Systems and methods for geomagnetic compensation and bias magnetic field generation for cold atom interferometry

Abstract

The application provides a system and method for geomagnetic compensation and bias magnetic field generation of cold atom interference, which comprises a three-axis magnetometer, a three-axis Helmholtz coil, a voltage-controlled current source and an FPGA control module; the three-axis magnetometer is used for collecting spatial magnetic field data at multiple monitoring positions in a space where the three-axis Helmholtz coil is located in real time; the FPGA control module is used for calculating the control voltage data required by the voltage-controlled current source according to the target magnetic field and any spatial magnetic field data collected by the three-axis magnetometer in each sampling period, controlling the coil current delivered to the three-axis Helmholtz coil, and iteratively circulating until the three-axis Helmholtz coil generates the target magnetic field at the multiple monitoring positions, which is a near-zero magnetic field in the X / Y direction, has constant magnetic field intensity in the Z direction and is a non-zero value. The application can respond to the change of the environmental magnetic field in real time, compensate the influence of the geomagnetic field and provide a stable and accurate magnetic field environment for the cold atom interference test.

Description

Technical Field

[0001] This invention relates to the technical field of quantum precision measurement, specifically to a system and method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry. Background Technology

[0002] In cold atom interferometry systems, magnetic field control is a crucial aspect of the processes of atomic cooling, confinement, interference, and detection. The performance of magnetic field control significantly impacts the stability of atomic clusters and the measurement accuracy of the atomic interferometer. For example, the residual geomagnetic field can affect the atomic temperature and number after laser cooling, and the inhomogeneity of the bias magnetic field can cause phase shifts in the cold atom interference fringes due to the second-order Zeeman effect.

[0003] In related technologies, cold atom interferometers mostly employ a combination of magnetic shielding and coils to achieve the aforementioned functions. This method is complex and costly, and the magnetic shielding requires periodic demagnetization to achieve optimal geomagnetic compensation. The bias coil uses a Helmholtz coil to generate the quantized axis required for atomic interference. Furthermore, magnetic field interference in real-world environments is complex and variable, and this approach lacks the ability to sense and adjust to changes in the environmental magnetic field, failing to effectively eliminate the impact of magnetic field interference on measurement accuracy. Summary of the Invention

[0004] This invention aims to at least partially solve one of the technical problems in related technologies. To this end, embodiments of this invention propose a system and method for geomagnetic compensation and bias magnetic field generation in cold atom interferometry. This system can respond in real time to changes in the ambient magnetic field, ensuring that the system is always in the optimal magnetic field operating state. Based on compensating for the influence of the geomagnetic field, it provides a stable and accurate magnetic field environment for cold atom interferometry experiments.

[0005] The system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry provided in this invention includes a triaxial magnetometer, a triaxial Helmholtz coil, a voltage-controlled current source, and an FPGA control module;

[0006] The triaxial magnetometer is used to collect spatial magnetic field data at multiple monitoring positions within the space where the triaxial Helmholtz coil is located in real time and transmit it to the FPGA control module. The multiple monitoring positions include the physical center position of the triaxial Helmholtz coil and the adjacent positions with the physical center as the origin.

[0007] The FPGA control module is used to calculate the voltage control data required by the voltage-controlled current source by taking any spatial magnetic field data collected by the triaxial magnetometer as the controlled signal and the preset target magnetic field as the expected signal in each set sampling period. Then, it controls the coil current delivered by the voltage-controlled current source to the triaxial Helmholtz coil according to the voltage control data. The above process is iterated until the triaxial Helmholtz coil generates the target magnetic field at multiple monitoring positions to achieve dynamic compensation of the environmental magnetic field. The target magnetic field is a uniform bias magnetic field with a near-zero magnetic field in the X / Y direction and a constant and non-zero magnetic field strength in the Z direction.

[0008] In summary, the geomagnetic compensation and bias magnetic field generation system for cold atom interferometry disclosed in this invention, through the closed-loop collaborative operation of a triaxial magnetometer, a triaxial Helmholtz coil, a voltage-controlled current source, and an FPGA control module, can respond in real time to changes in the ambient magnetic field, ensuring that the generated magnetic field is always in the optimal target magnetic field working state, and providing a stable and accurate magnetic field environment for cold atom interferometry experiments.

[0009] In some embodiments, the triaxial Helmholtz coil has a rectangular coil structure, and the inner and outer diameters of the three axes of the triaxial Helmholtz coil are different, with the spacing ratio of the coaxial coils being 0.5445±0.01.

[0010] In some embodiments, the FPGA control module is further used to perform average filtering on the spatial magnetic field data collected by the triaxial magnetometer, and then use the filtered spatial magnetic field data as the controlled signal.

[0011] In some embodiments, the FPGA control module includes a single-neural PID control unit, which includes a weight update subunit and a computation subunit. The single-neural PID control unit is used for...

[0012] The magnetic field strength error value, error integral value, and error derivative value for each sampling period are obtained based on the difference between the expected signal and the controlled signal.

[0013] The magnetic field strength error value, error integral value, and error differential value of the previous sampling period, as well as the voltage control data of the voltage-controlled current source of the previous sampling period, are input to the weight update subunit. The weight update subunit obtains the weight parameters of the current sampling period according to the preset weight update algorithm.

[0014] The calculation subunit calculates the voltage control data of the voltage-controlled current source for the current sampling period based on the magnetic field strength error value, error integral value, error differential value, and the weighting parameters of the current sampling period.

[0015] In some embodiments, the weight parameters include proportional term weight parameters, integral term weight parameters, and differential term weight parameters; the weight update subunit has at least four operating modes:

[0016] 1) When the absolute value of the magnetic field strength error is greater than the error threshold and the corresponding voltage control data is less than the control threshold, the first operating mode is executed, including increasing the growth rate of the proportional term weight parameter, or suppressing the integral term weight parameter and maintaining the stability of the derivative term weight parameter;

[0017] 2) When the absolute value of the magnetic field strength error is less than or equal to the error threshold and the corresponding voltage control data is greater than or equal to the control threshold, the second operating mode is executed, including increasing the decay rate of the proportional term weight parameter, or gradually increasing the integral term weight parameter, or increasing the derivative term weight parameter;

[0018] 3) When the magnetic field strength error value changes rapidly, the third operating mode is executed, including limiting the growth rate and speed of the proportional term weight parameter, or slowing down the accumulation speed of the integral term weight parameter, or limiting the growth rate of the differential term weight parameter;

[0019] 4) When the rate of change of the magnetic field strength error value approaches 0, execute the fourth operating mode, which includes gradually reducing the proportional term weight parameter, or reducing the integral term weight parameter, or reducing the differential term weight parameter.

[0020] Furthermore, the method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry provided by this invention includes the following steps:

[0021] S10, according to the set sampling period, acquire the spatial magnetic field data of multiple monitoring positions in the space where the triaxial Helmholtz coil is located, which are collected in real time by the triaxial magnetometer. The multiple monitoring positions include the physical center position of the triaxial Helmholtz coil and the adjacent positions with the physical center as the origin.

[0022] S20: In each sampling period, any acquired spatial magnetic field data is used as the controlled signal, and the preset target magnetic field is used as the expected signal to calculate the voltage control data required for the voltage-controlled current source.

[0023] S30, adjust the coil current supplied by the voltage-controlled current source to the triaxial Helmholtz coil according to the voltage control data;

[0024] Steps S10 to S30 are executed repeatedly until the triaxial Helmholtz coil generates the target magnetic field at multiple monitoring locations, thereby achieving dynamic compensation for the ambient magnetic field. The target magnetic field is a uniform bias magnetic field with a near-zero magnetic field in the X / Y direction and a constant and non-zero magnetic field strength in the Z direction.

