Method and system for controlling main magnetic field of nuclear magnetic resonance gyroscope based on active-disturbance-rejection control

Abstract

The invention belongs to the field of inertial navigation measurement, and discloses a nuclear magnetic resonance gyroscope main magnetic field control method and system based on active disturbance rejection control, and the method comprises the following steps: establishing a nuclear magnetic resonance gyroscope main magnetic field system differential equation; designing an active-disturbance-rejection controller based on a differential equation of a main magnetic field system of the nuclear magnetic resonance gyroscope; based on an active-disturbance-rejection controller, a nuclear magnetic closed-loop system is built in combination with a gyro prototype, and main magnetic field disturbance is restrained. The invention particularly provides a magnetic field control method based on linear active disturbance rejection control (LADRC) aiming at the key influence of the stability of a main magnetic field in a nuclear magnetic resonance gyroscope on the system output precision, which is used for solving the problems of insufficient control precision and poor robustness in the face of system disturbance, model uncertainty and nonlinear environment influence of the existing PID control method. Therefore, the zero-bias stability and the measurement precision of the nuclear magnetic resonance gyroscope are improved.

Description

Technical Field

[0001] The present invention belongs to the field of inertial navigation measurement, and in particular relates to a high-precision closed-loop control method for a magnetic field applied to a nuclear magnetic resonance gyroscope system. The present invention belongs to the category of high-precision control technology that intersects precision control and magnetic measurement technology, and specifically relates to a main magnetic field control method and system for a nuclear magnetic resonance gyroscope based on active disturbance rejection control. Background Art

[0002] As the core sensitive component of inertial navigation systems, gyroscope performance improvements and technological innovation have always been key to their development. Nuclear magnetic resonance gyroscopes (NMRGs) combine the precision of optical gyroscopes with the size and cost of micro-electromechanical (MEMS) gyroscopes, giving them broad application prospects.

[0003] The performance of an NMR gyroscope (NMRG) is closely linked to the main magnetic field. The controllability of the main magnetic field directly affects the stability of the nuclear spin resonance frequency, and thus the accuracy of the NMRG's measurement of the carrier's angular velocity. To ensure measurement accuracy, the accuracy of the magnetic field must be maintained. The magnetic field in an NMR gyroscope consists of the main magnetic field and the remanent magnetic field. The main magnetic field determines the nuclear spin observation frequency of atomic spins, providing a measurement benchmark for the nuclear spin ensemble. Its long-term stability determines the NMRG's drift performance.

[0004] Currently, the mainstream closed-loop control scheme for the main magnetic field mostly uses a proportional-integral-derivative (PID) controller. This control strategy relies on a feedback error signal for regulation. While it does not require accurate modeling and has a simple parameter structure, achieving good control results under some ideal operating conditions, it suffers from the following drawbacks when faced with complex disturbance environments (such as electromagnetic interference, temperature drift, and structural nonlinearity): First, its control hysteresis results in slow disturbance response, making rapid suppression difficult; second, the integral link is prone to system overshoot and phase lag, while the differential link is sensitive to high-frequency noise, which can easily cause output oscillation; third, its adaptability to system structural changes and model uncertainty is poor, making long-term stable operation difficult. Therefore, traditional PID control methods cannot meet the requirements of nuclear magnetic resonance gyroscopes for high-precision and robust control of the main magnetic field.

[0005] In a nuclear magnetic resonance gyroscope (NMR) magnetic field control system, the main magnetic field is affected by a variety of complex interference sources, including power supply noise, coil non-idealities, material temperature drift, and ambient magnetic field fluctuations. Using active disturbance rejection control (ADRC) for closed-loop magnetic field control enables online estimation and real-time compensation of these disturbances, potentially significantly improving the steady-state accuracy and dynamic response speed of magnetic field control, reducing system bias drift, and enhancing overall measurement performance. Therefore, researching and proposing an ADRC magnetic field control method for NMR gyroscope applications has important engineering practical value and theoretical significance. Summary of the Invention

[0006] In response to the deficiencies in the prior art, the present invention provides a main magnetic field control method and system for a nuclear magnetic resonance gyroscope based on active disturbance rejection control. Specifically, the present invention addresses the critical impact of the main magnetic field stability in the nuclear magnetic resonance gyroscope on the system output accuracy, and proposes a magnetic field control method based on linear active disturbance rejection control (LADRC). This method is used to address the problems of insufficient control accuracy and poor robustness of existing PID control methods when facing system disturbances, model uncertainties and nonlinear environmental influences, thereby improving the zero bias stability and measurement accuracy of the nuclear magnetic resonance gyroscope.

[0007] To achieve the above object, the present invention provides the following solutions:

[0008] A method for controlling a main magnetic field of a nuclear magnetic resonance gyroscope based on active disturbance rejection control, the method comprising:

[0009] Establish the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope;

[0010] Based on the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope, an active disturbance rejection controller is designed;

[0011] Based on the active disturbance rejection controller, a nuclear magnetic closed-loop system is built in combination with a gyroscope prototype to suppress main magnetic field disturbances.

[0012] Preferably, the method for establishing the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope includes:

[0013]

[0014] Where T2 represents the transverse relaxation time of the nucleus, is the first-order derivative of the input u, and They are the first and second order derivatives of the output y, and the corresponding PI parameters are k P With k I .

