Permanent magnet spherical rotor position identification method based on compressed sensing

Abstract

The application relates to a permanent-magnet spherical rotor position identification method based on compressed sensing, and a permanent-magnet spherical motor, which comprises a base, a spherical stator, a stator coil and a spherical rotor, the rotor surface is embedded with permanent-magnet magnetic poles, the magnetic poles are divided into two layers along the equator, each layer has four permanent-magnet magnetic poles, and N poles and S poles are alternately distributed; the rotor position is identified based on the radial magnetic field intensity information at the eighth-of-a-sphere air gap of the permanent-magnet spherical motor, and the identification comprises the following steps: first, determining the required number of sensors; second, determining the specific positions of the sensors; third, designing an observation matrix A in compressed sensing; fourth, identifying the rotor position of the permanent-magnet spherical motor, including data circle screening, magnetic pole center position calculation, magnetic pole position and rotor position conversion.

Description

Technical Field

[0001] This invention relates to a position detection method for a permanent magnet spherical motor rotor, belonging to the field of permanent magnet spherical motor control technology. Background Technology

[0002] With the development of modern technology, the requirements for the performance and structure of production tools are becoming increasingly stringent. Multi-degree-of-freedom motion structures hold significant strategic importance in fields such as industrial production and aerospace. Previous multi-degree-of-freedom motion devices utilized multiple single-degree-of-freedom motors in conjunction with corresponding mechanical devices. This not only resulted in complex structures and large system volumes but also significantly increased the system's failure rate, especially in the connections between the motors. Spherical motors, however, can achieve three-degree-of-freedom motion through a simple structure and relatively small size, thus attracting widespread attention from scholars both domestically and internationally. When implementing closed-loop control of a spherical motor, it is necessary to monitor the rotor position in real time.

[0003] Current research on position detection methods for spherical motor rotors can be broadly categorized into five types based on their working principles: methods based on mechanical frames, methods based on rotor surface features, methods based on novel sensors, methods based on specific structures, and methods based on Hall effect sensors. While all of these methods can identify rotor position, mechanical frame-based measurement systems are bulky, limiting the movement of the spherical camera; rotor surface characterization methods require image processing of the rotor surface, resulting in complex algorithms or significant dependence on the quality of the acquired images; among novel sensors, the sensitivity of optical mouse sensors is affected by the microscopic characteristics of the rotor surface, and their high-speed detection performance remains unclear; the output of MEMS sensors is also not stable enough.

[0004] Related literature

[0005] [1]Lee KM,Kwan CKDesign concept development of a sphericalstepper for robotic applications[J].IEEE Transactions on Robotics andAutomation 1991,7(1):175-181.

[0006] [2] Kim J, Son H. Two-DOF orientation measurement system for a magnet with single magnetic sensor and neural network [C]. 2017 14th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI). 2017.

[0007] [3]Lu Y, Hu C, WangQ, et al. A New Rotor Position Measurement Method for Permanent Magnet Spherical Motors[J]. Applied Sciences, 2018, 8(12).

[0008] [4] G.Li, J.Feng, B.Li, and H.Li, "An Orientation Measurement System of the Two-DOF Permanent Magnet Spherical Motor Based on Hall Ring Detectors," Measurement, vol.150, no.1, pp.107073, 2019.

[0009] [5] J. Zhang, L. Yuan, SL Chen, Y. Liang, X. Huang, C. Zhang, and G. Yang, "Asurvey on design of reaction spheres and associated speed and orientation measurement technologies," ISA Trans, vol.99, pp.417-431, Apr 2020. Summary of the Invention

[0010] The purpose of this invention is to provide a method for identifying the position of a permanent magnet spherical rotor based on compressed sensing. This method utilizes a linear Hall sensor array placed in the air gap to calculate the rotor position of the spherical motor based on the sensor output signals. Based on compressed sensing technology, this invention first designs a novel Hall sensor array, then reconstructs the magnetic field data of the spherical motor's air gap using the sensor output values, and finally calculates the rotor position of the permanent magnet spherical motor. The technical solution is as follows:

[0011] A method for position identification of a permanent magnet spherical rotor based on compressed sensing technology is applicable to a permanent magnet spherical motor, including a base, a spherical stator, stator coils, and a spherical rotor. The rotor surface is embedded with permanent magnet poles, which are divided into upper and lower layers along the equator, each layer having four permanent magnet poles, with N and S poles alternating. The rotor position is identified based on the radial magnetic field strength information at the air gap of one-eighth of the spherical surface of the permanent magnet spherical motor. A Hall sensor is placed in the S1 space, where S1 space is a spherical coordinate system. All of these fall within the 0–90° space, and this radial magnetic field strength information is obtained by processing information collected by a sensor array using compressed sensing technology; it includes the following steps:

[0012] The first step is to determine the required number of sensors.