[0025] In some embodiments, the magnetic field generation method further includes the following step before step S10:

[0026] A model for the relationship between magnetic field strength and current is established based on the vector superposition algorithm.

[0027] The coil spacing ratio is calculated by performing calculations on the magnetic field strength and current relationship model, wherein the coil spacing ratio is 0.5445±0.01;

[0028] Based on the coil spacing ratio, the structural parameters of the triaxial Helmholtz coil are determined, wherein the structural parameters include at least the inner diameter and the number of turns;

[0029] Based on the structural parameters, the triaxial Helmholtz coil is constructed. The triaxial Helmholtz coil has a rectangular coil structure, and the inner and outer diameters of the coils on the three axes are different.

[0030] In some embodiments, the magnetic field generation method further includes:

[0031] Using a preset average filtering algorithm, the spatial magnetic field data acquired in each sampling period is averaged and filtered, and then the filtered spatial magnetic field data is used as the controlled signal.

[0032] In some embodiments, the step of S20, which uses the acquired spatial magnetic field data as the controlled signal and the preset target magnetic field as the expected signal in each sampling period to calculate the voltage control data required for the voltage-controlled current source, specifically includes:

[0033] The magnetic field strength error value, error integral value, and error derivative value for each sampling period are obtained based on the difference between the expected signal and the controlled signal.

[0034] Based on the magnetic field strength error value, error integral value, and error differential value of the previous sampling period, the voltage control data of the voltage-controlled current source of the previous sampling period, and the preset weight update algorithm, the weight parameters of the current sampling period are obtained.

[0035] Based on the magnetic field strength error value, error integral value, error differential value, and the weighting parameters of the current sampling period, the voltage control data of the voltage-controlled current source for the current sampling period is calculated.

[0036] In some embodiments, the weight update algorithm uses the following formula:

[0037] (1)

[0038] In the formula: k is the sampling period code; For the k-th sampling period, the weight parameter is used. For the (k-1)th sampling period, the weight parameters are used. The learning rate is 0.2 to 0.5. Let be the magnetic field strength error value for the kth sampling period; This represents the magnetic field strength error value for the (k-1)th sampling period; This is the voltage control data corresponding to the (k-1)th sampling period.

[0039] In summary, the system and method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry provided in the embodiments of the present invention have at least the following advantages:

[0040] 1) The system adopts a closed loop consisting of a magnetometer, a Helmholtz coil, a voltage-controlled current source, and an FPGA module. It has a compact structure and the FPGA module can realize online cyclic iterative control, respond to environmental magnetic field fluctuations in real time, and improve the convergence speed of magnetic field error.

[0041] 2) A rectangular triaxial Helmholtz coil is used. The inner and outer diameters of the three axes of the rectangular coil are different, and the spacing ratio of the coaxial coils is 0.5445±0.01. This can form a uniform bias magnetic field with near-zero or near-zero magnetic field in the X / Y directions (e.g., a magnetic field environment with a magnetic field strength of less than 10 mG) and a constant non-zero magnetic field strength in the Z direction within a half-inch diameter space. This effectively suppresses Zeeman effect interference, ensures the efficiency of atomic state preparation, and helps to improve the contrast of interference fringes.

[0042] 3) A single-neural PID control unit is used to regulate the entire system, and the weights are adjusted online (learning rate). =0.2 to 0.5), compared to fixed parameter compensation methods, it can compensate for nonlinear disturbances such as hysteresis effect in real time. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the structure of a system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry provided in an embodiment of the present invention.

[0044] Figure 2 This is a schematic diagram of the structure of a triaxial Helmholtz coil provided in an embodiment of the present invention.

[0045] Figure 3 This is a block diagram illustrating the control principle of a single-nerve PID control unit provided in an embodiment of the present invention.

[0046] Figure 4A This is a schematic diagram of the linear signal of a system using a common PID algorithm in related technologies when the controlled object is nonlinear.

[0047] Figure 4B This is a schematic diagram of the linear signal of a single-neural PID control unit provided in an embodiment of the present invention when the controlled object is nonlinear.

[0048] Figure 4C yes Figure 4B The diagram shown is an enlarged view of a portion of the linear signal.

[0049] Figure 4D yes Figure 4B An enlarged view of another part of the signal in the schematic diagram of the linear signal shown.

[0050] Figure 5 This is a schematic flowchart of a method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry provided in an embodiment of the present invention.

[0051] Figure 6 This is a linear relationship diagram between the voltage and current source within a voltage-controlled current source provided in an embodiment of the present invention.

[0052] Figure label:

[0053] 10. Triaxial magnetometer; 20. Triaxial Helmholtz coil; 30. Voltage-controlled current source; 40. FPGA control module; 41. Average filtering unit; 42. Single-neuron PID control unit; 421. Weight update subunit; 422. Calculation subunit; 50. Communication line. Detailed Implementation

[0054] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0055] like Figure 1 As shown, one embodiment of the present invention provides a system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry, comprising a triaxial magnetometer 10, a triaxial Helmholtz coil 20, a voltage-controlled current source 30, and an FPGA control module 40. The triaxial magnetometer 10 is used to collect spatial magnetic field data in real time at multiple monitoring locations within the space where the triaxial Helmholtz coil 20 is located and transmit it to the FPGA control module 40. The multiple monitoring locations include the physical center of the triaxial Helmholtz coil 20 and adjacent locations with the physical center as the origin.

[0056] The FPGA control module 40 is used to calculate the voltage control data required by the voltage-controlled current source 30 by taking any spatial magnetic field data collected by the triaxial magnetometer 10 as the controlled signal and the preset target magnetic field as the expected signal in each set sampling period. Then, it controls the coil current delivered by the voltage-controlled current source 30 to the triaxial Helmholtz coil 20 according to the voltage control data, and iterates the above process until the triaxial Helmholtz coil 20 generates the target magnetic field at multiple monitoring locations (e.g., the physical center location and the adjacent location), thereby realizing dynamic compensation for the environmental magnetic field.

[0057] Specifically, the triaxial magnetometer 10, the triaxial Helmholtz coil 20, the voltage-controlled current source 30, and the FPGA control module 40 can be connected in a closed loop via a communication line 50 (e.g., an SPI bus). The triaxial Helmholtz coil 20 is the system's magnetic field generator, consisting of three mutually orthogonal coils corresponding to the X, Y, and Z directions, respectively. When the voltage-controlled current source 30 supplies current to the triaxial Helmholtz coil 20, the magnetic fields generated by the three coils superimpose, thus forming a composite magnetic field with a certain intensity and direction in the space. This composite magnetic field can compensate for the ambient magnetic field, generating the target magnetic field required for cold atom interference.

[0058] In this embodiment, the target magnetic field is set as a uniform bias magnetic field with near-zero magnetic fields in the X and Y directions and a constant non-zero magnetic field strength in the Z direction. Here, a near-zero magnetic field is a magnetic field with a magnetic field strength close to zero, such as a magnetic field environment with a magnetic field strength less than 10 mG (milligauss). The near-zero magnetic fields formed by the triaxial Helmholtz coils in the X and Y directions can achieve limited compensation for the ambient magnetic field; while the constant non-zero magnetic field strength formed in the Z direction can achieve the quantum state manipulation and precise measurement required for cold atom interferometry experiments.

[0059] It should be noted that the target magnetic field is preset according to the specific requirements of the cold atom interference experiment, and it represents the ideal magnetic field state required for the experiment.