[0015] Preferably, the active disturbance rejection controller includes: an extended state observer and a state error feedback control rate;

[0016] Among them, the extended state observer is:

[0017]

[0018] in, L=[l1 l2 l3] T is the observer gain matrix to be designed, C = [1 0 0], z = [z1, z2, z3] T is the state vector of the corresponding observer, and the derivative is z1, z2, z3 are state variables, L = [l1 l2 l3] T is the observer gain matrix to be designed, l1, l2, l3 are the gain values to be designed, and u is c =[uy] T As the input matrix of the observer, is the observation value of the system output by the observer, m0, m1, b0 are the parameters reflecting the main magnetic field system, and their relationship with the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is:

[0019]

[0020] |sI-(A-LC)|=(s+ω0) 3 , where s represents the complex frequency variable in Laplace transform, which is used to describe the frequency domain characteristics of the system, and ω0 is the observer bandwidth;

[0021] The state error feedback control rate is:

[0022]

[0023] s 2 +k fd s+k fp =(s+ω c ) 2 ,

[0024] Among them, ω c is the feedback control rate bandwidth, k fp =ω c 2 k fd =2ω c , r is the input reference signal, z1, z2, z3 are the state variables of the observer, u is the input control signal applied to the controlled system, u0 is the intermediate variable in the calculation process, k fp With k fd is the gain value of the linear error feedback rate that needs to be designed.

[0025] Preferably, the nuclear magnetic closed-loop system includes: a signal processing device, a controller, a host computer and a voltage-controlled current source;

[0026] The host computer communicates with the controller, which includes: an analog-to-digital conversion circuit, a microcontroller, and a digital-to-analog conversion circuit;

[0027] The signal processing device is used to extract information from the detection light and demodulate the nuclear spin observation frequencies of the two nuclei through a phase-locked amplifier and a phase-locked loop structure;

[0028] The analog-to-digital conversion circuit is used to collect the nuclear spin observation frequencies of the two nuclei, send the collected data to the microcontroller to run the active disturbance rejection control algorithm, calculate the control quantity and convert it into a current signal through the digital-to-analog conversion circuit and the voltage-controlled current source, and apply it to the z-axis coil, thereby realizing closed-loop control of the main magnetic field.

[0029] The present invention also provides a nuclear magnetic resonance gyroscope main magnetic field control system based on active disturbance rejection control, the system is used to implement the above method, the system includes: a first building module, a second building module and a third building module;

[0030] The first building block is used to establish a differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope;

[0031] The second building block is used to design an active disturbance rejection controller based on the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope;

[0032] The third building block is used to build a nuclear magnetic closed-loop system based on the active disturbance rejection controller in combination with a gyroscope prototype to suppress main magnetic field disturbances.

[0033] Preferably, the process of establishing the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope includes:

[0034]

[0035] Where T2 represents the transverse relaxation time of the nucleus, is the first-order derivative of the input u, and They are the first and second order derivatives of the output y, and the corresponding PI parameters are k P With k I .

[0036] Preferably, the active disturbance rejection controller includes: an extended state observer and a state error feedback control rate;

[0037] Among them, the extended state observer is:

[0038]

[0039] in, L=[l1 l2 l3] T is the observer gain matrix to be designed, C = [1 0 0], z = [z1, z2, z3] T is the state vector of the corresponding observer, and the derivative is z1, z2, z3 are state variables, L = [l1 l2 l3] T is the observer gain matrix to be designed, l1, l2, l3 are the gain values to be designed, and u isc =[uy] T As the input matrix of the observer, is the observation value of the observer on the system output, m0, m1, b0 are the parameters reflecting the main magnetic field system, and their relationship with the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is:

[0040]

[0041] |sI-(A-LC)|=(s+ω0) 3 , where s represents the complex frequency variable in Laplace transform, which is used to describe the frequency domain characteristics of the system, and ω0 is the observer bandwidth;

[0042] The state error feedback control rate is:

[0043]

[0044] s 2 +k fd s+k fp =(s+ω c ) 2 ,

[0045] Among them, ω c is the feedback control rate bandwidth, k fp =ω c 2 k fd =2ω c , r is the input reference signal, z1, z2, z3 are the state variables of the observer, u is the input control signal applied to the controlled system, u0 is the intermediate variable in the calculation process, k fp With k fd is the gain value of the linear error feedback rate that needs to be designed.

[0046] Preferably, the nuclear magnetic closed-loop system includes: a signal processing device, a controller, a host computer and a voltage-controlled current source;

[0047] The host computer communicates with the controller, which includes: an analog-to-digital conversion circuit, a microcontroller, and a digital-to-analog conversion circuit;

[0048] The signal processing device is used to extract information from the detection light and demodulate the nuclear spin observation frequencies of the two nuclei through a phase-locked amplifier and a phase-locked loop structure;

[0049] The analog-to-digital conversion circuit is used to collect the nuclear spin observation frequencies of the two nuclei, send the collected data to the microcontroller to run the active disturbance rejection control algorithm, calculate the control quantity and convert it into a current signal through the digital-to-analog conversion circuit and the voltage-controlled current source, and apply it to the z-axis coil, thereby realizing closed-loop control of the main magnetic field.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] The present invention does not rely on precise modeling and has strong adaptability: the control system does not need to rely on the precise mathematical model of the controlled object, and only requires the relative order information of the system to realize the controller design, which significantly reduces the dependence on the model identification accuracy. It is suitable for magnetic field control systems with complex situations such as nonlinearity, parameter uncertainty or time-varying models.