[0013] Let N be the amount of original data for the original signal X required by compressed sensing theory, and let K be the sparsity of the original signal and M be the amount of data for the observed signal Y, which need to satisfy formula (1).

[0014] M = K·ln(N / K) (1)

[0015] Based on the finite element simulation results, the sparsity K of the rotor air gap magnetic field information is determined to be in the range of 5 to 10. The amount of raw data used for position identification is N = 8100. According to formula (1), the amount of data M of the observed signal is in the range of 36 to 66, which is the number of Hall sensors required. The first few terms of the Fibonacci sequence are selected to determine the number of sensors in each layer. Since the sum of the first 8 terms of the Fibonacci sequence is 54, which is in the range of 36 to 66, the sensor array is designed to have 8 rows and a total of M = 54 sensors.

[0016] The second step is to determine the specific location of the sensor.

[0017] To determine the specific location of the sensor, i.e., latitude and longitude, a random number generation method is used, as follows:

[0018] 1) Determine the latitude of each row of sensors: First, divide the latitude covered by S1 space, i.e., 0 to 90°, into 8 equal parts, i.e. [0, 11.25], [11.25, 22.5], ..., and then generate random numbers within each latitude range as the latitude of each row.

[0019] 2) Determine the longitude of each sensor in each row: Let n be the number of sensors in each row. i , i = 1 to 8; when calculating the longitude of the sensor in the i-th row, first divide the longitude covered by S1 space, i.e., 0 to 90°, into n equal parts. i Parts, i.e. [0, 90 / n i ], [90 / n i ,2*(90 / n iThen, random numbers are generated within each longitude range as the longitude of each sensor.

[0020] The third step is the design of the observation matrix A in compressed sensing.

[0021] Suppose that the number of rows and columns of the observation matrix A are M = 54 and N = 8100, respectively. There are a total of M = 54 data blocks to be determined in A, and each block is related to the sensor position. The detailed steps are as follows:

[0022] 1) Let the i-th sensor be denoted as (i, J). i W i The coordinates are, in order: sensor number, longitude coordinates, and latitude coordinates.

[0023] 2) Calculate the corresponding elements in observation matrix A The coordinates (i, 90*(J)) i -1)+W i );

[0024] 3) Generate a 1*100 random Gaussian matrix and assign it to the corresponding elements in A. The 100 elements before and after it.

[0025] By processing the information collected by the sensor array based on this observation matrix A, the required air gap magnetic field information of one-eighth of the sphere can be obtained.

[0026] The fourth step is rotor position identification for the permanent magnet spherical motor, including data circle filtering, magnetic pole center position calculation, and conversion between magnetic pole position and rotor position. The method is as follows:

[0027] 1) Data circle filtering: The information after compressed sensing processing contains the radial magnetic field strength value at each integer latitude and longitude coordinate in S1 space. A preset threshold H is used to filter out the detection points whose absolute value of the radial magnetic field strength is greater than the set threshold H to form the data circle used for subsequent processing.

[0028] 2) Calculation of the position of the magnetic pole center; Let the latitude and longitude coordinates of the magnetic pole center O be (J O W O Given the latitude and longitude coordinates of each point in the data circle, the formula for calculating them is as follows:

[0029]

[0030] Among them, J i W i represents the latitude and longitude coordinates of each point in the data circle, and n represents the number of detection points selected to form the data circle.

[0031] 3) Conversion between magnetic pole position and rotor position: The initial latitude and longitude of the magnetic pole center are denoted as... Then, when the calculated latitude and longitude of the magnetic pole center are... At that time, the rotor position (Θ, Φ) is obtained by the following formula:

[0032]

[0033] The present invention has the following beneficial effects:

[0034] 1. The detection method proposed in this invention combines compressed sensing theory and linear Hall sensor, resulting in high calculation accuracy.

