A high-precision position detection method for permanent magnet motor system

Abstract

The present invention discloses a high-precision position detection method for a permanent magnet motor system, comprising the following steps: S1, establishing a harmonic back-EMF model of the permanent magnet motor and analyzing the influence of the harmonic back-EMF on position estimation error; S2, constructing an arcsine saturation function whose boundary layer thickness self-adjusts with the sliding surface error as a switching function; S3, establishing a mathematical model of a sliding mode observer based on the arcsine saturation function, and obtaining a parameter selection range using the Lyapunov stability criterion; S4, performing a Park transform on the output value of the sliding mode observer to obtain a DC quantity in a dq coordinate system; filtering the output value using a first-order low-pass filter to retain the fundamental back-EMF, which is then subjected to an inverse Park transform to extract the sinusoidal back-EMF; and S5, combining an orthogonal phase-locked loop to perform position estimation on the output sinusoidal back-EMF to obtain an estimated rotor position angle and an estimated rotor speed. The present invention can improve the accuracy and dynamic performance of sensorless control of permanent magnet motors.

Description

Technical Field

[0001] The present invention relates to the field of three-phase permanent magnet motor control, and in particular to a high-precision position detection method for a permanent magnet motor system. Background Art

[0002] Sensorless control of permanent magnet synchronous motors (PMSMs) uses current and voltage information measured by the motor itself, eliminating the need for additional sensors. This technology is popular in a variety of applications because it effectively reduces manufacturing costs and improves system reliability. Among sensorless control techniques for PMSMs operating at medium and high speeds, back-EMF-based methods are widely used. However, due to inverter nonlinearities and deviations in the actual motor manufacturing process, the back-EMF estimated in sensorless control methods based on sliding mode observers contains (6n±1)th harmonics, resulting in a 6nth harmonic error in the estimated rotor position, further causing torque ripple and speed jitter.

[0003] Current sensorless methods for addressing rotor position estimation errors can be categorized into two main categories: compensation-based methods and signal filtering-based methods. Compensation-based methods can reduce rotor position estimation errors by eliminating the effects of voltage source inverter nonlinearity on position estimation. However, these methods typically rely on precise control object parameters or require adjustment of multiple controller parameters. Signal filtering-based methods directly filter the harmonics in the estimated back EMF and extract the fundamental frequency component to suppress rotor position estimation errors. Signal filtering-based methods typically utilize a low-pass filter or require the design of multiple notch filters to filter out harmonic back EMFs of different orders. If the low-pass filter cutoff frequency is set too high, the estimated back EMF will still contain significant harmonics. If the low-pass filter cutoff frequency is set too low, a significant phase delay will occur, reducing system control accuracy. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a high-precision position detection method for a permanent magnet motor system that does not require adjustment of filter parameters and does not introduce phase delay, thereby achieving strong suppression capability for harmonic back EMF of any order, reducing jitter of estimated speed, and being highly robust to changes in motor parameters and external disturbances.

[0005] Technical solution: A high-precision position detection method for a permanent magnet motor system, comprising the following steps:

[0006] S1, through the drag experiment, the main back EMF harmonic components of the non-sinusoidal back EMF three-phase permanent magnet motor are analyzed, the harmonic back EMF model of the permanent magnet motor is established, and the influence of the harmonic back EMF on the position estimation error is analyzed;

[0007] S2, constructing an arcsine saturation function that self-adjusts the boundary layer thickness with the sliding surface error as a switching function;

[0008] S3, a mathematical model of the sliding mode observer is established based on the inverse sine saturation function, and the parameter selection range is obtained using the Lyapunov stability criterion;

[0009] S4, the output value of the sliding mode observer is subjected to Park transformation to obtain the DC quantity in the dq coordinate system; it is filtered using a first-order low-pass filter to retain the fundamental back EMF, and the fundamental back EMF is then subjected to inverse Park transformation to extract the sinusoidal back EMF;

[0010] S5, combined with the orthogonal phase-locked loop, estimates the position of the output sinusoidal back EMF to obtain the rotor estimation error, which is passed through the PI regulator to obtain the estimated speed, and then passed through the integrator to obtain the estimated rotor position angle.

[0011] Furthermore, in step S1, a harmonic back-EMF model of a three-phase permanent magnet synchronous motor with non-sinusoidal back-EMF in the αβ coordinate system is established:

[0012]

[0013] Where, ψ f is the fundamental permanent magnet flux, K ψ(6n±1) is the percentage of odd harmonic flux to fundamental permanent magnet flux, n is the harmonic order, ω e is the rotor speed; θ e is the rotor position angle; are the estimated back electromotive force in αβ coordinate system respectively;

[0014] The influence of harmonic back EMF on position estimation error is as follows:

[0015]

[0016] Where, To estimate the rotor speed, To estimate the rotor position angle.