[0060] For example, to eliminate the atomic energy level shifts and interference phase shifts caused by the Zeeman effect, a uniform bias magnetic field is needed to define the quantization axis, causing Zeeman splitting of the magneton energy levels of the ground hyperfine levels (F=1 and F=2 states of atoms), so that the atomic clusters can be prepared to the MF=0 state, which is insensitive to the magnetic field, before interference. Magnetic field fluctuations directly affect the Zeeman splitting of atomic energy levels, leading to a shift in transition frequencies. If the magnetic field fluctuation exceeds 10 mG, the corresponding energy level shift will be significantly higher than the transition linewidth, causing a decrease in state preparation efficiency or even failure. It also introduces phase noise into the atomic wavefunction, disrupting the coherence time of the atomic interferometer, leading to the accumulation of phase errors, significantly reducing the contrast of interference fringes, and greatly affecting the gravity measurement results. To address this, a target magnetic field can be set as a uniform bias magnetic field within a spatial sphere region with a diameter of half an inch, satisfying the technical specifications of near-zero magnetic fields in the X and Y directions, a magnitude of 100 mG in the Z direction, and a uniformity within 10 mG.

[0061] The triaxial magnetometer 10 can acquire magnetic field strength data in three orthogonal directions (X, Y, Z) at multiple monitoring locations within the space where the triaxial Helmholtz coil 20 is located. The spatial magnetic field data acquired by the triaxial magnetometer 10 is a superposition of the environmental magnetic field data and the composite magnetic field data formed by the triaxial Helmholtz coil 20.

[0062] Optionally, the triaxial magnetometer 10 is configured as a magnetometer with a range of ±2 Gauss and a resolution of 0.0667 mG / LSB, thereby providing high-precision measurement results while meeting the measurement range requirements. It accurately detects changes in the spatial magnetic field within a closed-loop system for magnetic field generation and control.

[0063] In this embodiment, the system also includes a moving mechanism that can move the triaxial magnetometer 10 within the space where the triaxial Helmholtz coil 20 is located. The triaxial magnetometer 10 monitors and collects at least the spatial magnetic field data at the physical center of the triaxial Helmholtz coil 20 and the spatial magnetic field data around the physical center as the origin, that is, the spatial magnetic field data corresponding to multiple adjacent positions with the physical center as the origin.

[0064] Preferably, there are at least 6 adjacent positions, with each pair of the 6 adjacent positions located on the X / Y / Z axes of the triaxial Helmholtz coil 20, and the distance from the adjacent position to the physical center position is less than or equal to 0.5 mm.

[0065] Optionally, the moving mechanism includes a robotic arm. The triaxial magnetometer 10 is located at the free end of the robotic arm, and the robotic arm drives the triaxial magnetometer 10 to move freely within the space where the triaxial Helmholtz coil 20 is located, so as to collect spatial magnetic field data at multiple monitoring positions.

[0066] In other embodiments of the present invention, multiple triaxial magnetometers 10 may be provided, and the multiple triaxial magnetometers 10 correspond one-to-one with the detection positions (e.g., the center position and the adjacent positions) in the space where the triaxial Helmholtz coil 20 is located, respectively monitoring and collecting spatial magnetic field data at the corresponding positions.

[0067] The FPGA control module 40 is responsible for processing and analyzing the spatial magnetic field data acquired by the triaxial magnetometer 10 and generating corresponding control commands. For example, in each sampling cycle, the FPGA control module 40 can compare and analyze the controlled signal and the expected signal, calculate the voltage control data required by the voltage-controlled current source 30, adjust the output of the voltage-controlled current source 30, and thus change the current and the magnetic field generated by the triaxial Helmholtz coil 20. This process is repeated until the error between the magnetic field generated by the triaxial Helmholtz coil 20 at multiple monitoring locations (such as the physical center and nearby locations) and the preset target magnetic field is less than a set error threshold, thereby achieving dynamic and effective compensation for the environmental magnetic field and generating a highly uniform bias field.

[0068] The voltage-controlled current source 30 can supply the corresponding coil current to the triaxial Helmholtz coil 20 according to the voltage control data provided by the FPGA control module 40, so as to provide the power source for the triaxial Helmholtz coil 20 to generate a magnetic field and to precisely control the magnetic field generated by the triaxial Helmholtz coil 20.

[0069] In summary, the geomagnetic compensation and bias magnetic field generation system for cold atom interferometry disclosed in this invention, through the closed-loop collaborative operation of the triaxial magnetometer 10, the triaxial Helmholtz coil 20, the voltage-controlled current source 30 and the FPGA control module 40, can respond to changes in the ambient magnetic field in real time, ensuring that the triaxial Helmholtz coil 20 generates the optimal target magnetic field, and providing a stable and accurate magnetic field environment for cold atom interferometry experiments.

[0070] The embodiments of this invention choose a triaxial Helmholtz coil to form the synthetic magnetic field because the triaxial Helmholtz coil, by independently controlling the magnitude and direction of the current in the triaxial coil, can achieve vector synthesis of magnetic fields in any space. Its symmetrical structure can effectively suppress spatial non-uniformity interference from the ambient magnetic field. Furthermore, through active magnetic compensation technology, the magnetic field fluctuation in the region where the triaxial Helmholtz coil 20 is located can be kept below 10 mG, meeting the experimental requirements.

[0071] like Figure 2As shown, in some embodiments, the triaxial Helmholtz coil 20 is configured as a rectangular coil structure, which can achieve a more uniform magnetic field over a larger area. Furthermore, rectangular coils are easier to stack and combine, reducing gaps between coils and forming a compact three-dimensional coil structure, thus improving space utilization. For example, in this embodiment, the triaxial Helmholtz coil 20 can form a target magnetic field within a spherical region with a diameter of half an inch.

[0072] Furthermore, the inner and outer diameters of the three axes of the triaxial Helmholtz coil 20 are different, which allows for more precise control of the magnetic field direction. This makes it easier to form the target magnetic field after the composite magnetic field generated by the triaxial Helmholtz coil 20 is superimposed with the ambient magnetic field.

[0073] By integrating the contribution of the unilateral magnetic field using the Biot-Savart law and considering the coil spacing, we obtain a model formula for the relationship between the total magnetic field strength and the current:

[0074] (2)

[0075] In the formula: The magnetic field strength; This refers to the coil spacing ratio; ρ is the permeability of free space, a physical constant; N is the number of turns of the coil; I is the coil current through the triaxial Helmholtz coil 20; L is the side length of the triaxial Helmholtz coil 20.

[0076] Solving the second derivative of the above formula, we get:

[0077] (3)

[0078] In the formula: For the coil spacing ratio The second derivative operator; The magnetic field strength; is the coil spacing ratio; N is the number of turns of the coil; I is the coil current through the triaxial Helmholtz coil 20; L is the side length of the triaxial Helmholtz coil 20; ρ is the vacuum permeability, a physical constant.

[0079] Based on the second derivative formula, the parameters of the coil spacing are continuously adjusted within the magnetic field strength and current relationship model. The magnetic field uniformity parameters within the region required for the cold atom interferometry experiment under different spacings are calculated, and through continuous optimization and analysis, the optimal spacing ratio of the coaxial coils can finally be determined. =0.54450546, the space magnetic field uniformity generated by the coil is the best.

[0080] Therefore, in some embodiments of the present invention, the spacing ratio of the coaxial coils is selected to be in the range of 0.5445±0.01, thereby enabling the formation of a magnetic field in the central region of the two coils where the magnetic field strength changes more slowly with distance and the magnetic field uniformity is higher. This ensures that the magnetic field generated by the triaxial Helmholtz coil 20 has high uniformity and meets the stringent requirements of cold atom interference experiments for the magnetic field environment.

[0081] It should be noted that the structural parameters of the triaxial Helmholtz coil 20 may include the inner diameter, outer diameter, and number of turns. To ensure that a spatially quantized axis is constructed using a uniform bias field in the Z-axis direction, the deviation in the Z-direction must first be minimized, and then the scheme with the smallest overall offset value should be selected.