[0035] 2. The linear Hall sensor used in this invention has low cost and simple hardware structure.

[0036] 3. The rotor position can be detected by using the data collected by the sensor. Attached Figure Description

[0037] Figure 1 Permanent magnet spherical motor structure

[0038] Figure 2 Flowchart of Compressed Sensing Algorithm

[0039] Figure 3 Fourier transform results of air gap magnetic field information

[0040] Figure 4 S1 Space Sensor Array Location Diagram

[0041] Figure 5 Flowchart of observation matrix construction

[0042] Figure 6 Comparison of compressed sensing reconstructed signal and original signal

[0043] Figure 7 Two-dimensional unfolded diagram of magnetic field information on an eighth-spherical surface

[0044] Figure 8 Diagram of the recognition range of a 1 / 8 sphere

[0045] Figure 9 Recognition range and accuracy as a function of threshold

[0046] Figure 10 Sensor output signal diagram at location 1

[0047] Figure 11 3D diagram of magnetic field information in space S1 at location 1

[0048] Figure 12 Location 1 identification result image

[0049] Figure 13 Sensor output signal diagram at location 2

[0050] Figure 14 3D diagram of magnetic field information in space S1 at location 2

[0051] Figure 15 Location 2 identification results image Detailed Implementation

[0052] This invention provides a design method for a permanent magnet spherical motor rotor position detection system that combines compressed sensing algorithm and linear Hall sensor, and verifies its correctness using a three-axis turntable.

[0053] The present invention is based on a Hall sensor method. First, a mapping relationship is established between the magnetic field information of the rotor permanent magnet at the air gap of the PTZ camera and the rotor position. Then, the position of the rotor is deduced by using the magnetic field values ​​measured by multiple Hall sensors installed on the outside of the PTZ motor.

[0054] The permanent magnet spherical rotor position identification method based on compressed sensing technology of the present invention mainly includes two parts: the design of a sensor array and rotor position identification based on air gap magnetic field information. The applicable motor is a permanent magnet spherical motor, including a base, a spherical stator, stator coils, and a spherical rotor. The rotor surface is characterized by permanent magnet poles embedded therein, with the poles divided into upper and lower layers along the equator, each layer containing four poles, with N and S poles alternating. This method identifies the rotor position based on the radial magnetic field strength information at the air gap of one-eighth of the spherical surface of the permanent magnet spherical motor, placing the sensor in the S1 space, where S1 space is a spherical coordinate system. All of these fall within the 0–90° space, and this magnetic field information is obtained by processing information collected by a sensor array using compressed sensing technology.

[0055] Includes the following steps:

[0056] (1) The method for designing a sensor array is as follows:

[0057] The method consists of two steps: determining the number of sensors and their specific locations.

[0058] The first step is to determine the required number of sensors:

[0059] According to the requirements of the compressed sensing algorithm, the compressed sensing theory requires that the data size N of the original signal X, the sparsity K of the original signal, and the data size M of the observed signal Y must satisfy formula (1).

[0060] M = K·ln(N / K) (1)

[0061] Based on the finite element simulation results, the sparsity K of the rotor air gap magnetic field information is determined to be 5 to 10, and the amount of raw data N used for position identification is 8100. Then, according to formula (1), the amount of data M of the observed signal is 36 to 66, which is the number of Hall sensors required.

[0062] The first n terms of the Fibonacci sequence are chosen to determine the number of sensors in each layer. The general formula for the Fibonacci sequence is:

[0063]

[0064] The sum of the first 8 terms is 54, which falls exactly between 36 and 66. Therefore, the sensor array is designed with 8 rows and a total of 54.

[0065] The second step is to determine the exact location of the sensor:

[0066] To determine the sensor's exact location, i.e., latitude and longitude, a random number generation method is used. The specific method is as follows:

[0067] 3) Determine the latitude of each row of sensors. First, divide the S1 spatial coverage latitude, i.e., 0 to 90°, into 8 equal parts, i.e. [0, 11.25], [11.25, 22.5], ..., and then generate random numbers within each latitude range as the latitude of each row.

