High-precision position detection method for permanent magnet motor system

Abstract

The invention discloses a high-precision position detection method for a permanent magnet motor system, and the method comprises the following steps: S1, building a harmonic counter electromotive force model of a permanent magnet motor, and analyzing the influence of the harmonic counter electromotive force on a position estimation error; s2, constructing an arcsine saturation function of which the boundary layer thickness is self-adjusted along with the error of the sliding mode surface as a switching function; s3, establishing a mathematical model of a sliding-mode observer based on an arcsine saturation function, and obtaining a parameter selection range by using a Lyapunov stability criterion; s4, carrying out Park conversion on the output value of the sliding-mode observer to obtain a direct current amount under a dq coordinate system; a first-order low-pass filter is used for filtering, fundamental wave counter electromotive force is reserved, and sine counter electromotive force is extracted from the fundamental wave counter electromotive force through Park inverse transformation; and S5, in combination with an orthogonal phase-locked loop, performing position estimation on the output sine counter electromotive force to obtain an estimated rotor position angle and an estimated rotor rotating speed. The precision and the dynamic performance of sensorless control of the permanent magnet motor can be improved.

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] The sensorless control of a permanent magnet synchronous motor (PMSM) uses the current and voltage information measured by the motor itself, without 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 the sensorless control technologies for PMSMs operating at medium and high speeds, back-EMF-based methods are widely used. However, due to the nonlinearity of the inverter and the deviations in the actual manufacturing process of the motor, the estimated back-EMF in the sliding mode observer-based sensorless control method has (6n±1) harmonics, resulting in a 6n harmonic error in the estimated rotor position, which further causes torque fluctuations and speed jitter.

[0003] At present, the position sensorless methods for rotor position estimation error can be divided into two categories: compensation-based method and signal filtering-based method. Among them, the compensation-based method can reduce the rotor position estimation error by eliminating the influence of the nonlinearity of the voltage source inverter on the position estimation. However, this method usually relies on accurate control object parameters, or requires the adjustment of multiple controller parameters. The signal filtering method directly filters the harmonics in the estimated back electromotive force and extracts the fundamental frequency component to suppress the rotor position estimation error. The signal filtering method usually directly uses a low-pass filter, or it is necessary to design multiple notch filters to filter out harmonic back electromotive forces of different orders. If the cutoff frequency of the low-pass filter is set too high, the harmonic content of the estimated back electromotive force after filtering is still large; if the cutoff frequency of the low-pass filter is set too low, there will be a large phase delay, which reduces the control accuracy of the system. 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 motor parameter changes and external disturbances.

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

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

[0007] S2, construct 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; a first-order low-pass filter is used to filter the output value to retain the fundamental back EMF, and the fundamental back EMF is then subjected to Park inverse transformation to extract the sinusoidal back EMF;

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

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

[0012]

[0013] In the formula, 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] In the formula, To estimate the rotor speed, To estimate the rotor position angle.

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

[0018]

[0019]

[0020]

[0021] In the formula, S = [s α s β ] Tis the column vector of the current estimation error, “T” represents the matrix transpose; s α 、s β is the current sliding 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 the α and β axes respectively, and

[0022] Further, in step S3, the three-phase stator current equation of the permanent magnet synchronous motor is expressed as:

[0023]

[0024] In the formula, 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:

[0025]

[0026] The sliding mode observer is expressed as follows:

[0027]

[0028] 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:

[0029]

[0030] According to 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:

[0031]

[0032] According to Lyapunov's second theorem, the stability of the system can only be guaranteed when dV / dt<0, then:

[0033]

[0034] The stability conditions are as follows:

[0035]

[0036] In the formula, k s is the sliding mode gain.

[0037] Further, 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:

[0038]

[0039] Then the fundamental back electromotive force is realized by Park inverse transformation Extraction:

[0040]

[0041] For the harmonic component of the sliding mode observer output, the expression is as follows:

[0042]

[0043] 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.

[0044] Further, in step S5, the sinusoidal back EMF 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

[0045] Compared with the prior art, the present invention has the following significant effects:

[0046] 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;

[0047] 2. In the present invention, the arcsine saturation function (F-arcsin) whose boundary layer thickness is self-adjusted with the sliding surface error is used as the switching function, thereby eliminating the front-stage low-pass filter structure in the traditional sliding mode observer, thereby avoiding the phase lag of estimating the back electromotive force;

[0048] 3. The F-arcsin-based sliding mode observer in the present invention can effectively reduce the jitter 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

[0049] Figure 1 The overall control structure diagram of PMSM without position sensor to suppress position estimation error;

[0050] Figure 2 This is the block diagram of sliding mode control based on F-arcsin and synchronous rotating filter;

[0051] Figure 3 Arcsin switching function for different boundary layer thicknesses;

