A method for compensating the transverse magnetic field of inert gas nuclear spin under angular velocity input

Abstract

A method for compensating and controlling the transverse magnetic field of inert gas nuclear spin under angular velocity input is proposed. First, a linear non-autonomous system model of the atomic spin ensemble is constructed, with the transverse magnetic field as the input and the unknown transverse angular velocity as the disturbance term. Then, a high-gain state observer is constructed to observe the transverse nuclear spin polarization intensity. Next, the magnetization constant is measured using the constructed high-gain state observer. Finally, a compensation controller is designed to generate a transverse magnetic field based on the observed transverse nuclear spin polarization intensity and apply it to the system to compensate for the transverse magnetic field generated by the nuclear spin under angular velocity input. This method achieves real-time measurement and compensation control of the transverse magnetic field of inert gas nuclear spin, is easy to implement in engineering, and is applicable to the field of atomic ensemble magnetic field measurement and control in atomic spin inertial measurement devices.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of inert gas nuclear spin transverse magnetic field compensation control method under angular velocity input, to realize the real-time measurement and compensation control of inert gas nuclear spin transverse magnetic field, it is applicable to atomic spin inertial measurement device atomic ensemble magnetic field measurement and control field. BACKGROUND

[0002] With the new theory and new technology in the field of quantum precision measurement are proposed and developed, various precision measurement instruments and equipment based on quantum effect are constantly breaking through the measurement limit of traditional instruments and meters. Compared with traditional measuring instruments, inertial measurement devices based on atomic spin effect have great advantages in performance indicators, and have become an important development direction of future high-precision inertial measurement.

[0003] The magnetic field generated by the polarization effect of atoms has an important influence on the dynamic characteristics of the entire atomic ensemble. Under the input of transverse angular velocity, the polarization direction of inert gas nuclear spin will project in the transverse direction, and its magnetic field direction will also deviate. The generation of this transverse magnetic field will limit the response speed of the system and reduce the inertial measurement capability. There is no good method to avoid this shortcoming at present. SUMMARY

[0004] The technical problem to be solved by the present application is that the transverse magnetic field generated by the inert gas nuclear spin under angular velocity input will reduce the response speed of the system. A transverse magnetic field compensation control method for inert gas nuclear spin under angular velocity input is proposed to reduce the deviation of nuclear spin magnetic field and improve the response speed of the system.

[0005] The technical solution of the present application is as follows:

[0006] A transverse magnetic field compensation control method for inert gas nuclear spin under angular velocity input, characterized in that it comprises the following steps:

[0007] Step 1, construct a linear non-autonomous system model of alkali metal-inert gas atomic spin ensemble, take the transverse magnetic field as the input term, and take the unknown transverse angular velocity as the disturbance term;

[0008] Step 2, construct a high-gain state observer to observe the transverse nuclear spin polarization intensity;

[0009] Step 3, measure the magnetization density constant based on the high-gain state observer constructed in step 2;

[0010] Step 4, design a compensation controller to generate a transverse magnetic field to apply to the system to compensate for the transverse magnetic field generated by nuclear spin under angular velocity input.

[0011] The linear non-autonomous system model in step 1 uses the following expression:

[0012]

[0013] y = Cx

[0014]

[0015] u = [B x , B y ] T

[0016] Ω = [Ω x , Ω y ] T

[0017]

[0018] where is the first derivative of x, x is the state variable, u is the lateral magnetic field input, i.e., the output of the compensation controller, Ω is the lateral angular velocity disturbance, y is the output of the system model, A, B, and W are matrices related to the system parameters and , is the alkali electron spin polarization intensity in the z-axis, is the non-autonomous term, C is a fourth-order identity matrix, and are the alkali electron spin polarization intensities in the x-axis and y-axis, respectively, and are the noble gas nuclear spin polarization intensities in the x-axis and y-axis, respectively, Bx is the applied magnetic field in the x-axis, By is the applied magnetic field in the y-axis, Ωx is the angular velocity in the x-axis, and Ωy is the angular velocity in the y-axis.

[0019] The high-gain state observer in Step 2 uses the following expression:

[0020]

[0021]

[0022] is the estimate of x, is the first derivative of , is the estimate of y, and H is the observer gain matrix, is the x-axis nuclear spin polarization intensity, is the y-axis nuclear spin polarization intensity.