[0068] 4) Determine the longitude of each sensor in each row. Let n be the number of sensors in each row. i , i = 1 to 8; when calculating the longitude of the sensor in the i-th row, first divide the S1 space covering longitude, i.e., 0 to 90°, into n equal parts. i Parts, i.e. [0, 90 / n i ], [90 / n i ,2*(90 / n i Then, random numbers are generated within each longitude range as the longitude of each sensor.

[0069] (2) The design method of the observation matrix A in compressed sensing is as follows:

[0070] In compressed sensing, the number of rows and columns of the observation matrix A are m and n, respectively. In this design, m = 54 and n = 8100. A contains a total of 54 data blocks to be determined, and each block is related to the sensor position. The detailed steps are as follows:

[0071] 4) Let the i-th sensor be denoted as (i, J). i W i The coordinates are, in order: sensor number, longitude coordinates, and latitude coordinates.

[0072] 5) Calculate the corresponding elements in observation matrix A The coordinates (i, 90*(J)) i -1)+W i );

[0073] 6) Generate a 1*100 random Gaussian matrix and assign it to the corresponding elements in A. The 100 elements before and after it.

[0074] By processing the information collected by the sensor array based on this observation matrix A, the required air gap magnetic field information of one-eighth of the sphere can be obtained.

[0075] (3) The rotor position identification method of permanent magnet spherical motor is as follows:

[0076] This section is divided into data circle filtering, magnetic pole center position calculation, and methods for converting magnetic pole position and rotor position. The detailed steps are as follows:

[0077] 1) Data Circle Filtering: The compressed sensing information contains radial magnetic field strength values ​​at each integer latitude and longitude coordinate in S1 space. Data circles with absolute values ​​greater than a set threshold H are filtered out to form data circles for subsequent processing. This method recommends setting the threshold H to 3.2 mT. At this setting, the theoretical identification range of this method is 86%, the theoretical calculation error is 1°, and the identification accuracy is very high.

[0078] 2) Method for calculating the position of the magnetic pole center; Let the latitude and longitude coordinates of the magnetic pole center O be (J O W O Given the latitude and longitude coordinates of each point in the data circle, the formula for calculating them is as follows:

[0079]

[0080] Among them, J i W i These are the latitude and longitude coordinates of each point in the data circle.

[0081] 3) Method for converting magnetic pole position and rotor position; Let the initial latitude and longitude of the magnetic pole center be denoted as... Then, when the calculated latitude and longitude of the magnetic pole center are... At that time, the rotor position (Θ, Φ) can be obtained by the following formula:

[0082]

[0083] The embodiments of the present invention will be further described below with reference to the accompanying drawings, focusing on aspects such as sensor array and observation matrix design, rotor position detection scheme, and experimental verification.

[0084] This invention is based on Figure 1 Taking the rotor structure shown as an example, the rotor model of the spherical motor consists of eight cylindrical permanent magnets. The S and N poles are symmetrically alternately distributed at the vertices of an inscribed regular hexahedron bounded by the rotor sphere. The poles are magnetized in parallel, and the material is NdFeB30. In this design, a Hall sensor bracket is installed between the stator and rotor spherical shells, specifically at... Figure 1 The S1 space is used to place the Hall sensor, which ensures that the placement of the Hall sensor is not affected by the location of the stator coil.

[0085] Compressed sensing, proposed by Donoho and Candes in 2008, is a sampling-reconstruction theory based on signal sparsity. Its signal sampling achieves a linear projection from a high-dimensional signal to a low-dimensional signal through an observation matrix. Compared to the traditional Nyquist sampling method, it effectively reduces the amount of sampled signal data and overcomes the drawbacks of high compression complexity and high hardware requirements at the sampling end. Signal reconstruction in compressed sensing involves solving an underdetermined system of linear equations to approximately and accurately reconstruct the original high-dimensional signal. The data processing process is as follows... Figure 2 As shown.

[0086] (1) Sensor array and observation matrix design

[0087] To ensure that the sensor positions meet the requirements of the compressed sensing algorithm, this design considers three aspects: the required number of sensors, the sensor positions, and the observation matrix corresponding to the sensors.

[0088] According to the requirements of the compressed sensing algorithm, the compressed sensing theory requires that the data size N of the original signal X, the sparsity K of the original signal, and the data size M of the observed signal Y must satisfy formula (1).