[0052] The present invention has active anti-interference capability and improves robustness: it uses an extended state observer (ESO) to estimate system disturbances in real time and actively compensates for disturbance effects through state error feedback, thereby achieving dynamic suppression of unknown disturbances (such as power supply fluctuations, temperature drift, electromagnetic noise, etc.), significantly enhancing the system's robustness and environmental adaptability.

[0053] The present invention improves dynamic response speed and steady-state accuracy: the controller can flexibly adjust the feedback bandwidth and observer bandwidth according to system performance requirements, thereby taking into account both fast response and output stability.

[0054] The structure of the present invention is simple to implement and the parameter setting is intuitive: it adopts the linear active disturbance rejection control structure (LADRC), the controller structure is simple, the implementation method is clear, and there are few key control parameters (mainly two bandwidth parameters), which is convenient for engineering deployment and system debugging, and has good practicality and portability.

[0055] This invention is highly compatible with the requirements of NMR gyro control systems: Designed around the crucial role of the stability of the main magnetic field in NMR gyros on frequency drift and measurement accuracy, it effectively suppresses magnetic field fluctuations caused by weak perturbations, improving the long-term consistency of the Larmor frequency and the stability of the output bias. Its control accuracy and dynamic robustness meet the core requirements of high-sensitivity NMR inertial measurement systems, demonstrating high system compatibility and widespread application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0057] Figure 1 This is a flow chart of a method for controlling the main magnetic field of a nuclear magnetic resonance gyroscope based on active disturbance rejection control according to an embodiment of the present invention;

[0058] Figure 2This is a schematic diagram of a nuclear magnetic resonance gyro phase ring model under single-nucleus conditions according to an embodiment of the present invention;

[0059] Figure 3 Schematic diagram of the main magnetic field control model of the nuclear magnetic resonance gyroscope under dual-nucleon conditions according to an embodiment of the present invention;

[0060] Figure 4 Schematic diagram of a linear active disturbance rejection controller according to an embodiment of the present invention;

[0061] Figure 5 Schematic diagram of a linear state observer according to an embodiment of the present invention;

[0062] Figure 6 Schematic diagram of a nuclear magnetic closed-loop system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0064] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0065] Example 1

[0066] As can be seen from the background technology,

[0067] In recent years, active disturbance rejection control has demonstrated superior performance in multiple engineering fields due to its advantages such as independence from precise system models, strong anti-disturbance capability, and simple parameter adjustment. It has been widely used in practical scenarios such as power electronics, motor drives, robotic control, and chemical process control. Related research and engineering cases are becoming increasingly abundant, and the control effects have been widely recognized.

[0068] Although the theory of active disturbance rejection (ADRC) is relatively well-established, its application in the main magnetic field control system of nuclear magnetic resonance gyroscopes (NMR gyroscopes) remains largely unexplored. Currently, PID control is still the primary method for controlling the main magnetic field. Some research has attempted to employ fuzzy or neural network control methods for compensation and adjustment, but these methods still have limitations in handling complex disturbances, modeling uncertainty, or achieving high-precision dynamic adjustment. ADRC, with its core mechanism of "disturbance estimation plus active compensation," is naturally well-suited for NMR systems subject to multiple disturbance sources and difficult-to-accurately model structures.

[0069] Existing NMR gyroscope main magnetic field control systems generally use a proportional-integral-derivative (PID) control strategy. This method achieves feedback closed-loop control by adjusting the proportional, integral, and differential terms of the system error. It has the advantages of simple structure and easy implementation, and can achieve certain control performance under conditions of small system disturbances and a relatively deterministic model. However, in high-precision, weak-signal measurement systems such as NMR gyroscopes, traditional PID control methods have the following significant drawbacks:

[0070] Insufficient anti-interference ability: PID control relies entirely on error signals for feedback adjustment and is unable to identify and model the source of disturbances. Especially when facing external disturbances such as electromagnetic interference, temperature fluctuations, and material nonlinearity, the system control accuracy is easily affected, making it difficult to achieve highly robust and stable control.

[0071] Obvious control lag: Since PID control is a passive controller, the response must wait until the error occurs before making adjustments, and there is a significant delay. Especially in the process of rapid disturbance or dynamic change, the lag effect can easily cause system oscillation or overshoot, reducing the response speed and stability of the control system.

[0072] Parameter tuning relies on experience: The selection of PID parameters usually relies on manual experiments or empirical adjustment, and lacks a systematic adaptive mechanism. As a result, it is difficult to automatically adapt to or maintain optimal performance when the working environment or control object changes, affecting its wide range of engineering applications.

[0073] The differential link is susceptible to noise pollution: In high-sensitivity systems, the measurement signal is often accompanied by high-frequency noise. The differential link is extremely sensitive to high-frequency components and can easily amplify the noise into the control channel, causing fluctuations in the control output and even causing system instability.

[0074] In summary, the existing PID control scheme is difficult to meet the performance requirements in the nuclear magnetic resonance gyroscope magnetic field control system with high precision and high robustness requirements. There is an urgent need for a new control strategy with stronger disturbance suppression capability, fast dynamic response and strong adaptability to achieve higher stability control of the main magnetic field, thereby improving the angular velocity measurement accuracy and the long-term zero bias stability of the gyroscope.