[0082] According to the above requirements, in one embodiment of the present invention, the coil spacing of the three axes of the triaxial Helmholtz coil 20 can be set to 88.6 mm, 84.6 mm, and 80.6 mm, respectively; the corresponding inner diameters are 188 mm, 158 mm, and 128 mm; and the outer diameter is increased by 6 mm compared to the inner diameter. By adopting a triaxial Helmholtz coil compensation structure with outer diameter = inner diameter + 6 mm, it helps to counteract the magnetic field distortion caused by the physical constraints of quantum instruments.

[0083] In some embodiments, the FPGA control module 40 includes an averaging filter unit 41, which is used to average and filter the spatial magnetic field data collected by the triaxial magnetometer 10, and then use the filtered spatial magnetic field data as the controlled signal. This makes the filtered spatial magnetic field data closer to the real magnetic field value. Using it as the controlled signal can more accurately sense changes in the magnetic field, thereby more precisely adjusting the control output and improving control accuracy.

[0084] When the triaxial magnetometer 10 acquires spatial magnetic field data of the space where the triaxial Helmholtz coil 20 is located, it is subject to various random noises, such as thermal noise from electronic components and electromagnetic interference. These noises cause fluctuations in the acquired data, affecting its accuracy and stability. Averaging filtering, by averaging multiple acquisitions of data, can effectively suppress these random noises, making the filtered data closer to the true magnetic field value.

[0085] Due to nonlinear disturbances such as hysteresis in real-world magnetic field systems, the fixed gain parameters of traditional PID controllers are inadequate and may even diverge, making effective control impossible. However, single-neuron PID controllers can achieve this through an online weight adjustment mechanism (learning rate). =0.2 to 0.5), real-time compensation for system changes, achieving precise current control, and meeting the control requirements of practical nonlinear magnetic field systems.

[0086] The biggest difference between a single-neuron PID algorithm and a regular PID algorithm is that it can automatically adjust the PID parameters according to changes in the system's properties. It adapts to changes in the external magnetic field by continuously adjusting the weights.

[0087] In some embodiments, see Figure 1 The FPGA control module 40 includes a single-neural PID control unit 42, which contains a weight update subunit 421 and an operation subunit 422. The single-neural PID control unit 42 is used for:

[0088] The difference between the expected signal and the controlled signal is used to obtain the magnetic field strength difference, error integral value, and error differential value for each sampling period;

[0089] The magnetic field strength error value, error integral value, and error differential value of the previous sampling period, as well as the voltage control data of the voltage-controlled current source 30 of the previous sampling period, are input to the weight update subunit 421. The weight update subunit 421 obtains the weight parameters of the current sampling period according to the preset weight update algorithm.

[0090] The operation subunit 422 calculates the voltage control data of the voltage-controlled current source 30 for the current sampling period based on the magnetic field strength error value, error integral value, error differential value and weight parameters of the current sampling period.

[0091] The expected signal refers to the relevant parameters of the target magnetic field that the system hopes to achieve, while the controlled signal is the spatial magnetic field data collected by the triaxial magnetometer 10 and processed by averaging and filtering. After calculating the error parameters, the single-neural PID control unit 42 inputs the magnetic field strength error value, error integral value, and error derivative value of the previous sampling period, as well as the voltage control data of the voltage-controlled current source 30 of the previous sampling period, into the weight update subunit 421. The weight update subunit 421 then processes the input data according to the preset weight update algorithm to calculate the weight parameters for the current sampling period.

[0092] For example, if the error integral value of the previous sampling period is large, it indicates that there is a long-term accumulation of deviation. The weight update algorithm can appropriately increase the weight of the error integral value so that more attention is paid to correcting the accumulated error in the current sampling period, thereby realizing the dynamic adjustment of the weight parameters.

[0093] In embodiments of the present invention, the weight update algorithm adopts the following formula:

[0094] (1)

[0095] In the formula: k is the sampling period code; For the k-th sampling period, the weight parameter is used. For the (k-1)th sampling period, the weight parameters are used. The learning rate is between 0.2 and 0.5. Let be the magnetic field strength error value for the kth sampling period; This represents the magnetic field strength error value for the (k-1)th sampling period; This is the voltage control data corresponding to the (k-1)th sampling period.

[0096] Further derivation of the above weight update algorithm yields:

[0097] (4)

[0098] In the formula: The change in the weighting parameters; The learning rate is between 0.2 and 0.5. Let be the magnetic field strength error value for the kth sampling period; This refers to the voltage control data corresponding to the (k-1)th sampling period; This represents the change in error between the k-th sampling period and the (K-1)-th sampling period.

[0099] Regarding the above The algorithm formula was simulated using MATLAB, and the four weight change trends shown in Table 1 are obtained:

[0100]

[0101] The first trend is: when the absolute value of the magnetic field strength error is greater than the error threshold and the corresponding voltage control data is less than the control threshold, the weight parameters are rapidly increased to accelerate convergence.

[0102] The second trend is: when the absolute value of the magnetic field strength error is less than or equal to the error threshold and the corresponding voltage control data is greater than or equal to the control threshold, the weight parameters are rapidly decayed to prevent oscillation.

[0103] The third trend is to improve system stability by limiting the weighting parameters when the magnetic field strength error value changes rapidly.

[0104] The fourth trend is that when the rate of change of the magnetic field strength error value approaches 0, the weight parameters are reduced to avoid parameter drift.

[0105] See Figure 3 In some embodiments, the weight parameters of the weight update algorithm include proportional term weight parameters, integral term weight parameters, and derivative term weight parameters, which correspond to the contribution of the proportional (P), integral (I), and derivative (D) components in the single-neural PID control unit 42 to the control output, respectively. According to Table 1, the weight update subunit 421 has at least four operating modes:

[0106] 1) When the absolute value of the magnetic field strength error is greater than the error threshold and the corresponding voltage control data is less than the control threshold, the first operating mode is executed, which includes increasing the growth rate of the proportional term weight parameter or suppressing the integral term weight parameter and maintaining the stability of the differential term weight parameter, with the aim of accelerating convergence;

[0107] Specifically, when the absolute value of the magnetic field strength error is greater than the preset error threshold and the corresponding voltage control data is less than the set control threshold, it indicates that the spatial magnetic field formed in the current sampling period (the superposition of the synthetic magnetic field formed by the three-axis Helmholtz coil 20 and the ambient magnetic field) has a large deviation from the target magnetic field, but the coil current output by the voltage-controlled current source 30 is relatively small and fails to effectively correct the error.

[0108] At this time, the weight update subunit 421 can increase the growth rate of the proportional term weight parameter, thereby generating a larger control output in the proportional control loop, prompting the voltage-controlled current source 30 to output a larger current, thereby adjusting the magnetic field strength more quickly and reducing the error.

[0109] In other embodiments, the weight update subunit 421 can also suppress the integral term weight parameter to avoid excessive accumulation of error leading to excessive control output, causing system overshoot or even oscillation. Simultaneously, it maintains the stability of the derivative term weight parameter, thereby allowing timely adjustment of the control strategy based on the error's changing trend, enabling the system to smoothly reduce error.

[0110] 2) When the absolute value of the magnetic field strength error is less than or equal to the error threshold and the corresponding voltage control data is greater than or equal to the control threshold, the second operating mode is executed, including increasing the decay rate of the proportional term weight parameter, or gradually increasing the integral term weight parameter, or increasing the derivative term weight parameter, in order to prevent oscillation.

[0111] Specifically, when the absolute value of the magnetic field strength error is less than or equal to the error threshold, and the corresponding voltage control data is greater than or equal to the control threshold, it means that the error between the bias magnetic field formed in the current sampling period and the target magnetic field is already small, but the control output is relatively large, which may lead to over-adjustment or instability of the system.