[0017] Furthermore, in step S2, the mathematical model of the arcsine saturation function S-arcsin is:

[0018]

[0019] Where, S=[s α s β ] T is the column vector of the current estimation error, “T” represents the matrix transpose; s α 、s β is the current sliding mode surface under the defined α and β axes, sgn() is the sign function, λ is the basic boundary layer thickness, iα 、i β are the actual currents under the α and β axes respectively, are the estimated currents under the α and β axes, are the current estimation errors under α and β axes respectively, and there is

[0020] Furthermore, in step S3, the three-phase stator current equation of the permanent magnet synchronous motor is expressed as:

[0021]

[0022] Where ρ is the differential operator, R s is the stator resistance, L s is the stator inductance; u α 、u β is the stator voltage in the αβ coordinate system; e α 、e β is the extended back EMF in the αβ coordinate system, and satisfies:

[0023]

[0024] The sliding mode observer is expressed as follows:

[0025]

[0026] In the formula, the superscript “^” indicates an estimated value; v α 、v β are the estimated back electromotive force of the α-axis and β-axis respectively, and they satisfy:

[0027]

[0028] Since the absolute value of the switching function in the continuous control region is less than 1, the expression of the Lyapunov function is as follows:

[0029]

[0030] According to Lyapunov's second theorem, the stability of the system can only be guaranteed when dV / dt < 0, so:

[0031]

[0032] The stability conditions are as follows:

[0033]

[0034] Where k s is the sliding mode gain.

[0035] Furthermore, in step S4, the fundamental component output by the sliding mode observer is After Park transformation, the DC quantity in the dq coordinate system is obtained The expression is as follows:

[0036]

[0037] Then the fundamental back electromotive force is realized by Park inverse transformation Extraction:

[0038]

[0039] For the harmonic component of the sliding mode observer output, the expression is as follows:

[0040]

[0041] Among them, e dn is the nth harmonic content in the d-axis back electromotive force, e qn is the nth harmonic content in the q-axis back electromotive force.

[0042] Furthermore, in step S5, the sinusoidal back electromotive force obtained by filtering is Input into the orthogonal phase-locked loop structure to obtain the rotor estimation error The rotor estimation error is passed through the PI regulator to estimate the speed Then the estimated rotor position angle is obtained through the integrator

[0043] Compared with the prior art, the present invention has the following significant effects:

[0044] 1. The zero-phase-shift synchronous rotating filter in the present invention can effectively filter out any order of back-EMF harmonics other than the fundamental wave, making the estimated back-EMF more sinusoidal; accordingly, the position estimation error can be reduced from 0.0153 rad to 0.0079 rad, which can effectively suppress the rotor position estimation error;

[0045] 2. In the present invention, the inverse sine saturation function (S-arcsin) that self-adjusts the boundary layer thickness with the sliding surface error is used as the switching function, eliminating the front-stage low-pass filter structure in the traditional sliding mode observer, thereby avoiding the phase lag in estimating the back EMF;

[0046] 3. The S-arcsin-based sliding mode observer in the present invention can effectively reduce the chattering of the estimated speed, and the speed estimation error can be reduced from 25r / min to 3r / min, effectively improving the steady-state performance of position sensorless control. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Figure 1. The overall control structure of PMSM without position sensor to suppress position estimation error.

[0048] Figure 2 This is the block diagram of sliding mode control based on S-arcsin and synchronous rotating filter;

[0049] Figure 3 Arcsin switching function at different boundary layer thicknesses;

[0050] Figure 4 This is the design flow chart of the synchronous rotating filter;

[0051] Figure 5(a) shows the estimated waveform of the α-β axis back electromotive force based on the traditional low-pass filter at 50 r / min;

[0052] Figure 5(b) is the estimated waveform of the α-β axis back electromotive force of the base synchronous rotating filter at 50 r / min;

[0053] Figure 5(c) shows the actual position, estimated position, and position error diagram based on the traditional low-pass filter at 200 r / min;

[0054] Figure 5(d) shows the actual position, estimated position, and position error of the base synchronous rotating filter at 200 r / min;

[0055] Figure 5(e) shows the waveforms of speed estimation, position estimation, and back-EMF estimation based on the traditional low-pass filter at 500 r / min;

[0056] Figure 5(f) shows the waveforms of speed estimation, position estimation, and back-EMF estimation based on the S-arcsin function and synchronous rotating filter at 500 r / min. DETAILED DESCRIPTION

[0057] The present invention will be described in further detail below with reference to the accompanying drawings and specific implementations.