[0075] Specifically, Patent ①: An active magnetic compensation method for ultra-sensitive atomic magnetometer (CN110568384A)

[0076] Abstract: This paper discloses an active magnetic compensation method for an ultrasensitive atomic magnetometer. The method obtains the slope and intercept of the linearly varying voltage fit between the magnetic field value and the linearly varying voltage. The method also sets the output voltage range, damping factor, and sampling rate of the DAC conversion unit. The amplitude and phase of the power-frequency magnetic field noise are calculated, and the DAC conversion unit outputs the compensation voltage to the voltage-controlled current source module. The method is suitable for compensating for both static and power-frequency magnetic field noise, and can also compensate for high-frequency magnetic field noise.

[0077] Patent ②: A three-axis active magnetic compensation system based on decoupling control and parameter design method (CN116679546A)

[0078] Abstract: Disclosed are a three-axis active magnetic compensation system based on decoupling control and a parameter design method, belonging to the technical field of active magnetic shielding. The three-axis active magnetic compensation system based on decoupling control uses a three-axis PID magnetic field controller to perform closed-loop control on the three-axis magnetic field components at the center point of the magnetic shielding cabin. The parameter design of the three-axis PID magnetic field controller includes three steps. First, the mathematical model of the three-axis active magnetic compensation system is obtained by using the sweep frequency method. Then, the coupling channel of the model is equivalent to the main channel to obtain the mathematical model of the three-axis active magnetic compensation system in the decoupling state. Finally, the parameters of the three-axis PID magnetic field controller are designed according to the decoupling model of the three-axis active magnetic compensation system. The three-axis active magnetic compensation system based on decoupling control of the present invention can realize decoupling between the variables of the three-axis active magnetic compensation system, suppress the interference magnetic field in the environment surrounding the magnetic shielding cabin, and improve the dynamic stability of the magnetic field at the center of the magnetic shielding cabin.

[0079] The limitation of the existing patent ① is that its compensation mechanism is mainly aimed at static and power-frequency magnetic field noise. However, it has weaker applicability for nuclear magnetic resonance gyroscope application scenarios with more complex noise environments and is difficult to effectively suppress high-order or dynamic noise interference.

[0080] The greatest advantage of existing patent ② lies in its excellent three-axis decoupling performance, enabling independent and precise control of the three-axis magnetic field. However, in an NMR gyroscope, the z-axis is less coupled with the transverse magnetic field, and the coupled magnetic field is not a major influencing factor. Therefore, the applicability of this method in this application scenario is relatively limited.

[0081] Applying the self-disturbance rejection control method to the magnetic field control system of the nuclear magnetic resonance gyroscope to improve its anti-disturbance performance and control accuracy is still a blank in existing patents and has great innovation space and application prospects.

[0082] The purpose of the present invention is to overcome the technical defects of the existing nuclear magnetic resonance gyroscope main magnetic field control system, such as control lag, difficulty in parameter adjustment and poor adaptability to complex disturbance environments, and to provide a nuclear magnetic resonance gyroscope magnetic field closed-loop control method based on active disturbance rejection control.

[0083] This paper aims to achieve high-precision, robust control of the main magnetic field by introducing an extended state observer to estimate magnetic field disturbances and internal system uncertainties in real time, and actively compensate for them through state feedback. The proposed control method not only adapts to modeling errors and external disturbances, but also boasts fast response, high steady-state accuracy, and a simple implementation structure. It is suitable for the critical application scenario of main magnetic field control in high-precision inertial measurement equipment.

[0084] The present invention can significantly improve the main magnetic field stability and control accuracy of the nuclear magnetic resonance gyroscope in complex environments, reduce the angular velocity measurement zero bias drift, enhance the long-term working reliability of the system, and provide technical support for the miniaturized application of nuclear magnetic resonance gyroscopes.

[0085] like Figure 1 As shown, the present invention discloses a method for controlling the main magnetic field of a nuclear magnetic resonance gyroscope based on self-disturbance rejection control. First, a differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is established, and a self-disturbance rejection controller is designed based on the differential equation. Finally, a closed-loop system is built in combination with a gyroscope prototype to achieve the purpose of suppressing the main magnetic field disturbance. The entire system is designed specifically for the main magnetic field control system of a miniaturized nuclear magnetic resonance gyroscope. It includes: ① Targeted modeling based on the main magnetic field of the nuclear magnetic resonance gyroscope ② Designing a controller that fully considers the influence of the actual parameters of the nuclear magnetic resonance gyroscope, and introducing gyroscope parameters in the expanded state observer to ensure the observer's observation effect on the disturbance. The key points and inventive points are:

[0086] 1. Design of linear active disturbance rejection control structure based on the characteristics of nuclear magnetic resonance system

[0087] This paper, incorporating the structural characteristics of the main magnetic field system of a nuclear magnetic resonance gyroscope, constructs a linear active disturbance rejection controller (LADRC) based on an extended state observer and a linear error feedback mechanism. By treating unmodelable factors in the magnetic field system, such as power supply noise, material nonlinearity, and temperature fluctuations, as a "total disturbance," and estimating their dynamic changes online in real time, this system achieves active compensation and precise suppression of disturbances. This control structure offers the advantages of simplicity, flexible tuning, and strong robustness, significantly improving the control system's stability and tracking performance in complex disturbance environments.