[0112] At this time, the weight update subunit 421 can increase the decay rate of the proportional term weight parameter, accelerate the decay of the proportional term weight parameter, and make the system more stable when approaching the target magnetic field strength, avoiding the magnetic field strength exceeding the expected value due to excessive control output.

[0113] The weight update subunit 421 can also appropriately increase the integral term weight parameter, which can further eliminate any possible minor deviations and make the bias magnetic field more accurately reach the target magnetic field. In addition, the weight update subunit 421 can also increase the differential term weight parameter, which can enable the system to detect these fluctuations more quickly and adjust the control output in a timely manner, suppress further changes in error, and improve the stability and response speed of the system.

[0114] 3) When the magnetic field strength error value changes rapidly, the third operating mode is executed to suppress changes in the weight parameters. The specific manifestations of the third operating mode include: limiting the growth rate and magnitude of the proportional term weight parameters, or slowing down the accumulation rate of the integral term weight parameters, or limiting the growth rate of the derivative term weight parameters. This allows the system to control the output more smoothly when facing rapid error fluctuations, avoiding the exacerbation of system instability due to drastic adjustments in weights, thereby improving the overall stability of the system.

[0115] 4) When the rate of change of the magnetic field strength error value approaches 0, the fourth operating mode is executed, which includes gradually reducing the proportional term weight parameter, or reducing the integral term weight parameter, or reducing the derivative term weight parameter, thereby maintaining system stability, avoiding parameter drift and ensuring control accuracy.

[0116] In this embodiment, due to the nonlinear disturbances such as hysteresis in the actual environmental magnetic field system, the fixed gain parameters of traditional PID controllers cannot adapt and may even diverge, making effective control impossible. The single-neuron PID control unit can perform online weight correction through a weight update subunit, real-time compensation for system changes, and adaptive adaptation to external magnetic field changes, achieving precise current control and meeting the control requirements of actual nonlinear magnetic field systems.

[0117] For example, the desired signal is set as:

[0118] (5)

[0119] The controlled object is:

[0120] (6)

[0121] In the formula: yd(k) is the sampled value of yd(t) at time t=k·ts, used to simulate the unsteady reference input; yd(t) is the function of the desired output (or desired signal) changing with continuous time t; k is the sampling period; ts is the time interval between two adjacent samples; pi is pi. This is the output of the system in the kth sampling period; : Output at time k-1 (output at the previous time step); This is the output at time k-2 (the output of the previous two time steps); This is the input at time k-1 (the input from the previous time step). This is the input at time k-2 (the input from the previous two time steps).

[0122] like Figure 4A , Figure 4B , Figure 4C and Figure 4D As shown in the figure, the red line represents the desired signal, and the black line represents the tracking signal. When the controlled object becomes nonlinear, as in the equation: A comparison of nonlinear systems between a conventional PID control unit and a single-nerve PID control unit is shown in the figure below. Figure 4A and Figure 4B As shown.

[0123] When the controlled object exhibits nonlinear characteristics, such as Figure 4C and Figure 4D As shown, the dynamic response of the system signal is significantly improved compared to the transition characteristics of a linear object in the peak region. This indicates that the single-neural PID control unit, through its adaptive weight adjustment mechanism (weight update sub-unit), exhibits stronger adaptability and control advantages when facing complex nonlinear characteristics.

[0124] In this embodiment, the weight update subunit in the single-neural PID control unit contains a first operating mode, a second operating mode, a third operating mode, and a fourth operating mode. Specifically, when the absolute value of the magnetic field strength error is greater than the error threshold and the corresponding voltage control data is less than the control threshold, the weight update subunit executes the first operating mode to increase the weight parameters and accelerate convergence. When the absolute value of the magnetic field strength error is less than or equal to the error threshold and the corresponding voltage control data is greater than or equal to the control threshold, the weight update subunit executes the second operating mode to achieve rapid weight decay and prevent oscillation. When the magnetic field strength error changes rapidly, the weight update subunit executes the third operating mode to suppress changes in the weight parameters and improve system stability. When the rate of change of the magnetic field strength error approaches 0, the weight update subunit executes the fourth operating mode to decrease the weight parameters and avoid drifting and instability in the output voltage control data.

[0125] Having the same inventive concept as the aforementioned cold atom interferometry magnetic field generation system, an embodiment of the present invention also provides a method for generating geomagnetic compensation and bias magnetic fields for cold atom interferometry. This method is applicable to the geomagnetic compensation and bias magnetic field generation systems for cold atom interferometry provided in any of the above embodiments. Therefore, the implementation principles and technical effects not mentioned in the method embodiments can be referred to the corresponding content in the foregoing system embodiments. It is conceivable that parts not detailed in the system embodiments can also be referred to in the method embodiments.

[0126] See Figure 5The magnetic field generation method of the present invention is executed by the FPGA control module 40 in the aforementioned system, and includes the following steps:

[0127] S10: According to the set sampling period, the spatial magnetic field data of the three-axis Helmholtz coil in the space where the three-axis magnetometer 10 is located is acquired in real time. The multiple monitoring positions include the physical center position of the three-axis Helmholtz coil and the adjacent positions with the physical center as the origin.

[0128] Specifically, the triaxial magnetometer 10 is always running to collect spatial magnetic field data at multiple monitoring locations within the space where the triaxial Helmholtz coil is located in real time. This spatial magnetic field data is the magnetic field data formed by the superposition of the synthetic magnetic field generated by the triaxial Helmholtz coil 20 and the ambient magnetic field in three axes (X, Y, Z axes).

[0129] It should be noted that the sampling period can be set as needed to meet the magnetic field accuracy requirements of cold atom interferometry experiments. For example, in one embodiment of the present invention, the sampling period can be set to 2 to 5 milliseconds, such as 2 milliseconds, 3 milliseconds, or 5 milliseconds, so that the magnetic field can be sampled and adjusted frequently, errors can be corrected in time, the magnetic field can be made to more accurately approach the target value, and the accuracy of magnetic field control can be improved.

[0130] S20: In each sampling period, the number of spatial magnetic fields of any one of the multiple monitoring locations is used as the controlled signal, and the preset target magnetic field is used as the expected signal to calculate the voltage control data required by the voltage-controlled current source 30.

[0131] Specifically, in each sampling period, the FPGA control module 40 uses the newly acquired spatial magnetic field data as the controlled signal and the preset target magnetic field as the expected signal. The difference between the controlled signal and the expected signal reflects the deviation between the current magnetic field state and the expected magnetic field state. Then, based on the controlled signal and the expected signal, the voltage control data required by the voltage-controlled current source 30 is calculated.

[0132] S30 adjusts the coil current supplied by the voltage-controlled current source 30 to the triaxial Helmholtz coil 20 according to the voltage control data.

[0133] Steps S10 to S30 are executed repeatedly until the triaxial Helmholtz coil 20 generates the target magnetic field to achieve environmental magnetic field compensation. The target magnetic field is a uniform bias magnetic field with near-zero magnetic field in the X and Y directions and constant and non-zero magnetic field strength in the Z direction.

[0134] In other words, during the execution of the magnetic field generation method, steps S10 to S30 are executed cyclically. During this cycle, the FPGA control module 40 continuously monitors the changes in the magnetic field. When the error between the actual magnetic field and the target magnetic field is less than a set error threshold, it is considered that the target magnetic field has been successfully generated within that sampling period, achieving dynamic compensation for the environmental magnetic field. At this point, cold atom interferometry experiments can be performed in the target magnetic field environment generated by the method of this invention, greatly improving the accuracy and reliability of the experiments.