[0058] like Figure 1 The figure shows the overall control structure of the high-precision position detection method for the permanent magnet motor system of this embodiment, which collects the three-phase current i of the motor. a 、i b 、i c and voltage u α 、u β The back EMF is estimated through the output of the sliding mode observer, and the front-stage low-pass filter of the sliding mode observer is removed by the S-arcsin function (inverse sine saturation function). Then, any order harmonic back EMF except the fundamental back EMF is filtered out by the synchronous rotating filter, and finally the rotor position angle and speed are obtained using the orthogonal phase-locked loop.

[0059] The block diagram of sliding mode control based on S-arcsin and synchronous rotating filter is as follows: Figure 2 The waveform of S-arcsin at different boundary layer thicknesses is shown in Figure 3As shown in Figure 1, outside the boundary layer, the function is the sign function signum(s). Increasing the boundary layer thickness λ expands the range of linear state feedback control, thereby better suppressing system chattering, but it also reduces the system's convergence rate. Therefore, the S-arcsin, which automatically adjusts the boundary layer thickness to the sliding surface error, ensures good control performance of the sliding mode observer under different operating conditions.

[0060] like Figure 4 The design flow chart of the synchronous rotating filter of this embodiment is shown, which mainly includes three steps:

[0061] Step 1: Park transform is used to separate and estimate the fundamental and harmonic components of the back EMF;

[0062] Step 2: Low-pass filter extracts and estimates the back EMF;

[0063] Step 3: Use Park inverse transform to restore the three parts of the estimated back EMF.

[0064] In this embodiment, the high-precision position detection method of the permanent magnet motor system specifically includes the following steps:

[0065] Step 1: Analyze the main back-EMF harmonic components of the non-sinusoidal back-EMF three-phase permanent magnet motor through a drag experiment, establish a harmonic back-EMF model of the permanent magnet motor, and analyze its impact on the position estimation error;

[0066] In order to accurately model the harmonic back EMF model of the three-phase permanent magnet synchronous motor with non-sinusoidal back EMF is established in the αβ coordinate system:

[0067]

[0068] Where, ψ f is the fundamental permanent magnet flux, K ψ(6n±1) is the percentage of odd harmonic flux to fundamental permanent magnet flux, n is the harmonic order, ω e is the rotor speed; θ e is the rotor position angle; are the estimated back electromotive force in the αβ coordinate system respectively.

[0069] Under steady-state conditions, the estimated speed can be considered and the actual speed ω e Equal. The estimated back EMF is input into the orthogonal phase-locked loop, and the influence of harmonic back EMF on position estimation error is obtained:

[0070]

[0071] Where, To estimate the rotor speed, To estimate the rotor position angle.

[0072] It can be seen from this that the (6n±1)th harmonic back EMF will cause a (6n)th position estimation error.

[0073] Step 2: Different from the traditional continuous function, an arcsine saturation function (S-arcsin) is proposed as the switching function, which can self-adjust the boundary layer thickness with the sliding surface error. This eliminates the front-stage low-pass filter structure in the traditional sliding mode observer, thus avoiding the phase lag in estimating the back EMF.

[0074] The mathematical model of the inverse sine saturation function S-arcsin is designed as follows:

[0075]

[0076] Where, S=[s α s β ] T is the column vector of the current estimation error, and “T” represents the matrix transpose. α 、s β is the current sliding mode surface under the defined α and β axes, sgn() is the sign function, λ is the basic boundary layer thickness, i α 、i β are the actual currents under the α and β axes respectively, are the estimated currents under the α and β axes, are the current estimation errors under α and β axes respectively, and there is

[0077] Step 3: Establish a mathematical model of the sliding mode observer based on the S-arcsin function and use the Lyapunov stability criterion to obtain the parameter selection range;

[0078] The three-phase stator current equation of the permanent magnet synchronous motor can be expressed as:

[0079]

[0080] Where ρ is the differential operator, R s is the stator resistance, L s is the stator inductance; u α 、u β are the stator voltages of the α-axis and β-axis respectively; e α 、e β are the extended back EMF of the α-axis and β-axis respectively, and satisfy:

[0081]

