Hall position measurement optimization method of moving magnet type magnetic suspension planar motor

Abstract

According to the Hall position measurement optimization method of the moving-magnet type magnetic suspension planar motor, the magnetic field characteristics of a Halbach permanent magnet array are combined, an orthogonal Hall array is adopted to obtain a magnetic induction intensity signal, and a cascade delay elimination algorithm is introduced to suppress harmonic distortion, so that the displacement calculation precision is improved. A time delay signal elimination method is a method for eliminating signal interference caused by time delay, a harmonic signal is effectively eliminated by carrying out time delay processing on a voltage signal and combining the voltage signal with an original signal, and meanwhile the integrity of a fundamental component can be reserved. The signal is delayed by a quarter of a period by using the voltage quantity under the alpha and beta coordinate systems, and is combined with the original signal. In the process, a harmonic component in the signal can be eliminated, and a fundamental component is ensured not to be influenced by delay attenuation, so that a phase error caused by harmonic waves can be effectively avoided. Experimental results show that harmonic waves can be effectively filtered out.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of magnetic levitation planar motor and position detection. Taking the Halbach permanent magnet array with a moving magnet structure as the research object, aiming at the problem of precision decline caused by harmonic interference when the array is used for position detection in a magnetic levitation planar motor, a displacement measurement method based on a Hall sensor array is proposed, and a cascaded delay signal cancellation (CDSC) algorithm is introduced to effectively suppress high-order harmonics and improve the linearity and stability of displacement calculation. BACKGROUND

[0002] Magnetic levitation planar motors are widely used in precision manufacturing, semiconductor processing and automated transportation due to their advantages of non-contact, high precision and high response speed. In particular, magnetic levitation planar motors with a moving magnet structure have very high requirements for displacement detection accuracy and real-time performance, which are key factors affecting the dynamic performance and control stability of the motor.

[0003] Currently, displacement monitoring of planar motors often uses traditional sensors such as capacitive sensors, eddy current sensors, grating scales and laser interferometers, but these methods generally have high cost, complex structure, are easily disturbed by the environment, and are not suitable for large-scale motion. In contrast, magnetic field detection schemes based on Hall sensors have the advantages of low cost, small size, simple installation and good environmental adaptability, and are increasingly valued. However, in practical applications, due to installation errors of the permanent magnet array, non-ideal magnetic field and non-linearity of the Hall element itself, high-order harmonic components are often included in the detection signal, which seriously affects the displacement calculation accuracy. The cascaded delay cancellation method proposed in the application solves the problem of non-linearity between the Hall sensor and the permanent magnet array. SUMMARY

[0004] Therefore, the purpose of the application is to provide a Hall position measurement optimization method for a moving magnet type magnetic levitation planar motor to solve the problems in the prior art.

[0005] The technical solution adopted by the application is as follows:

[0006] In order to improve the mover, the application proposes a Hall position measurement optimization method for a moving magnet type magnetic levitation planar motor, which includes the following steps:

[0007] S1, a Halbach array with a width of 40mm and a height of 10mm is established by two-dimensional finite element simulation. Since there is a difference in the magnetic flux measured by the Hall sensor at different heights, far from the array will cause the measured magnetic flux density to decrease, and the signal-to-noise ratio will decrease, and close to the array will make the magnetic field harmonic more significant. Therefore, in order to analyze the magnetic induction intensity and its harmonic content in the horizontal and vertical directions at different heights, the simulation range is set from 1mm below the array to 20mm, and then by analyzing the harmonic content, the optimal position of the Hall sensor is selected, and the data at this position is extracted to calculate the displacement.

[0008] S2, the output voltage model of the Hall sensor is established, the corresponding signal data of the selected optimal sensor position is input into the cascade delay elimination model, and the harmonic suppression effect of the model at this position is analyzed and verified by simulation means, so as to realize the effective elimination of the harmonic interference in the Hall sensor signal.

[0009] Further, in step S1, the magnetic induction intensity and the harmonic content of the magnetic induction intensity at different heights of the Halbach array are determined by two-dimensional finite element simulation, and the total harmonic distortion THD of the magnetic induction intensity is calculated:

[0010]

[0011] In the formula: is the amplitude of each harmonic component of the magnetic induction intensity. k is the harmonic number. x1 represents the fundamental wave in the x direction.