[0088] 2. Improve magnetic field control accuracy and response speed to achieve system zero bias suppression

[0089] Based on the above control structure, the present invention achieves rapid response to main magnetic field disturbances, reduces main magnetic field fluctuations, and effectively improves the zero-bias stability and long-term consistency of the angular velocity output of the nuclear magnetic resonance gyroscope.

[0090] 3. Propose a universal anti-disturbance control method suitable for weak signal precision measurement systems

[0091] The control method of the present invention has good structural versatility and parameter adjustability. It is particularly suitable for application scenarios with extremely high requirements for magnetic field control stability in high-sensitivity weak-signal inertial measurement systems such as nuclear magnetic resonance gyroscopes, SERF atomic gyroscopes, and atomic clocks. It has good engineering promotion and integrated application value.

[0092] The specific implementation process includes:

[0093] Step (1): Establish the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope:

[0094] The main magnetic field of the NMR gyroscope is a DC field along the z-axis of the atomic gas chamber. Due to the prototype's size, it is not possible to use an external magnetometer or fluxgate for detection. Instead, an in-situ magnetometer composed of alkali metal elements within the atomic gas chamber must be used to indirectly measure the main magnetic field. The detection light along the x-axis passes through a signal conditioning circuit to generate an AC signal containing the main magnetic field information. This process requires a second-order phase-locked loop to decompose the main magnetic field signal from the modulated signal.

[0095] Specifically, the Xe nucleus maintains precession under the maintenance of the transverse excitation magnetic field. The precession frequency is called the nuclear spin observation frequency. The nuclear spin observation frequency ω is related to the magnitude of the main magnetic field strength B0, specifically:

[0096] ω=γB0

[0097] Where γ represents the gyromagnetic ratio of the nucleus.

[0098] When the nuclear gas cell is on a moving carrier, the nuclear spin observation frequency in the above equation becomes:

[0099] ω a =ω L +ω R =γB0+ω R

[0100] Where, ω a 、ω L 、ω R They are respectively the nuclear spin observation frequency in the carrier coordinate system, the nuclear spin observation frequency in the stationary coordinate system and the carrier motion angular velocity.

[0101] In order to reduce the drift error of the gyroscope and improve the measurement accuracy, a dual-nucleon differential scheme is adopted. Its main principle is to fill the gas chamber with two nuclei with different gyromagnetic ratios and measure the carrier angular velocity at the same time. The differential operation is performed using the two nuclear spin observation frequencies obtained to reduce the error in the angular velocity measurement. Usually, in order to reduce the error introduced by the mutual influence between different nuclei, different isotopes of the same nucleus are used as nuclei. The system of the present invention uses two isotopes of xenon atoms. 129 Xe and 131Xe is used as the measurement nucleon. The observation frequencies of the binary nuclear spins are:

[0102]

[0103] Where ω1 and ω2 are 129 Xe and 131 The observed frequencies of Xe nuclear spin are in opposite directions, γ1 and γ2 are respectively 129 Xe and 131 The gyromagnetic ratio of Xe is γ1>0 and γ2<0.

[0104] From this, the carrier angular velocity measurement value and the main magnetic field measurement value can be deduced as follows:

[0105]

[0106] As long as the relationship between the nuclear spin observation frequencies ω1 and ω2 and the given value of the main magnetic field B0 is derived, the open-loop transfer function of the system can be derived. This relationship is mainly related to the second-order phase-locked loop structure.

[0107] The classic second-order phase-locked loop (PLL) structure is a negative feedback system consisting of a phase detector, a loop filter, and a voltage-controlled oscillator. The loop filter is implemented using a PID controller, and the implementation of the phase detector and voltage-controlled oscillator is related to the nuclear spin resonance system model of a nuclear magnetic resonance gyroscope.

[0108] According to the classic Bloch equation theory, the steady-state model of the phase-locked loop during normal operation is:

[0109]

[0110] Where γ represents the gyromagnetic ratio of the nucleus, which is an inherent property of the nucleus; B0 represents the magnetic induction intensity of the main magnetic field; T2 represents the transverse relaxation time of the nucleus; φ and θ are the actual phase and the phase set by the phase-locked loop.

[0111] Define β = φ - θ, then β represents the detuned phase between the actual and the set value, which can be converted to:

[0112]

[0113] Define α=dθ / dt, then α represents the output frequency of the phase-locked loop.

[0114] Perform Laplace transform on the above formula,

[0115]

[0116] Since the operating point of the nuclear magnetic gyro system is β(0) = 0, the detuning phase is very small during operation, and the tan function can be linearized to obtain:

[0117]

[0118] The transfer function of the nuclear spin resonance system is deduced as:

[0119]

[0120] Therefore, the NMR gyro phase ring model under single-nucleon conditions can be derived as follows Figure 2 shown. Figure 2 In, G c (s) is the transfer function of the loop filter in the phase-locked loop. Here, a PI controller is used, and the corresponding PI parameters are k P With k I .G p (s) is the transfer function of the spin resonance system, R(s) is the expected value, and Y(s) is the output magnetic field observation value.