[0089] M = K·ln(N / K) (1)

[0090] Since the sparsity K was not obtained, a model of a spherical motor rotor was built in Ansoft software, and sampling was performed within a selected one-eighth of the sphere, where θ ranges from 0° to 90°. The range is 0° to 90°, with a sampling precision of 1°. Fourier analysis is performed on the sample, and the results are as follows: Figure 3 As shown.

[0091] It can be seen that the sparsity K of the rotor air gap magnetic field information is 5 to 10. The amount of raw data N used for position identification is more suitable to be 8100. According to formula (1), the amount of data M of the observed signal is 36 to 66, which is the number of Hall sensors required.

[0092] Within the selected one-eighth of a sphere, the number of sensors that can be placed gradually increases from the top downwards; therefore, the sensor array design should be layer-by-layer. Furthermore, considering that the distribution of each sensor needs to divide the selected spherical area as evenly as possible, the first n terms of the Fibonacci sequence, known as the "golden ratio," are chosen to determine the number of sensors in each layer.

[0093] The general term formula for the Fibonacci sequence is:

[0094]

[0095] Therefore, the first n terms of the sequence are 1, 1, 2, 3, 5, 8, 13, 21, ..., and the sum of the first 8 terms is 54, which is exactly between 36 and 66. Therefore, the sensor array is designed with 8 rows and a total of 54, which is between 36 and 66, satisfying the sensor quantity requirement analyzed above.

[0096] In this design, the sensor positions directly affect the composition of the observation matrix. Common observation matrices include Gaussian random matrices, random Bernoulli matrices, and partial Hadamard matrices, all characterized by a random distribution of elements. Therefore, random numbers are generated to determine the latitude and longitude of each row of sensors. To avoid excessive concentration of random numbers, the latitude is first divided into eight equal parts, and then random numbers are generated within each latitude range to serve as the latitude coordinates for each row. The longitude coordinates of each sensor in each row are also determined using the same method.

[0097] The final sensor positions in S1 space are as follows Figure 4 As shown.

[0098] In compressed sensing, the number of rows and columns of the observation matrix A are m and n, respectively. In this design, m = 54 and n = 8100. According to formula (3), each element of the low-dimensional signal Y is related to a certain row of the observation matrix A and all elements of the high-dimensional signal X. Taking the first element of Y as an example, it satisfies formula (4).

[0099] Y = AX = AΨS(3)

[0100]

[0101] Based on formulas (3) and (4), this design establishes the relationship between each sensor position and the corresponding row of the observation matrix. The coordinates of the first sensor in the sensor array are (4, 55), so the first element in Y can also be denoted as y(1, 4, 55), which corresponds to the 325th element in the first row of A, denoted as... Considering the requirement of the compressed sensing theory for the randomness of the observation matrix, A total of 100 elements are designed to satisfy a random Gaussian matrix, thus obtaining the first row of the observation matrix. The remaining rows are designed in the same way. The specific flowchart is shown below. Figure 5 As shown, the final obtained observation matrix A contains the positions of the Hall sensor array but is incoherent with the sparse matrix of the original signal X. The result of compressed sensing of the original signal using this observation matrix is ​​shown below. Figure 6 As shown.

[0102] (2) Rotor position detection scheme

[0103] The rotor position detection method in this design is simple. Its core lies in determining the center of the data circle that meets the requirements in the reconstructed signal from the compressed sensing method. The position of this center is the position of the rotor magnetic poles, and the rotor position can be obtained through a simple transformation. This part is divided into the calculation of the magnetic pole center position, the design of the data filtering threshold, and the conversion method between the magnetic pole position and the rotor position.

[0104] 1) Calculation method for the position of the magnetic pole center

[0105] from Figure 7 It can be seen that the magnetic field information is approximately distributed in concentric circles, that is, it diffuses outward from the rotor magnetic pole center O, and the magnetic field strength decreases as the distance from the center O increases. For the obtained magnetic field data, if a certain threshold H is set, and data points greater than this threshold are extracted, then the data points meeting the condition can form a circle in the magnetic field information unfolded diagram, and the center of this circle is exactly the magnetic pole center O, hence it is denoted as circle O. (See...) Figure 7 The black circle in the diagram is denoted by its radius r, which is the radius of the circle obtained under the threshold H.