[0012] Further, in step S1, the installation position of the Hall sensor is determined by simulation, and the displacement is calculated by detecting the magnetic induction intensity in the horizontal and vertical directions at the same position and then performing arctangent calculation, and the calculation formula is:

[0013]

[0014] In the formula: K is the proportional coefficient. x is the magnetic induction intensity in the horizontal direction. y is the magnetic induction intensity in the vertical direction.

[0015] Further, in step S2, the output voltage v(t) of the Hall sensor can be represented by Fourier series expansion:

[0016]

[0017] In the formula v dc is the direct current component of the Hall sensor output signal; vf ω f , The distribution represents the amplitude, angular velocity, and phase of the fundamental wave in the output signal. 2n+1 , (2n+1)ω f , v 2n ,2nω f , These represent the amplitude, angular velocity, and phase of the odd harmonic voltage and the even harmonic voltage in the output signal of the linear Hall sensor, respectively.

[0018] The expression for eliminating the output signal delay is established by using the Hall sensor output signal:

[0019]

[0020] In the formula, t represents time, T is the fundamental period, and n is a multiple.

[0021] In the DSC model of the α and β coordinate systems, the output model signals of the two Hall sensors are established:

[0022]

[0023] In the formula This refers to the output signal in the α and β coordinate system. a This represents the output amplitude in the α coordinate system. β This represents the output amplitude in the β coordinate system. The harmonic orders h = ±1, ±2...±H.

[0024] Furthermore, in step S2, using the Hall signal output model of a single DSC model in the α and β coordinate systems, the signal output expression of Cascaded Delayed Signal Compensation (CDSC) in the d and q coordinate systems is further derived:

[0025]

[0026] Where V is the voltage amplitude, and ω is the angular frequency. This is the harmonic phase angle.

[0027] The d-axis and q-axis output signals processed by DSC are combined into a single space vector:

[0028]

[0029] in This refers to the output signal in the d and q coordinate system. For DSC n For the hth harmonic The harmonic gain of the signal and phase angle The representative signal is processed by the DSC n The amplification and delay of the original signal after processing.

[0030] Through analysis, only the harmonic gain is 0, the harmonic of the d, q axis can be eliminated, therefore, let The following can be obtained:

[0031]

[0032] Further, in step S2, since the d, q coordinate system is obtained by synchronous rotation of the a, β coordinate system at the fundamental wave speed angular velocity, the DSC operator under the d, q coordinate system is transformed to the α, β coordinate system to obtain:

[0033]

[0034] Using Euler formula, the above formula is transformed to the time domain to have

[0035]

[0036] In the formula, is the output signal under the α, β coordinate system.

[0037] Compared with the prior art, the present application has the beneficial effects that:

[0038] The application provides a dynamic magnetic type suspension plane motor position measurement optimization method based on a Hall sensor, introduces a cascade delay signal elimination algorithm, and solves problems of serious harmonic interference, complex algorithm, poor real-time performance and the like in a traditional position detection scheme. Existing detection methods depend on high-precision sensors such as lasers and gratings or complex filtering algorithms. Although these methods can improve precision, they are high in cost, sensitive to the environment or large in calculation resource consumption, and are difficult to meet the dual requirements of economy and real-time performance in industrial applications.

[0039] By combining the orthogonal Hall array and the CDSC filtering, the multiple high-frequency harmonic interference caused by the Halbach permanent magnet array is effectively suppressed, especially the fifth and higher harmonics are significantly suppressed, so that the linearity and sinusoidality of the displacement measurement signal are improved. The CDSC algorithm has the advantages of simple operation structure, good real-time performance and easy implementation in an embedded control system, does not depend on complex modeling or large-scale training process, and can directly act on the sampling signal and filter out the interference of a specific frequency band. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced. Obviously, the drawings in the following description only relate to the preferred embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort based on these drawings.

[0041] Figure 1 , Halbach array magnetic field line distribution diagram.

[0042] Figure 2, the component curve of the magnetic induction intensity of the Halbach array under different air gap heights. Figure 2(a) is the horizontal direction component curve of the magnetic induction intensity of the Halbach array under different air gap heights, and figure 2(b) is the vertical direction component curve of the magnetic induction intensity of the Halbach array under different air gap heights.