[0121] calculate Figure 2 The transfer function of the phase-locked loop in is:

[0122]

[0123] In particular, k is usually p >>1 / T2, the coefficient of the first-order term in the denominator is approximately equal to k p .

[0124] In order to reduce the drift error of the gyroscope and improve the measurement accuracy, a dual-nuclear differential scheme is used. Its main principle is to fill the gas chamber with two nuclei with different gyromagnetic ratios and measure the carrier angular velocity at the same time. The differential operation is performed using the two nuclear spin observation frequencies to reduce the error in the angular velocity measurement. Usually, in order to reduce the error introduced by the mutual influence between different nuclei, two isotopes of xenon atoms are used. 129 Xe and 131 Xe is used as the measurement nucleus. The main magnetic field control model of the NMR gyro under the dual nucleus condition is as follows: Figure 3 shown.

[0125] where γ1 and γ2 are 129 Xe and 131 The gyromagnetic ratio of Xe is γ1>0 and γ2<0. c (s) and G c '(s) are the transfer functions of the two core phase-locked loop filters. Usually, the PID control parameters of the two cores are selected to be consistent. p (s) and G p '(s) are the transfer functions of the two nuclear spin resonance systems, G d (s) is the controller transfer function to be designed, and U(s) is the controller output signal.

[0126] The open-loop transfer function of the main magnetic field system of the nuclear magnetic resonance gyroscope is deduced as follows:

[0127]

[0128] Wherein, T2' and T2" represent 129 Xe and 131 Transverse relaxation time of Xe.

[0129] Assume that the input of the main magnetic field system of the nuclear magnetic resonance gyroscope is u and the output is y. According to the above formula,

[0130] (T2s 2 +k p s+k I )Y(s)=(k p s+k I )U(s)

[0131] The input and output equations of the system are established as follows:

[0132]

[0133] In the formula is the first-order derivative of the input u, and are the first and second order derivatives of the output y respectively.

[0134] Step (2): Design an ADRC controller based on differential equations:

[0135] The designed linear active disturbance rejection controller consists of two parts: an extended state observer and a state error feedback control rate, such as Figure 4 As shown in Figure 2, the extended state observer is the core component of ADRC, addressing the disturbance observation problem in ADRC. The state error feedback control factor is used to generate a control signal based on the estimated state quantity according to the linear feedback law, thereby regulating the system state and tracking the target output.

[0136] The first is the linear extended state observer.

[0137] Assuming the disturbance is d(s), the input and output equations of the system in the presence of disturbance are:

[0138]

[0139] Comparison with standard input-output equations m0, m1, and b0 are parameters that reflect the main magnetic field system, and their relationship with the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is:

[0140]

[0141] Select state variables Convert the input and output equations (differential equations of the main magnetic field system of the nuclear magnetic resonance gyroscope) into a continuous state space description:

[0142]

[0143] Among them, x1, x2, and x3 are the state variables of the state space of the input-output equation, and the corresponding first-order derivatives are The output of the system is y, and the corresponding first-order derivative is f is the disturbance variable, and the first-order derivative is d is the total disturbance including unknown system state and uncertain sudden disturbance.

[0144] remember C=

[100] , the above state space equation can be simplified as:

[0145] Among them, A, B, C, and E are just abbreviations of matrices and have no actual physical meaning.

[0146]

[0147] According to the state observer theory and the state space equation of the system, the corresponding continuous extended state observer is established as:

[0148]

[0149] where z = [z1, z2, z3] T is the state vector of the corresponding observer, and its derivative is z1, z2, z3 are state variables. L=[l1 l2 l3] T is the observer gain matrix to be designed, l1, l2, l3 are the gain values to be designed, and u is c =[uy] T As the input matrix of the observer. is the observation value of the system output by the observer. It should be noted that the state variable z is used in the subsequent calculation of the control quantity.

[0150] |sI-(A-LC)|=(s+ω0) 3 , where s represents the complex frequency variable in the Laplace transform, which is used to describe the frequency domain characteristics of the system, and ω0 is the observer bandwidth.

[0151] In order to reduce the workload of controller parameter tuning, the observer gain matrix and the observer bandwidth ω need to be combined. o Connect them together and place all the zeros and poles to the left of the imaginary axis of the root locus diagram. I is the unit matrix. The characteristic equation of the observer is:

[0152]

[0153] The observer gain can be obtained as:

[0154]

[0155] Redesign the linear error feedback rate:

[0156] The role of the state error feedback control rate is to use the state variables z1, z2, and z3 estimated by the observer to calculate the control signal u. The input of this subsystem is the state variable z estimated by the observer and the given reference signal r, and the output is the input control signal u applied to the controlled system. Since the observer has estimated the total disturbance of the system (including internal disturbance and external disturbance), the integral control (I) used by PID control to eliminate static error is no longer necessary. At the same time, in order to avoid differentiating the reference signal and avoiding system oscillation due to rapid changes in the reference signal, the states z1, z2, ..., z3 estimated by the observer are used. k-1 The linear combination of replaces the differential control.

[0157] The improved PD controller is used as the linear state error feedback control rate, which is in the form of:

[0158]

[0159] Where r is the input reference signal. z1, z2, and z3 are the state variables of the observer. u is the input control signal applied to the controlled system, and u0 is the intermediate variable in the calculation process. fp With k fd is the gain value of the linear error feedback rate that needs to be designed.