[0052] Figure 4 This is the design flow chart of the synchronous rotating filter;

[0053] Figure 5(a) is a waveform diagram of the estimated back electromotive force of the α-β axis based on a traditional low-pass filter at 50 r / min;

[0054] FIG5( b ) is a waveform diagram of the estimated back electromotive force of the α-β axis of the base synchronous rotating filter at 50 r / min;

[0055] Figure 5(c) shows the actual position, estimated position, and position error diagram based on the traditional low-pass filter at 200 r / min;

[0056] Figure 5(d) is a diagram showing the actual position, estimated position, and position error of the base synchronous rotating filter at 200 r / min;

[0057] Figure 5(e) is the waveform diagram of speed estimation, position estimation, and back-EMF estimation based on the traditional low-pass filter at 500 r / min;

[0058] Figure 5(f) shows the waveforms of speed estimation, position estimation, and back-EMF estimation based on the F-arcsin function and the synchronous rotating filter at 500 r / min. DETAILED DESCRIPTION

[0059] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0060] 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, the front-stage low-pass filter of the sliding mode observer is removed through the F-arcsin function (inverse sine saturation function), and then the harmonic back EMF of any order except the fundamental back EMF is filtered out through the synchronous rotating filter, and finally the rotor position angle and speed are obtained using the orthogonal phase-locked loop.

[0061] The block diagram of sliding mode control based on F-arcsin and synchronous rotating filter is as follows: Figure 2 The waveform of F-arcsin at different boundary layer thicknesses is shown in Figure 3 As shown in the figure, 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 the system chattering, but it will reduce the system convergence speed. Therefore, F-arcsin with the function of self-adjusting the boundary layer thickness with the sliding surface error can ensure that the sliding mode observer has good control performance under different working conditions.

[0062] like Figure 4 The design flow chart of the synchronous rotating filter of this embodiment is shown, which mainly includes three steps:

[0063] Step 1: Park transform separates and estimates the fundamental and harmonic components of the back EMF;

[0064] Step 2: Low-pass filter extracts the estimated back EMF;

[0065] Step 3: Park's inverse transform restores the three parts of the estimated back EMF.

[0066] In this embodiment, the high-precision position detection method of the permanent magnet motor system specifically includes the following steps:

[0067] Step 1, by analyzing the main back-EMF harmonic components of the non-sinusoidal back-EMF three-phase permanent magnet motor through a drag experiment, a harmonic back-EMF model of the permanent magnet motor is established, and its influence on the position estimation error is analyzed;

[0068] In order to accurately model the harmonic back-EMF model of the three-phase permanent magnet synchronous motor with non-sinusoidal back-EMF in the αβ coordinate system is established:

[0069]

[0070] In the formula, 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.

[0071] Under steady-state conditions, the estimated speed can be considered With 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:

[0072]

[0073] In the formula, To estimate the rotor speed, To estimate the rotor position angle.

[0074] It can be seen from this that the (6n±1)th harmonic back EMF will cause a (6n)th position estimation error.

[0075] Step 2: Different from the traditional continuous function, an arcsine saturation function (F-arcsin) that self-adjusts the boundary layer thickness with the sliding surface error is proposed as a switching function, which eliminates the front-stage low-pass filter structure in the traditional sliding mode observer, thereby avoiding the phase lag of estimating the back EMF.

[0076] The mathematical model of the arcsine saturation function F-arcsin is designed as:

[0077]

[0078]

[0079]

[0080] In the formula, 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 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,

[0081] are the current estimation errors under the α and β axes respectively, and

[0082] Step 3, a mathematical model of the sliding mode observer is established based on the F-arcsin function, and the parameter selection range is obtained using the Lyapunov stability criterion;

[0083] The three-phase stator current equation of the permanent magnet synchronous motor can be expressed as:

[0084]

[0085] In the formula, ρ is the differential operator, R s is the stator resistance, L s is the stator inductance; u α 、u βare 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:

[0086]

[0087] The sliding mode observer is expressed as follows:

[0088]

[0089] 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:

[0090]

[0091] 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 F-arcsin function has a stricter standard. In order to find this stable range, the Lyapunov function is as follows:

[0092]

[0093] 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:

[0094]

[0095] By substituting (3) and (8) into (11), the following inequality can be derived to satisfy the stability condition:

[0096]

[0097] In formula (12), the first inequality is always valid, and the following stability conditions are derived from the second and third inequalities:

[0098]

[0099] In the formula, k s is the sliding mode gain.

[0100] Step 4: The output value of the sliding mode observer After Park transformation, the DC quantity in the dq coordinate system is obtained A first-order low-pass filter is used to filter out any order of harmonic back EMF except the fundamental back EMF, and then the fundamental back EMF is transformed through Park inverse transformation to extract the sinusoidal back EMF.