[0135] In summary, the method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry provided in this embodiment of the invention can dynamically adapt to changes in the environmental magnetic field through cyclic adjustment, ensuring a stable and uniform bias magnetic field environment for cold atom interferometry experiments under various complex conditions.

[0136] In this embodiment, the spatial magnetic field data acquired in step S10 at multiple monitoring locations includes at least the spatial magnetic field data located at the physical center of the triaxial Helmholtz coil 20, and the spatial magnetic field data corresponding to neighboring locations with the physical center as the origin. Multiple neighboring locations are provided, each located on the X / Y / Z axes of the triaxial Helmholtz coil. Furthermore, the distance from each neighboring location to the physical center is less than or equal to 0.5 mm.

[0137] During the execution of the magnetic field generation method, the triaxial magnetometer 10 collects in real time the spatial magnetic field data at the physical center of the triaxial Helmholtz coil 20, as well as the corresponding spatial magnetic field data at neighboring locations with the physical center as the origin. Preferably, there are at least 6 neighboring locations, and each pair of the 6 neighboring locations is located on the X / Y / Z axes of the triaxial Helmholtz coil.

[0138] Taking the kth sampling period as an example, the spatial magnetic field data at the physical center of the triaxial Helmholtz coil 20 is first used as the controlled signal, and the preset target magnetic field is used as the expected signal to calculate the voltage control data required by the voltage-controlled current source; and the coil current supplied by the voltage-controlled current source 30 to the triaxial Helmholtz coil 20 is adjusted according to the voltage control data.

[0139] The spatial magnetic field data at the physical center of the three-axis Helmholtz coil 20 is determined to satisfy the magnetic field data of the target magnetic field. Then, it is determined whether the spatial magnetic field data corresponding to multiple adjacent positions satisfy the magnetic field data of the target magnetic field.

[0140] If the spatial magnetic field data corresponding to multiple nearby locations all satisfy the magnetic field data of the target magnetic field, it indicates that the triaxial Helmholtz coil has generated a uniform bias magnetic field that can compensate for the environmental magnetic field.

[0141] If one of the spatial magnetic field data corresponding to multiple neighboring locations does not satisfy the target magnetic field, then the spatial magnetic field data corresponding to that neighboring location is used as the controlled signal, and steps S20 to S30 are executed. For example, if there is a neighboring location A among multiple neighboring locations that does not satisfy the target magnetic field, then the spatial magnetic field data corresponding to that neighboring location A is used as the controlled signal, and steps S20 to S30 are executed.

[0142] The process continues until the spatial magnetic field data corresponding to the nearest location A meets the magnetic field data of the target magnetic field. Then, it is determined whether the physical center location and other corresponding nearby locations meet the magnetic field data of the target magnetic field.

[0143] Finally, when the spatial magnetic field data at the physical center of the three-axis Helmholtz coil 20 and the spatial magnetic field data at the adjacent positions both satisfy the target magnetic field data, the loop execution steps S20 to S30 end. At this point, it can be considered that the three-axis Helmholtz coil 20 has generated a uniform bias magnetic field that can compensate for the environmental magnetic field.

[0144] In this embodiment, the magnetic field generation method further includes the following step before step S10:

[0145] A model for the relationship between magnetic field strength and current is established based on the vector superposition algorithm.

[0146] The relationship between magnetic field strength and current was calculated to obtain the coil spacing ratio, which is 0.5445±0.01.

[0147] Based on the coil spacing ratio, determine the structural parameters of the triaxial Helmholtz coil 20, wherein the structural parameters include at least the inner diameter and the number of turns;

[0148] Based on the structural parameters, a triaxial Helmholtz coil 20 is constructed. The triaxial Helmholtz coil 20 has a rectangular coil structure, and the inner and outer diameters of the three axes of the triaxial Helmholtz coil 20 are different.

[0149] In other words, before implementing the magnetic field generation method of the present invention, a triaxial Helmholtz coil 20 needs to be constructed in advance to ensure that the constructed triaxial Helmholtz coil 20 can generate the structural requirements of the magnetic field environment (target magnetic field) required for cold atom interference experiments.

[0150] For each coil in the triaxial Helmholtz coil 20, it is considered to be composed of countless current elements. The magnetic field generated by each current element at a certain point in space can be accurately calculated using the Biot-Savart law. Then, the magnetic fields generated by all current elements at that point are vector-superimposed to obtain the magnetic field strength generated by a single coil at that point. Next, considering the superposition of the magnetic fields generated by the three axial coils, and combining the relative positions of the coils and the magnitude of the current, a mathematical model is established to accurately describe the relationship between the magnetic field strength and the current of the total magnetic field.

[0151] It should be noted that, in the process of constructing the triaxial Helmholtz coil 20, the magnetic field strength calculation and magnetic field simulation analysis described in the above system embodiment can be used to ensure that the structural parameters of the triaxial Helmholtz coil meet the target magnetic field requirements of cold atom interference.

[0152] In some embodiments, the magnetic field generation method further includes: using a preset average filtering algorithm to perform average filtering on the spatial magnetic field data acquired in each sampling period, and then using the filtered spatial magnetic field data as the controlled signal.

[0153] Specifically, within each set sampling period, the triaxial magnetometer 10 continuously collects multiple spatial magnetic field data points. For example, in a sampling period of 10 milliseconds, the triaxial magnetometer 10 will collect 10 magnetic field data points within that period at a higher frequency (e.g., once every 1 millisecond). These data points contain magnetic field strength information along three axes (X, Y, and Z axes).

[0154] Then, the multiple magnetic field data points collected in each sampling period are grouped according to the collection order. For example, the above 10 data points are grouped into one group as the data set used for averaging filtering in that sampling period.

[0155] For the magnetic field data along each axis, calculate the average value of the data points in that group. Specifically, for the magnetic field data along the X-axis, add up the 10 X-axis magnetic field strength values ​​in that group, then divide by 10 to obtain the average value of the X-axis magnetic field strength; similarly, calculate the average values ​​of the magnetic field strength along the Y-axis and Z-axis respectively.

[0156] Finally, the calculated average magnetic field strengths along the three axes are combined to form filtered spatial magnetic field data, which is then used as the controlled signal. This controlled signal is smoother and more accurate than the unfiltered data, and can more realistically reflect the current magnetic field state within the system.

[0157] In this embodiment, it is assumed that the N continuously collected magnetic field data are as follows: Let y be the filtered magnetic field data. The average filtering algorithm includes the following formula:

[0158] (7)

[0159] In some embodiments, step S20 above uses the acquired spatial magnetic field data as the controlled signal and the preset target magnetic field as the expected signal in each sampling period to calculate the voltage control data required by the voltage-controlled current source 30, specifically including:

[0160] The magnetic field strength error value, error integral value, and error differential value for each sampling period are obtained based on the difference between the expected signal and the controlled signal.

[0161] Based on the magnetic field strength error value, error integral value, and error differential value of the previous sampling period, the voltage control data of the voltage-controlled current source 30 of the previous sampling period, and the preset weight update algorithm, the weight parameters of the current sampling period are obtained.

[0162] Based on the magnetic field strength error value, error integral value, error differential value, and weighting parameters of the current sampling period, the voltage control data of the voltage-controlled current source 30 for the current sampling period is calculated.

[0163] Wherein, it is assumed that the magnetic field strength error value of the kth sampling period is... k is the sampling period encoding; the error integral value is The error differential value is The time interval between two adjacent sampling periods is T.