[0082] The sliding mode observer is expressed as follows:

[0083]

[0084] In the formula, “^” represents the estimated value, v α 、v β Estimate the back electromotive force for the α-axis and β-axis respectively, and satisfy:

[0085]

[0086] Different from the traditional sliding mode observer k s >max{e α , e β Since the absolute value of the switching function in the continuous control region is less than 1, the sliding mode observer based on the S-arcsin function has a stricter standard. In order to find this stable range, the Lyapunov function is as follows:

[0087]

[0088] According to Lyapunov's second theorem, the stability of the system can only be guaranteed when dV / dt < 0. Therefore, the time derivative of equation (10) is expressed as follows:

[0089]

[0090] By substituting (3) and (8) into (11), the following inequality can be derived to satisfy the stability condition:

[0091]

[0092] In formula (12), the first inequality is always true. The second and third inequalities lead to the following stability conditions:

[0093]

[0094] Where k s is the sliding mode gain.

[0095] Step 4: The output value of the sliding mode observer After Park transformation, the DC quantity in the dq coordinate system is obtained Use a first-order low-pass filter to filter out any order harmonic back EMF except the fundamental back EMF, and then extract the sinusoidal back EMF through the Park inverse transform of the fundamental back EMF

[0096] Fundamental component of the sliding mode observer output After Park transformation, the DC quantity in the dq coordinate system is obtained The expression is as follows:

[0097]

[0098] Then the fundamental back electromotive force is realized by Park inverse transformation Extraction:

[0099]

[0100] For the harmonic component of the sliding mode observer output, the expression is as follows:

[0101]

[0102] Among them, e dn is the nth harmonic content in the d-axis back electromotive force, e qn is the nth harmonic content in the q-axis back electromotive force.

[0103] When n=1,

[0104]

[0105] From formula (17), we can see that for a signal with a frequency of ω, the cutoff frequency is ω. c The first-order low-pass filter, the amplitude becomes the original signal times, and the phase lag is arctan(ω / ω) compared to the original signal c ). For the DC signal frequency ω=0, the amplitude remains unchanged and the phase remains unchanged. Therefore, the ω of the low-pass filter is c It can be set to a smaller value without introducing phase delay while ensuring the harmonic suppression capability.

[0106] Step 5: Combine the orthogonal phase-locked loop to output the sinusoidal back EMF Perform position estimation and obtain rotor estimation error The error is adjusted by the PI regulator to obtain the estimated speed Then the estimated rotor position angle is obtained through the integrator

[0107] The fundamental back EMF obtained by filtering is αf 、e βf In the input quadrature phase-locked loop structure, the rotor estimation error After the proportional integral PI regulator and the integral link, the estimated rotor position angle is obtained and estimated rotor speed

[0108] Figure 5(a) 、 5(b)Comparisons of experimental waveforms at 50 rpm are shown. Figure 5(a) shows the estimated back-EMF waveforms for the α and β axes using a traditional low-pass filter, while Figure 5(b) shows the estimated back-EMF waveforms for the α and β axes using a synchronously rotating filter. Figure 5(a) shows that the traditional low-pass filter has limited ability to suppress mid- and low-frequency harmonics, resulting in significant distortion in the estimated back-EMF waveform. Figure 5(b) shows that the estimated back-EMF using the synchronously rotating filter has significantly reduced harmonic content, and its waveform has become more sinusoidal.

[0109] Figure 5(c) 、 5(d) The experimental waveform comparison at 200 r / min is shown. Figure 5(c) shows the actual position, estimated position, and estimated position error waveforms based on a traditional low-pass filter, while Figure 5(d) shows the actual position, estimated position, and estimated position error based on a synchronous rotating filter. Figure 5(c) shows that a large phase lag occurs between the actual position and the estimated position using the traditional low-pass filter, and a significant sixth-order pulsation error occurs in the estimated position. Figure 5(d) shows that with the proposed synchronous rotating filter, there is no phase lag between the actual position and the estimated position, and the sixth-order pulsation error is effectively suppressed.

[0110] Figure 5(e) 、 5(f) A comparison of experimental waveforms at 500 r / min is shown, with Figure 5(e) showing the speed estimation, position estimation, and back EMF estimation waveforms based on a traditional low-pass filter, and Figure 5(f) showing the speed estimation, position estimation, and back EMF estimation waveforms based on the S-arcsin function and synchronous rotating filter. Figure 5(e) shows that under the traditional first-order low-pass filter + sign switching function strategy, the estimated speed exhibits severe chattering, and the estimated back EMF contains components dominated by the 5th and 7th harmonics. Figure 5(f) shows that with the proposed S-arcsin function and synchronous rotating filter, the estimated back EMF becomes more sinusoidal, effectively alleviating the speed chattering phenomenon.