[0101] 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:

[0102]

[0103] Then the fundamental back electromotive force is realized by Park inverse transformation Extraction:

[0104]

[0105] For the harmonic component of the sliding mode observer output, the expression is as follows:

[0106]

[0107] 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.

[0108] When n=1,

[0109]

[0110] 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 converts the amplitude to the original signal times, and the phase lag is arctan(ω / ω) compared to the original signal c ). For a 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.

[0111] Step 5: Combine the orthogonal phase-locked loop to output the sinusoidal back EMF Perform position estimation and obtain the 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

[0112] The fundamental back EMF obtained by filtering 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

[0113] Figure 5(a) , 5(b) The experimental waveform comparison at 50r / min is shown, where Figure 5(a) is the estimated back EMF waveform under the α and β axes based on the traditional low-pass filter, and Figure 5(b) is the estimated back EMF waveform under the α and β axes based on the synchronous rotating filter. As shown in Figure 5(a), the traditional low-pass filter has limited ability to suppress medium- and low-frequency harmonics, and the estimated back EMF wave is significantly distorted. As shown in Figure 5(b), the estimated back EMF harmonic content based on the synchronous rotating filter is significantly reduced, and its waveform becomes more sinusoidal.

[0114] Figure 5(c) , 5(d) The experimental waveform comparison at 200r / min is shown, where Figure 5(c) is the actual position, estimated position, and estimated position error waveform based on the traditional low-pass filter, and Figure 5(d) is the actual position, estimated position, and estimated position error based on the synchronous rotating filter. As shown in Figure 5(c), there is a large phase lag between the actual position and the estimated position based on the traditional low-pass filter, and there is an obvious 6-order pulsation error in the estimated position. As shown in Figure 5(d), there is no phase lag between the actual position and the estimated position based on the proposed synchronous rotating filter, and the 6-order pulsation error is effectively suppressed.

[0115] Figure 5(e) , 5(f) The experimental waveform comparison at 500r / min is shown, where Figure 5(e) shows the speed estimation, position estimation, and back EMF estimation waveforms based on the traditional low-pass filter, and Figure 5(f) shows the speed estimation, position estimation, and back EMF estimation waveforms based on the F-arcsin function and the synchronous rotating filter. As shown in Figure 5(e), under the traditional first-order low-pass filter + sign switching function strategy, the estimated speed has serious jitter phenomenon, and the estimated back EMF contains components dominated by the 5th and 7th harmonics. As shown in Figure 5(f), based on the proposed F-arcsin function and the synchronous rotating filter, the estimated back EMF becomes more sinusoidal, and the jitter phenomenon of the speed is effectively alleviated.

[0116] The above is only a description of the preferred embodiment of the present invention. For those skilled in the art, other advantages and variations can be easily associated with the above embodiment. Therefore, the present invention is not limited to the above embodiment, which is only used as an example to provide a detailed and exemplary description of one form of the present invention. Without departing from the scope of the purpose of the present invention, the usual changes and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included in the protection scope 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, analyze the main back-EMF harmonic components of the non-sinusoidal back-EMF three-phase permanent magnet motor through drag experiment, establish the harmonic back-EMF model of the permanent magnet motor, and analyze the influence of the harmonic back-EMF on the position estimation error; S2, construct 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; a first-order low-pass filter is used to filter the output value to retain the fundamental back EMF, and the fundamental back EMF is then subjected to Park inverse transformation to extract the sinusoidal back EMF; S5, combined with an orthogonal phase-locked loop, estimates the position of the output sinusoidal back EMF to obtain the rotor estimation error, and obtains the estimated speed through a PI regulator, and then obtains the estimated rotor position angle through an integrator.

2. The method for high-precision position detection of a permanent magnet motor system according to claim 1, characterized in that: In step S1, a harmonic back-EMF model of a three-phase permanent magnet synchronous motor with non-sinusoidal back-EMF in an αβ coordinate system is established: In the formula, 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: In the formula, To estimate the rotor speed, To estimate the rotor position angle.

3. The method for high-precision position detection of a permanent magnet motor system according to claim 2, characterized in that: In step S2, the mathematical model of the arcsine saturation function F-arcsin is: In the formula, 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 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 the α and β axes respectively, and 4. The method for high-precision position detection of a permanent magnet motor system according to claim 3, characterized in that: In step S3, the three-phase stator current equation of the permanent magnet synchronous motor is expressed as: Where ρ is the differential operator, Rs is the stator resistance, Ls 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: According to 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, then: The stability conditions are as follows: In the formula, k s is the sliding mode gain.

5. The method for high-precision position detection of a permanent magnet motor system according to claim 4, characterized in that: In step S4, the fundamental component of the sliding mode observer output 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.

6. The method for high-precision position detection of a permanent magnet motor system according to claim 5, characterized in that: In step S5, the sinusoidal back electromotive force obtained by filtering 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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