[0043] Figure 3 , the harmonic content of the horizontal direction component of the magnetic induction intensity of the Halbach array under different air gap heights.

[0044] Figure 4 , the harmonic content of the vertical direction component of the magnetic induction intensity of the Halbach array under different air gap heights.

[0045] Figure 5 , the position solution without filtering.

[0046] Figure 6, comparison of simulation magnetic field signal before and after harmonic elimination, figure 6(a) is the comparison of horizontal direction harmonic elimination magnetic induction intensity signal, and figure 6(b) is the comparison of vertical direction harmonic elimination magnetic induction intensity signal. DETAILED DESCRIPTION

[0047] The present application will be described in detail below in combination with the drawings and embodiments. The listed embodiments are only used to explain the present application, and are not used to limit the scope of the present application.

[0048] S1, determine the magnetic induction intensity and the harmonic content of the magnetic induction intensity of the Halbach array under different heights by two-dimensional finite element simulation, and calculate the total harmonic distortion THD (Total Harmonic Distortion) of the magnetic induction intensity:

[0049]

[0050] In the formula: is the amplitude of each harmonic component of the magnetic induction intensity. K is the harmonic number. B x1 is the fundamental wave in x direction. The harmonic content under different air gap heights is as shown in Figure Three 、 Four ​

[0051] The installation position of the Hall sensor was determined through simulation, and the displacement was calculated by arctangent calculation after detecting the magnetic induction intensity in both the horizontal and vertical directions at the same location. The calculation formula is as follows:

[0052]

[0053] In the formula: K is the proportionality coefficient. B x B represents the magnetic field strength in the horizontal direction. y Let be the magnetic flux density in the vertical direction. Displacement calculation is as follows: Figure 5 As shown.

[0054] S2. The output voltage v(t) of the Hall sensor can be expressed by Fourier series expansion:

[0055]

[0056] In the formula v dc The DC component of the Hall sensor output signal; v f ω f , The distribution represents the amplitude, angular velocity, and phase of the fundamental wave in the output signal. 2n+1 , (2n+1)ω f , v 2n ,2nω f , These represent the amplitude, angular velocity, and phase of the odd harmonic voltage and the even harmonic voltage in the output signal of the linear Hall sensor, respectively.

[0057] The expression for eliminating the output signal delay is established by using the Hall sensor output signal:

[0058]

[0059] In the formula, t represents time, T is the fundamental period, and n is a multiple.

[0060] In the DSC model of the α and β coordinate systems, the output model signals of the two Hall sensors are established:

[0061]

[0062] In the formula This refers to the output signal in the α and β coordinate system. a This represents the output amplitude in the α coordinate system. β This represents the output amplitude in the β coordinate system. The harmonic orders h = ±1, ±2...±H.

[0063] Furthermore, in step S2, using the Hall signal output model of a single DSC model in the α and β coordinate systems, the signal output expression of Cascaded Delayed Signal Compensation (CDSC) in the d and q coordinate systems is further derived:

[0064]

[0065] Where V is the voltage amplitude, and ω is the angular frequency. This is the harmonic phase angle.

[0066] The d-axis and q-axis output signals processed by DSC are combined into a single space vector:

[0067]

[0068] in This refers to the output signal in the d and q coordinate system. For DSC n For the hth harmonic The harmonic gain. Its magnitude and phase angle The representative signal passes through DSC n The original signal is amplified and delayed after processing.

[0069] Analysis shows that simply setting the harmonic gain to 0 can eliminate the harmonics along the d and q axes. Therefore, let... We can obtain:

[0070]

[0071] Furthermore, in step S2, since the d and q coordinate systems are obtained by synchronously rotating the α and β coordinate systems with the fundamental wave velocity and angular velocity, the DSC operator in the d and q coordinate systems can be transformed to the α and β coordinate systems to obtain:

[0072]

[0073] Using Euler's formula, the above equation can be transformed to the time domain.

[0074]

[0075] In the formula, This refers to the output signal in the a and β coordinate system.

[0076] Finally, the above calculations show the comparison of the simulated magnetic field signal before and after harmonic elimination, as shown in Figure 6.