[0164] Therefore, the integral value of the error is calculated using the following formula:

[0165] (8)

[0166] In the formula: k is the sampling period code, representing the current sampling period; This is the integral value of the error in the k-th sampling period; This is the integral value of the error in the (k-1)th sampling period; is the magnetic field strength error value of the k-th sampling period; T is the time interval between two adjacent sampling periods;

[0167] The differential value of the error is calculated using the following formula:

[0168] (9)

[0169] In the formula: Let be the differential value of the error in the k-th sampling period; Let be the magnetic field strength error value for the kth sampling period; is the magnetic field strength error value of the (k-1)th sampling period; T is the time interval between two adjacent sampling periods.

[0170] In this embodiment, the step of calculating the voltage control data of the voltage-controlled current source 30 for the current sampling period based on the magnetic field strength error value, error integral value, error differential value, and weighting parameters of the current sampling period adopts the following formula:

[0171] (10)

[0172] In the formula, k is the sampling period encoding; This is the voltage control data corresponding to the current sampling period (the kth sampling period); The weight parameter for the proportional term in the k-th sampling period; The integral term weight parameter for the k-th sampling period; The differential term weight parameter for the k-th sampling period; Let be the magnetic field strength error value for the kth sampling period; Let be the integral value of the magnetic field strength error in the k-th sampling period; be Let be the differential value of the magnetic field strength error in the kth sampling period.

[0173] The weight update algorithm uses the following formula:

[0174] (11)

[0175] In the formula: k is the sampling period code; For the k-th sampling period, the weight parameter is used. For the (k-1)th sampling period, the weight parameters are used. The learning rate is 0.2 to 0.5. Let be the magnetic field strength error value for the kth sampling period; This represents the magnetic field strength error value for the (k-1)th sampling period; This is the voltage control data corresponding to the (k-1)th sampling period.

[0176] According to the above weight update algorithm formula, the weight update algorithm executes at least one of the first running mode, the second running mode, the third running mode, and the fourth running mode.

[0177] First operating mode: When the absolute value of the magnetic field strength error is greater than the error threshold and the corresponding voltage control data is less than the control threshold, the weight update algorithm executes the first operating mode. By executing the weight update algorithm, the growth rate of the proportional term weight parameter is increased, or the integral term weight parameter is suppressed and the differential term weight parameter is kept stable.

[0178] Second operating mode: When the absolute value of the magnetic field strength error is less than or equal to the error threshold and the corresponding voltage control data is greater than or equal to the control threshold, the weight update algorithm executes the second operating mode. By executing the weight update algorithm, the decay rate of the proportional term weight parameter is increased, or the integral term weight parameter is gradually increased, or the derivative term weight parameter is increased.

[0179] The third operating mode: When the magnetic field strength error value changes rapidly, the weight update algorithm executes the third operating mode to suppress the change of weight parameters. Specifically, it limits the growth rate and speed of the proportional term weight parameter, or slows down the accumulation speed of the integral term weight parameter, or limits the growth rate of the differential term weight parameter. This allows the system to control the output more smoothly when facing rapid error fluctuations, avoids exacerbating the instability of the system due to drastic weight adjustments, and thus improves the overall stability of the system.

[0180] Fourth operating mode: When the rate of change of the magnetic field strength error value approaches 0, the weight update algorithm executes the fourth operating mode. By executing the weight update algorithm, the proportional term weight parameter, or the integral term weight parameter, or the derivative term weight parameter is gradually reduced, thereby maintaining system stability, avoiding parameter drift and ensuring control accuracy.

[0181] In some embodiments, the FPGA control module 40 calculates the coil current data required by the triaxial Helmholtz coil 20 based on the voltage control data and the preset voltage and current fitting relationship model, and then controls the voltage-controlled current source 30 to supply coil current to the triaxial Helmholtz coil 20 based on the coil current data.

[0182] In one embodiment, the voltage-current fitting relationship model uses the following formula:

[0183] (12)

[0184] In the formula: U represents voltage data, and I represents current data.

[0185] In this embodiment, the linear relationship between voltage and current in the voltage-controlled current source 30 is shown in the figure below. Figure 6 As shown, the above formula is obtained by fitting a function to the system. In other words, this formula is obtained by fitting the characteristics of the actual system. Within the normal operating range, using this formula to convert mechanical energy into voltage and current can reduce error fluctuations caused by model inaccuracies and achieve a current control error of less than ±1mA.

[0186] The FPGA control module 40 can use various methods to determine whether the triaxial Helmholtz coil 20 has generated the target magnetic field.

[0187] For example, in some embodiments, the FPGA control module 40 determines whether the magnetic field strength error value in the spatial magnetic field data collected in the current sampling period meets the preset error threshold; if the magnetic field strength error value meets the preset error threshold, it is considered that the magnetic field bias effect required for the target magnetic field has been achieved, the data is recorded, and a verification report is generated; otherwise, it is determined that the magnetic field formed by the triaxial Helmholtz coil 20 in the current sampling period has not yet achieved the magnetic field bias effect, and steps S10 to S30 are continued.

[0188] In some embodiments, the FPGA control module 40 can also calculate the change in magnetic field strength in adjacent sampling periods based on the spatial magnetic field data of the triaxial magnetometer 10 in multiple consecutive sampling periods; determine whether the change in magnetic field strength in adjacent sampling periods meets the preset change threshold; if the change meets the preset change threshold, it indicates that the geomagnetic interference has disappeared, record the data, and generate a verification report; otherwise, it is determined that the geomagnetic interference still exists, and steps S10 to S30 are continued.

[0189] In other embodiments, the FPGA control module 40 can also divide the magnetic field space formed by the triaxial Helmholtz coil 20 into multiple measurement regions; based on the spatial magnetic field data collected by the triaxial magnetometer 10 in different measurement regions, the magnetic field uniformity parameter is calculated, including the mean or standard deviation; if the magnetic field uniformity parameter meets the preset uniformity threshold, it is considered that the magnetic field formed by the triaxial Helmholtz coil 20 in the current sampling period meets the target magnetic field required for cold atom interference.

[0190] Specifically, dividing the magnetic field space formed by the triaxial Helmholtz coil 20 into multiple measurement regions allows for a more detailed detection of the magnetic field distribution in space and a comprehensive assessment of the magnetic field uniformity. For each measurement region, the triaxial magnetometer 10 measures the magnetic field strength along three axes (X, Y, and Z). The magnetic field strength data along the same axis in all measurement regions are summarized, and their arithmetic mean and standard deviation are calculated. The arithmetic mean reflects the average strength level of the magnetic field within the entire measurement region. By comparing it with the magnetic field strength data of the preset target magnetic field, a preliminary judgment can be made as to whether the magnetic field has met the expected strength requirements. The standard deviation measures the dispersion of the magnetic field strength across different measurement regions. The smaller the standard deviation, the smaller the fluctuation of the magnetic field strength between different regions, and the better the uniformity of the magnetic field; conversely, the larger the standard deviation, the worse the uniformity of the magnetic field.

[0191] If the magnetic field uniformity parameters (mean and standard deviation) both meet the preset uniformity threshold, that is, the mean of the magnetic field strength in each axis is close to the target value and the standard deviation is within the allowable range, then the magnetic field formed by the triaxial Helmholtz coil 20 in the current sampling period is considered to meet the target magnetic field required for cold atom interference; if any uniformity parameter does not meet the threshold requirement, it indicates that the magnetic field uniformity has not met the standard, and the coil current of the triaxial Helmholtz coil 20 needs to be adjusted, the magnetic field is regenerated and verified, that is, steps S10 to S30 are executed repeatedly.

[0192] In some embodiments, the FPGA control module 40 can also calculate the corresponding average value and standard deviation based on the magnetic field strength data of each axis in the spatial magnetic field data collected by the triaxial magnetometer 10, and draw a trend graph, thereby enabling real-time monitoring of the changes in magnetic field strength over time. If the curve in the trend graph is relatively stable, it indicates that the magnetic field is stable; if the curve shows obvious fluctuations or trend changes, it indicates that the magnetic field may be affected by external interference or that the system itself has unstable factors.