[0106] Let the latitude and longitude coordinates of the magnetic pole center O be (J O W O Given the latitude and longitude coordinates of each point in the data circle, the formula for calculating them is as follows:

[0107]

[0108] Among them, J i W i These are the latitude and longitude coordinates of each point in the data circle.

[0109] 2) Threshold design method for data filtering

[0110] The choice of threshold H directly affects the identification range and accuracy of the proposed method. Figure 7 It can be seen that the position of the magnetic pole center can only be obtained by calculating the center of the circle using the above method when the circle O completely exists in the S1 space, that is, when the rotor magnetic pole center O is in the T space (the spherical space obtained by shrinking the length of space S1 inward). Since the radius of the circle O is determined by the threshold H, the position identification range corresponding to the threshold H is as follows: Figure 8 As shown.

[0111] In this invention, the light-colored triangle ABC represents space S1 with radius R, and the dark-colored one-eighth of the sphere is the space that the rotor position identification method proposed in this invention can measure, denoted as space T, with radius R-2r. Both spaces are spherical triangles; therefore, the identification range P of the proposed method can be obtained by calculating the ratio of the areas of space T and space S1. According to the relevant knowledge of spherical triangles, their area is positively correlated with the sum of their interior angles and the radius of the sphere. Figure 8Since the sum of the interior angles of the two spherical triangles is the same, the formula for calculating the identification range is as follows:

[0112]

[0113] Combination Figure 6 and Figure 7 It can be seen that the computational accuracy and recognition range of the proposed method change as the threshold setting changes. From... Figure 6 It can be seen that the amplitude variation range of the magnetic field information in space S1 is [0, -3.30]. When the variation step size is set to 0.04mH, the recognition range and recognition error change with the threshold as follows: Figure 9 As shown.

[0114] As the selected threshold increases, the calculation accuracy of the magnetic pole center decreases, but the identification range expands. To simultaneously obtain a large identification range and optimal identification accuracy, this invention selects a threshold of 3.2 mH. At this threshold, the theoretical identification range of this method is 86%, the theoretical calculation error is 1°, and the identification accuracy is very high.

[0115] 3) Methods for converting magnetic pole position and rotor position

[0116] Since the rotor magnetic poles are relatively stationary with respect to the rotor, this invention selects magnetic poles whose initial positions fall within space S1. Let the initial latitude and longitude of the magnetic pole center be denoted as... Then, when the calculated latitude and longitude of the magnetic pole center are... At that time, the rotor position (Θ,Φ) can be obtained by the following formula:

[0117]

[0118] (3) Experimental verification

[0119] To verify the effectiveness of the proposed rotor position detection method, an experimental platform was built. The platform includes a spherical motor rotor, two two-phase four-wire stepper motors, 54 Allegro A1302 Hall sensors, and a parallel AD data acquisition circuit based on FPGA. The acquisition circuit is connected to a PC via a serial port for data processing.

[0120] Table 1. Experimental apparatus and parameters used in the experiment.

[0121]

[0122] Based on the given rotor rotation axis, the radial component of the spherical magnetic field during rotor rotation is measured using a Hall sensor array. The data is then transmitted to a PC to calculate the rotor position and simultaneously calculate the error of the identification method.

[0123] Experiment 1:

[0124] Before the experiment, ensure the spherical motor rotor is in the specified initial position. After the experiment begins, collect sensor data and filter it; the results are as follows. Figure 10 As shown. After information acquisition is completed, the magnetic field information of the spherical motor acquired by the sensor is first reconstructed into high-dimensional magnetic field information using compressed sensing, such as... Figure 11 As shown. Then, the rotor position is calculated according to formulas (6) and (8), as follows. Figure 12 As shown, the latitude error of the identification results is 0.32°, and the longitude error is 0.59°.

[0125] Experiment 2:

[0126] Before the experiment, ensure that the spherical motor rotor reaches the specified position after one rotation and one pitch motion. After the experiment begins, collect sensor data and filter it; the results are as follows. Figure 13 As shown. After information acquisition is completed, the magnetic field information of the spherical motor acquired by the sensor is first reconstructed into high-dimensional magnetic field information using compressed sensing, such as... Figure 14 As shown. Then, the rotor position is calculated according to formulas (6) and (8), as follows. Figure 15 As shown, the latitude error of the identification results is 0.97° and the longitude error is 1.08°.