[0077] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An optimization method for Hall position measurement of a moving-magnet magnetic levitation planar motor, characterized in that: S1. A Halbach array with a width of 40 mm and a height of 10 mm was established using two-dimensional finite element simulation. Since the magnetic flux measured by the Hall sensor varies at different heights, moving away from the array will reduce the measured magnetic flux density and the signal-to-noise ratio, while moving closer to the array will make the magnetic field harmonics more significant. Therefore, in order to analyze the magnetic induction intensity and its harmonic content in the horizontal and vertical directions at different heights, the simulation range was set from 1 mm below the array to 20 mm. Then, by analyzing the harmonic content, the optimal position of the Hall sensor was selected, and the data at this position was extracted to calculate its displacement. S2. Establish the output voltage model of the Hall sensor. Based on the selected optimal sensor position, input the corresponding signal data into the cascaded delay elimination model. Use simulation to analyze and verify the harmonic suppression effect of the model at this position, thereby achieving effective elimination of harmonic interference in the Hall sensor signal.

2. The Hall position measurement optimization method for a moving-magnet magnetic levitation planar motor according to claim 1, characterized in that: In step S1, the magnetic flux density and harmonic content of the magnetic flux density at different heights of the Halbach array are determined by two-dimensional finite element simulation, and the total harmonic distortion (THD) of the magnetic flux density is calculated. In the formula: This represents the amplitude of each harmonic component of the magnetic flux density. k is the harmonic order. B x1 It is represented as the fundamental wave in the x-direction.

3. The Hall position measurement optimization method for a moving-magnetic levitation planar motor according to claim 1, characterized in that: In step S1, the installation position of the Hall sensor is determined through simulation, and the displacement is calculated by arctangent calculation after detecting the magnetic induction intensity in both the horizontal and vertical directions at the same position. The calculation formula is as follows: In the formula: K is the proportionality coefficient. B x B represents the magnetic flux density in the horizontal direction. y The magnetic flux density is in the vertical direction.

4. The Hall position measurement optimization method for a moving-magnetic levitation planar motor according to claim 1, characterized in that: In step S2, the output voltage v(t) of the Hall sensor can be represented by a Fourier series expansion. In the formula v dc The DC component of the Hall sensor output signal; v f ω f , The distribution represents the amplitude, angular velocity, and phase of the fundamental wave in the output signal. 2n+1 , (2n+1)ω f , v 2n ,2nω f , These represent the amplitude, angular velocity, and phase of the odd harmonic voltage and the even harmonic voltage in the output signal of the linear Hall sensor, respectively. The expression for eliminating the output signal delay is established by using the Hall sensor output signal: In the formula, t represents time, T is the fundamental period, and n is a multiple. Further, in the DSC model of the α and β coordinate systems, the output model signals of the two Hall sensors are established: In the formula This refers to the output signal in the α and β coordinate system. ɑ This represents the output amplitude in the α coordinate system. β This represents the output amplitude in the β coordinate system. The harmonic orders h = ±1, ±2...±H.

5. The Hall position measurement optimization method for a moving-magnet type magnetic levitation planar motor according to claim 1, characterized in that: Using the Hall signal output model of a single DSC model in the α and β coordinate systems, the signal output expression of Cascaded Delayed Signal Compensation (CDSC) in the d and q coordinate systems is further derived: Where V is the voltage amplitude, and ω is the angular frequency. This is the harmonic phase angle. The d-axis and q-axis output signals processed by DSC are combined into a single space vector: in This refers to the output signal in the d and q coordinate system. For DSC n For the hth harmonic The harmonic gain. Its magnitude and phase angle The representative signal passes through DSC n The original signal is amplified and delayed after processing. Analysis shows that simply setting the harmonic gain to 0 can eliminate the harmonics along the d and q axes. Therefore, let... We can obtain:

6. The Hall position measurement optimization method for a moving-magnet magnetic levitation planar motor according to claim 1, characterized in that: Since the d-q coordinate system is obtained by synchronously rotating the α-β coordinate system with the fundamental wave velocity and angular velocity, the DSC operator in the d-q coordinate system can be transformed to the α-β coordinate system to obtain... Using Euler's formula, the above equation can be transformed to the time domain. In the formula, This refers to the output signal in the α and β coordinate system.

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