[0111] The above merely describes a preferred embodiment of the present invention. A person skilled in the art will readily appreciate other advantages and variations based on the above embodiment. Therefore, the present invention is not limited to the above embodiment, which serves only as an example to provide a detailed, illustrative description of one form of the present invention. Any common changes and substitutions made by a person skilled in the art within the scope of the present invention's technical solution, without departing from the spirit of the present invention, should be included within the scope of protection of the present invention.

Claims

1. A high-precision position detection method for a permanent magnet motor system, characterized in that: The following steps are involved: S1, through the drag experiment, the main back EMF harmonic components of the non-sinusoidal back EMF three-phase permanent magnet motor are analyzed, the harmonic back EMF model of the permanent magnet motor is established, and the influence of the harmonic back EMF on the position estimation error is analyzed; S2, constructing an arcsine saturation function that self-adjusts the boundary layer thickness with the sliding surface error as a switching function; S3, a mathematical model of the sliding mode observer is established based on the inverse sine saturation function, and the parameter selection range is obtained using the Lyapunov stability criterion; S4, the output value of the sliding mode observer is subjected to Park transformation to obtain the DC quantity in the dq coordinate system; it is filtered using a first-order low-pass filter to retain the fundamental back EMF, and the fundamental back EMF is then subjected to inverse Park transformation to extract the sinusoidal back EMF; S5, combined with the orthogonal phase-locked loop, estimates the position of the output sinusoidal back EMF to obtain the rotor estimation error, which is passed through the PI regulator to obtain the estimated speed, and then through the integrator to obtain the estimated rotor position angle; In step S1, a harmonic back-EMF model of a three-phase permanent magnet synchronous motor with non-sinusoidal back-EMF is established in the αβ coordinate system: Where, ψ f is the fundamental permanent magnet flux, K ψ(6n±1) is the percentage of odd harmonic flux to fundamental permanent magnet flux, n is the harmonic order, ω e is the rotor speed; θ e is the rotor position angle; are the estimated back electromotive force in αβ coordinate system respectively; The influence of harmonic back EMF on position estimation error is as follows: Where, To estimate the rotor speed, To estimate the rotor position angle; In step S2, the mathematical model of the arcsine saturation function S-arcsin is: Where, S=[s α s β ] T is the column vector of the current estimation error, "T" represents the matrix transpose; s α 、s β is the current sliding mode surface under the α and β axes, sgn() is the sign function, λ is the basic boundary layer thickness, i α 、i β are the actual currents under the α and β axes respectively, are the estimated currents under the α and β axes, are the current estimation errors under α and β axes respectively, and there is In step S3, the three-phase stator current equation of the permanent magnet synchronous motor is expressed as: Where ρ is the differential operator, R s is the stator resistance, L s is the stator inductance; u α 、u β is the stator voltage in the αβ coordinate system; e α 、e β is the extended back EMF in the αβ coordinate system, and satisfies: The sliding mode observer is expressed as follows: In the formula, the superscript "^" indicates an estimated value; v α 、v β are the estimated back electromotive force of the α-axis and β-axis respectively, and they satisfy: Since the absolute value of the switching function in the continuous control region is less than 1, the expression of the Lyapunov function is as follows: According to Lyapunov's second theorem, the stability of the system can only be guaranteed when dV / dt < 0, so: The stability conditions are as follows: Where k s is the sliding mode gain.

2. The high-precision position detection method for a permanent magnet motor system according to claim 1, characterized in that: In step S4, the fundamental component output by the sliding mode observer is After Park transformation, the DC quantity in the dq coordinate system is obtained The expression is as follows: Then the fundamental back electromotive force is realized by Park inverse transformation Extraction: For the harmonic component of the sliding mode observer output, the expression is as follows: Among them, e dn is the nth harmonic content in the d-axis back electromotive force, e qn is the nth harmonic content in the q-axis back electromotive force.

3. The high-precision position detection method for a permanent magnet motor system according to claim 2, characterized in that: In step S5, the sinusoidal back electromotive force obtained by filtering is Input into the orthogonal phase-locked loop structure to obtain the rotor estimation error The rotor estimation error is passed through the PI regulator to estimate the speed Then the estimated rotor position angle is obtained through the integrator

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