Claims

1. A method for position identification of a permanent magnet spherical rotor based on compressed sensing, the applicable permanent magnet spherical motor including a base, a spherical stator, stator coils and a spherical rotor, the rotor surface is embedded with permanent magnet poles, the poles are divided into upper and lower layers along the equator, each layer has 4 permanent magnet poles, N poles and S poles are alternately distributed; The rotor position is identified based on the radial magnetic field strength information at the air gap of one-eighth of the spherical surface of a permanent magnet spherical motor. A Hall sensor is placed in space S1, where S1 is θ in the spherical coordinate system. All of these fall within the 0–90° space, and this radial magnetic field strength information is obtained by processing information collected by the sensor array using compressed sensing technology. Includes the following steps: The first step is to determine the required number of sensors. Let N be the amount of original data for the original signal X required by compressed sensing theory, and let K be the sparsity of the original signal and M be the amount of data for the observed signal Y, which need to satisfy formula (1). M = K·ln(N / K) (1) Based on the finite element simulation results, the sparsity K of the rotor air gap magnetic field information is determined to be in the range of 5 to 10. The amount of raw data used for position identification is N = 8100. According to formula (1), the amount of data M of the observed signal is in the range of 36 to 66, which is the number of Hall sensors required. The first few terms of the Fibonacci sequence are selected to determine the number of sensors in each layer. Since the sum of the first 8 terms of the Fibonacci sequence is 54, which is in the range of 36 to 66, the sensor array is designed to have 8 rows and a total of M = 54 sensors. The second step is to determine the specific location of the sensor. To determine the specific location of the sensor, i.e., latitude and longitude, a random number generation method is used, as follows: 1) Determine the latitude of each row of sensors: First, divide the latitude covered by S1 space, i.e., 0 to 90°, into 8 equal parts, i.e., [0, 11.25], [11.25, 22.5], ..., and then generate random numbers within each latitude range as the latitude of each row; 2) Determine the longitude of each sensor in each row: Let n be the number of sensors in each row. i i = 1 to 8; When calculating the longitude of the sensor in the i-th row, first divide the longitude covered by S1 space, i.e., 0 to 90°, into n equal parts. i Parts, i.e. [0, 90 / n i ],[90 / n i ,2*(90 / n i Then, random numbers are generated within each longitude range to serve as the longitude of each sensor; The third step is the design of the observation matrix A in compressed sensing. Suppose that the number of rows and columns of the observation matrix A are M = 54 and N = 8100, respectively. There are a total of M = 54 data blocks to be determined in A, and each block is related to the sensor position. The detailed steps are as follows: 1) Let the i-th sensor be denoted as (i, J). i W i The coordinates are, in order: sensor number, longitude coordinates, and latitude coordinates. 2) Calculate the corresponding elements in observation matrix A The coordinates (i, 90*(J)) i -1)+W i ); 3) Generate a 1*100 random Gaussian matrix and assign it to the corresponding elements in A. The first and last 100 elements; By processing the information collected by the sensor array based on this observation matrix A, the required air gap magnetic field information for one-eighth of the sphere can be obtained; The fourth step is rotor position identification for the permanent magnet spherical motor, including data circle filtering, magnetic pole center position calculation, and conversion between magnetic pole position and rotor position. The method is as follows: 1) Data Circle Filtering: The information after compressed sensing processing contains the radial magnetic field strength value at each integer latitude and longitude coordinate in S1 space. A preset threshold H is used to filter out detection points whose absolute value of radial magnetic field strength is greater than the set threshold H, forming a data circle for subsequent processing; 2) Calculation of the position of the magnetic pole center; Let the latitude and longitude coordinates of the magnetic pole center O be (J O W O Given the latitude and longitude coordinates of each point in the data circle, the formula for calculating them is as follows: Among them, J i W i Here, represents the latitude and longitude coordinates of each point within the data circle, and n represents the number of detection points selected to form the data circle. 3) Conversion between magnetic pole position and rotor position: The initial latitude and longitude of the magnetic pole center are denoted as... Then, when the calculated latitude and longitude of the magnetic pole center are... At that time, the rotor position (Θ,Φ) is obtained by the following formula: 。

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