[0160] At this point, the subsystem becomes a second-order system without zeros, and its transfer function is:

[0161]

[0162] The same design idea as the observer design is to combine the pole of the subsystem with the bandwidth ω of the subsystem (linear error feedback rate) c Connect, that is, s 2 +k fd s+k fp =(s+ω c ) 2 , where ω c is the feedback control rate bandwidth, we can get:

[0163] k fp =ω c 2 k fd =2ω c

[0164] The linear active disturbance rejection controller is mainly composed of a linear state observer and a linear error feedback rate. The linear state observer takes the control input u and the system output y of the (controlled object) nuclear magnetic resonance system as input, its bandwidth is related to the variable parameter ω0, and the output is the state variable z of the observer. i (i=1,2,3); the input of the linear error feedback rate is the error setting value r (usually set to 0) and the state variable z of the observer i (i=1,2,3), the output is the control quantity u applied to the controlled object, and its bandwidth is related to the variable parameter ω c Related. Figure 5 shown.

[0165] There are two parameters that need to be tuned for the linear active disturbance rejection controller, ω0 and ω c It is related to the bandwidth and directly affects the performance of the controller. By adjusting the two parameters, the linear active disturbance rejection controller can achieve satisfactory control effect.

[0166] Step (3): Build a closed-loop NMR system:

[0167] Build as Figure 6 The high-precision control system of the nuclear magnetic resonance gyroscope magnetic field shown in the figure, in which the main magnetic field system of the nuclear magnetic resonance gyroscope is composed of a voltage-controlled current source, a signal processing device, an atomic gas chamber, a detection light, a pumping light, and x, y, and z axis coils. The transfer function of the entire main magnetic field system is:

[0168]

[0169] The analog-to-digital conversion circuit primarily collects the output signal y from the main magnetic field control system. The collected data is fed into the microcontroller to run the anti-disturbance control algorithm, calculate the control variable u (this process is step (2)), and apply it to the main magnetic field system after passing through the digital-to-analog conversion circuit, thereby achieving closed-loop control of the main magnetic field. The microcontroller can use a DSP chip.

[0170] Example 2

[0171] The present invention also provides a nuclear magnetic resonance gyroscope main magnetic field control system based on active disturbance rejection control, the system is used to implement the method described in embodiment 1, the system includes: a first building block, a second building block and a third building block;

[0172] The first building block is used to establish a differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope;

[0173] The second building block is used to design an active disturbance rejection controller based on the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope;

[0174] The third building block is used to build a nuclear magnetic closed-loop system based on the active disturbance rejection controller in combination with a gyroscope prototype to suppress main magnetic field disturbances.

[0175] In this embodiment, the process of establishing the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope includes:

[0176]

[0177] Where T2 represents the transverse relaxation time of the nucleus, is the first-order derivative of the input u, and They are the first and second order derivatives of the output y, and the corresponding PI parameters are k P With k I .

[0178] In this embodiment, the active disturbance rejection controller includes: an extended state observer and a state error feedback control rate;

[0179] Among them, the extended state observer is:

[0180]

[0181] in, L=[l1 l2 l3] T is the observer gain matrix to be designed, C = [1 0 0], z = [z1, z2, z3] T is the state vector of the corresponding observer, and the derivative is z1, z2, z3 are state variables, L = [l1 l2 l3] T is the observer gain matrix to be designed, l1, l2, l3 are the gain values to be designed, and u is c =[uy] T As the input matrix of the observer, is the observation value of the observer on the system output, m0, m1, b0 are the parameters reflecting the main magnetic field system, and their relationship with the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is:

[0182]

[0183] |sI-(A-LC)|=(s+ω0) 3 , where s represents the complex frequency variable in Laplace transform, which is used to describe the frequency domain characteristics of the system, and ω0 is the observer bandwidth;

[0184] The state error feedback control rate is:

[0185]

[0186] s2 +k fd s+k fp =(s+ω c ) 2 ,

[0187] Among them, ω c is the feedback control rate bandwidth, k fp =ω c 2 k fd =2ω c , r is the input reference signal, z1, z2, z3 are the state variables of the observer, u is the input control signal applied to the controlled system, u0 is the intermediate variable in the calculation process, k fp With k fd is the gain value of the linear error feedback rate that needs to be designed.

[0188] In this embodiment, the nuclear magnetic closed-loop system includes: a signal processing device, a controller, a host computer and a voltage-controlled current source;

[0189] The host computer communicates with the controller, which includes: an analog-to-digital conversion circuit, a microcontroller, and a digital-to-analog conversion circuit;

[0190] The signal processing device is used to extract information from the detection light and demodulate the nuclear spin observation frequencies of the two nuclei through a phase-locked amplifier and a phase-locked loop structure;

[0191] The analog-to-digital conversion circuit is used to collect the nuclear spin observation frequencies of the two nuclei, send the collected data to the microcontroller to run the active disturbance rejection control algorithm, calculate the control quantity and convert it into a current signal through the digital-to-analog conversion circuit and the voltage-controlled current source, and apply it to the z-axis coil, thereby realizing closed-loop control of the main magnetic field.

[0192] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for controlling the main magnetic field of a nuclear magnetic resonance gyroscope based on active disturbance rejection control, characterized in that: The method comprises: Establish the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope; Based on the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope, an active disturbance rejection controller is designed; Based on the active disturbance rejection controller, a nuclear magnetic closed-loop system is built in combination with a gyroscope prototype to suppress main magnetic field disturbances.