[0193] It needs to be made clear that, Figure 5 The flowchart illustrating the method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry shown herein is merely a representation of the logical order provided by one of the many embodiments of this invention. This order is intended to clearly illustrate the execution flow of the method in a specific application scenario. However, in practical applications, the flexibility and scalability of this invention allow those skilled in the art to adjust the order of the above steps according to different practical needs and environmental conditions, such as having parallel or concurrent relationships between some steps, which will not be elaborated upon here.

[0194] Furthermore, those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0195] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 A means for a process or multiple processes and / or a block diagram (one or more blocks) specifying the functions.

[0196] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 A process or multiple processes and / or a block diagram (one or more blocks) specifying the functions.

[0197] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0198] Additionally, any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of the invention pertain.

Claims

1. A system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry, characterized by, The application relates to a three-axis magnetic field compensation system. The three-axis magnetic field compensation system comprises a three-axis magnetic field sensor, a three-axis Helmholtz coil, a voltage-controlled current source and an FPGA control module. The three-axis magnetic field sensor is used for collecting space magnetic field data at multiple monitoring positions in the space where the three-axis Helmholtz coil is located and transmitting the space magnetic field data to the FPGA control module, wherein the multiple monitoring positions include a physical center position of the three-axis Helmholtz coil and adjacent positions with the physical center as the origin. The FPGA control module is used for taking any space magnetic field data collected by the three-axis magnetic field sensor as a controlled signal, taking a preset target magnetic field as an expected signal, calculating voltage control data required by the voltage-controlled current source, and then controlling the coil current of the three-axis Helmholtz coil delivered by the voltage-controlled current source according to the voltage control data. The control process of the FPGA control module is iterated until the three-axis Helmholtz coil generates the target magnetic field at the multiple monitoring positions, thereby realizing dynamic compensation of the environmental magnetic field, wherein the target magnetic field is a uniform bias magnetic field with near-zero magnetic field in X / Y direction, constant magnetic field intensity in Z direction and non-zero value. The three-axis Helmholtz coil has a rectangular coil structure, the inner and outer diameters of the three axes of the three-axis Helmholtz coil are different, and the spacing ratio of the coaxial coils is 0.5445+ / -0.

01.

2. The system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry of claim 1, wherein, The FPGA control module comprises an average filtering unit, which is used for performing average filtering on the space magnetic field data collected by the three-axis magnetic field sensor, and taking the filtered space magnetic field data as the controlled signal.

3. The system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry of claim 1 or 2, wherein, The FPGA control module comprises a single neural PID control unit, which is provided with a weight updating subunit and an operation subunit, and is used for, obtaining a magnetic field intensity error value, an error integral value and an error differential value of each sampling period according to the difference between the expected signal and the controlled signal; inputting the magnetic field intensity error value, the error integral value and the error differential value of the last sampling period and the voltage control data of the voltage-controlled current source of the last sampling period into the weight updating subunit, and obtaining a weight parameter of the current sampling period according to a preset weight updating algorithm by the weight updating subunit; the operation subunit calculates the voltage control data of the voltage-controlled current source of the current sampling period according to the magnetic field intensity error value, the error integral value, the error differential value and the weight parameter of the current sampling period.

4. The system for geomagnetic compensation and bias magnetic field generation for cold atom interferometry of claim 3, wherein, The weight parameter comprises a proportional term weight parameter, an integral term weight parameter and a differential term weight parameter; and the weight updating subunit has at least four operating modes: 1) the first operating mode is executed when the absolute value of the magnetic field intensity error value is greater than an error threshold value and the corresponding voltage control data is less than a control threshold value, which comprises increasing the growth rate of the proportional term weight parameter or inhibiting the integral term weight parameter and maintaining the differential term weight parameter stable; 2) performing the second operation mode when the absolute value of the magnetic field intensity error value is less than or equal to the error threshold value and the corresponding voltage control data is greater than or equal to the control threshold value, including increasing the decay rate of the proportional term weight parameter, or gradually increasing the integral term weight parameter, or increasing the differential term weight parameter; 3) performing the third operation mode when the magnetic field intensity error value changes rapidly, including limiting the growth amplitude and speed of the proportional term weight parameter, or slowing down the accumulation speed of the integral term weight parameter, or limiting the growth amplitude of the differential term weight parameter; 4) performing the fourth operation mode when the change rate of the magnetic field intensity error value tends to 0, including gradually reducing the proportional term weight parameter, or reducing the integral term weight parameter, or reducing the differential term weight parameter.

5. A method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry, characterized in that, The method comprises the following steps: S10, acquiring the spatial magnetic field data at multiple monitoring positions in the space where the three-axis Helmholtz coil is located, which is collected by the three-axis magnetometer in real time according to a set sampling period, wherein the multiple monitoring positions include the physical center position of the three-axis Helmholtz coil and the adjacent positions with the physical center as the origin; S20, in each sampling period, taking any acquired spatial magnetic field data as the controlled signal, taking the preset target magnetic field as the expected signal, and calculating the voltage control data required by the voltage-controlled current source; S30, controlling the coil current delivered by the voltage-controlled current source to the three-axis Helmholtz coil according to the voltage control data; Steps S10 to S30 are executed in a loop until the three-axis Helmholtz coil generates the target magnetic field at the multiple monitoring positions, thereby realizing dynamic compensation of the environmental magnetic field, wherein the target magnetic field is a uniform bias magnetic field with near-zero magnetic field in X / Y direction and constant magnetic field intensity in Z direction and non-zero value; Before step S10, the method further comprises the following steps: Based on the vector superposition algorithm, a magnetic field intensity and current relationship model is established; The magnetic field intensity and current relationship model is operated to obtain a coil spacing ratio, wherein the coil spacing ratio is 0.5445±0.01; According to the coil spacing ratio, the structure parameters of the three-axis Helmholtz coil are determined, wherein the structure parameters at least include the inner diameter and the number of turns; According to the structure parameters, the three-axis Helmholtz coil is constructed, and the three-axis Helmholtz coil is a rectangular coil structure, and the inner and outer diameters of the coils of the three axes are different.

6. The method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry of claim 5, wherein, The method further comprises: Using a preset average filtering algorithm, the spatial magnetic field data acquired in each sampling period is subjected to average filtering processing, and the filtered spatial magnetic field data is taken as the controlled signal.

7. The method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry of claim 5, wherein, The step S20 in each sampling period, the spatial magnetic field data is taken as the controlled signal, the preset target magnetic field is taken as the expected signal, and the voltage control data required by the voltage-controlled current source is calculated, specifically comprising: According to the difference between the expected signal and the controlled signal, the magnetic field intensity error value, the error integral value and the error differential value of each sampling period are obtained; According to the magnetic field intensity error value, the error integral value and the error differential value of the last sampling period, the voltage control data of the voltage-controlled current source of the last sampling period, and a preset weight updating algorithm, a weight parameter of a current sampling period is obtained; According to the magnetic field intensity error value, the error integral value, the error differential value and the weight parameter of the current sampling period, voltage control data of the voltage-controlled current source of the current sampling period is calculated.

8. The method for geomagnetic compensation and bias magnetic field generation for cold atom interferometry of claim 7, wherein, The weight updating algorithm adopts the following formula: （1） In the formula, k is a sampling period code; is a weight parameter of the kth sampling period; is a weight parameter of the k-1th sampling period; is a learning rate, which is 0.2 to 0.5; is a magnetic field intensity error value of the kth sampling period; is a magnetic field intensity error value of the k-1th sampling period; is voltage control data corresponding to the k-1th sampling period.

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