite set phase-locked loop using the Newton iteration method, Verify the convergence of Newton's iteration, and the convergence domain is , and the sufficient conditions for the local convergence of Newton's iteration are as follows: Convergence condition 1: The derivative of the estimated position is not 0; ； That is, is established; Convergence condition two: The first and second derivatives of exist within the convergence domain; ； Convergence condition three: The absolute value of the first derivative of the iterative formula with respect to is less than 1 within the convergence domain; ； Within the convergence domain , the above conditions are satisfied.

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

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

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