2. The method according to claim 1, characterized in that The method of establishing the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope includes: Where T2 represents the transverse relaxation time of the nucleus, is the first-order derivative of the input u, and They are the first and second order derivatives of the output y, and the corresponding PI parameters are k P With k I .

3. The method according to claim 2, characterized in that The active disturbance rejection controller includes: an extended state observer and a state error feedback control rate; Among them, the extended state observer is: in, C = [100], z = [z1, z2, z3] T is the state vector of the corresponding observer, and the derivative is z1, z2, z3 are state variables, L = [l1l2 l3] T is the observer gain matrix to be designed, l1, l2, l3 are the gain values to be designed, and u is c =[uy] T As the input matrix of the observer, is the observation value of the system output by the observer, m0, m1, b0 are the parameters reflecting the main magnetic field system, and their relationship with the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is: |sI-(A-LC)|=(s+ω0) 3 , where s represents the complex frequency variable in Laplace transform, which is used to describe the frequency domain characteristics of the system, and ω0 is the observer bandwidth; The state error feedback control rate is: s 2 +k fd s+k fp =(s+ω c ) 2 , Among them, ω c is the feedback control rate bandwidth, k fp =ω c 2 k fd =2ω c , r is the input reference signal, z1, z2, z3 are the state variables of the observer, u is the input control signal applied to the controlled system, u0 is the intermediate variable in the calculation process, k fp With k fd is the gain value of the linear error feedback rate that needs to be designed.

4. The method according to claim 1, wherein The nuclear magnetic closed-loop system includes: signal processing device, controller, host computer and voltage-controlled current source; The host computer communicates with the controller, which includes: an analog-to-digital conversion circuit, a microcontroller, and a digital-to-analog conversion circuit; The signal processing device is used to extract information from the detection light and demodulate the nuclear spin observation frequencies of the two nuclei through a phase-locked amplifier and a phase-locked loop structure; The analog-to-digital conversion circuit is used to collect the nuclear spin observation frequencies of the two nuclei, send the collected data to the microcontroller to run the active disturbance rejection control algorithm, calculate the control quantity and convert it into a current signal through the digital-to-analog conversion circuit and the voltage-controlled current source, and apply it to the z-axis coil, thereby realizing closed-loop control of the main magnetic field.

5. A nuclear magnetic resonance gyroscope main magnetic field control system based on active disturbance rejection control, the system being used to implement the method according to any one of claims 1 to 4, characterized in that: The system comprises: a first building module, a second building module and a third building module; The first building block is used to establish a differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope; The second building block is used to design an active disturbance rejection controller based on the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope; The third building block is used to build a nuclear magnetic closed-loop system based on the active disturbance rejection controller in combination with a gyroscope prototype to suppress main magnetic field disturbances.

6. The system according to claim 5, characterized in that The process of establishing the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope includes: Where T2 represents the transverse relaxation time of the nucleus, is the first-order derivative of the input u, and They are the first and second order derivatives of the output y, and the corresponding PI parameters are k P With k I .

7. The system according to claim 5, characterized in that The active disturbance rejection controller includes: an extended state observer and a state error feedback control rate; Among them, the extended state observer is: in, L=[l1l2 l3] T is the observer gain matrix to be designed, C = [100], z = [z1, z2, z3] T is the state vector of the corresponding observer, and the derivative is z1, z2, z3 are state variables, L = [l1l2 l3] T is the observer gain matrix to be designed, l1, l2, l3 are the gain values to be designed, and u is c =[uy] T As the input matrix of the observer, is the observation value of the observer on the system output, m0, m1, b0 are the parameters reflecting the main magnetic field system, and their relationship with the differential equation of the main magnetic field system of the nuclear magnetic resonance gyroscope is: |sI-(A-LC)|=(s+ω0) 3 , where s represents the complex frequency variable in Laplace transform, which is used to describe the frequency domain characteristics of the system, and ω0 is the observer bandwidth; The state error feedback control rate is: s 2 +k fd s+k fp =(s+ω c ) 2 , Among them, ω c is the feedback control rate bandwidth, k fp =ω c 2 k fd =2ω c , r is the input reference signal, z1, z2, z3 are the state variables of the observer, u is the input control signal applied to the controlled system, u0 is the intermediate variable in the calculation process, k fp With k fd is the gain value of the linear error feedback rate that needs to be designed.

8. The system according to claim 5, characterized in that The nuclear magnetic closed-loop system includes: signal processing device, controller, host computer and voltage-controlled current source; The host computer communicates with the controller, which includes: an analog-to-digital conversion circuit, a microcontroller, and a digital-to-analog conversion circuit; The signal processing device is used to extract information from the detection light and demodulate the nuclear spin observation frequencies of the two nuclei through a phase-locked amplifier and a phase-locked loop structure; The analog-to-digital conversion circuit is used to collect the nuclear spin observation frequencies of the two nuclei, send the collected data to the microcontroller to run the active disturbance rejection control algorithm, calculate the control quantity and convert it into a current signal through the digital-to-analog conversion circuit and the voltage-controlled current source, and apply it to the z-axis coil, thereby realizing closed-loop control of the main magnetic field.

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