[0023] The measurement magnetization density constant in Step 3 includes the following steps:

[0024] Step 3.1, operate the atomic ensemble at the magnetic compensation point;

[0025] Step 3.2, applying a step magnetic field B on the y-axis y0 ;

[0026] Step 3.3, recording the observed y-axis nuclear spin polarization intensity at steady state

[0027] Step 3.4, magnetization density constant λM n is represented by the following formula:

[0028] The expression of the compensation controller output u in Step 4 is as follows:

[0029]

[0030] where K is a proportional coefficient.

[0031] The technical effects of the present application are as follows: The angular velocity input under the inert gas nuclear spin transverse magnetic field compensation control method of the present application first constructs a linear non-autonomous system model of atomic spin ensemble, takes the transverse magnetic field as an input term, and takes the unknown transverse angular velocity as a disturbance term; then constructs a high-gain state observer to observe the transverse nuclear spin polarization intensity; then measures the magnetization density constant using the constructed high-gain state observer; finally, a compensation controller is designed to generate a transverse magnetic field according to the observed transverse nuclear spin polarization intensity, which is applied to the system to compensate for the transverse magnetic field generated by the nuclear spin under the angular velocity input, thereby realizing real-time measurement and compensation control of the inert gas nuclear spin transverse magnetic field, and being easy to implement in engineering, suitable for the field of atomic spin inertial measurement device atomic ensemble magnetic field measurement and control.

[0032] The advantages of the present application compared with the prior art are:

[0033] (1) An angular velocity input under the inert gas nuclear spin transverse magnetic field compensation control method establishes a linear non-autonomous system model of alkali metal-inert gas atomic spin ensemble taking the angular velocity term as a disturbance term, and designs a high-gain observer, thereby realizing real-time observation of the inert gas transverse nuclear spin intensity under the transverse angular velocity input.

[0034] (2) An angular velocity input under the inert gas nuclear spin transverse magnetic field compensation control method measures the magnetization density constant using the established high-gain state observer, and further designs a controller to perform real-time compensation control of the nuclear spin transverse magnetic field, which suppresses the precession of the nuclear spin to the transverse direction without affecting the final measurement result, and improves the response speed of the system. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a flowchart of the angular velocity input under the inert gas nuclear spin transverse magnetic field compensation control method of the present application.Figure 1 The process includes: Step 1, constructing a linear non-autonomous system model of the atomic spin ensemble; Step 2, constructing a high-gain observer; Step 3, measuring the magnetization density constant; Step 4, designing a compensation controller; and Step 5, writing the control algorithm code and burning it into the electronic control system.

[0036] Figure 2 This is a schematic diagram illustrating the algorithm control principle of an inert gas nuclear spin transverse magnetic field compensation control method under angular velocity input according to the present invention. Figure 2 It includes a system model, observer, controller, and differencer; Ω is the longitudinal electron spin polarization intensity, ω is the input angular velocity (or disturbance quantity, or unknown transverse angular velocity), and u is the controller output (or the system model input control quantity, or the observer input control quantity). It is the first derivative of x, where x is a state variable, and A, B, and W are all related to the system parameters and The relevant matrix is ​​y, which is the output of the system model, and C is the fourth-order identity matrix. It is an estimator of x. yes The first derivative, H is an estimator of y, and H is the observer gain matrix. It is the x-axis nuclear spin polarization intensity. It is the y-axis nuclear spin polarization intensity. Figure 2 The system model is based on u, And Ω form y, the observer is based on u, The output of the sum and difference is obtained and The differencer is based on y, and The controller receives the differential output and then... and Wait until you get u. Detailed Implementation

[0037] The following is in conjunction with the attached diagram ( Figures 1-2 The invention will be described in the following sections and examples.

[0038] Figure 1 This is a flowchart illustrating the implementation of the present invention: a method for compensating and controlling the transverse magnetic field of inert gas nuclear spin under angular velocity input. Figure 2 This is a schematic diagram illustrating the control principle of the algorithm for a method to compensate for the transverse magnetic field of an inert gas nucleus spin under angular velocity input, as described in this invention. (Reference) Figures 1-2As shown, a method for controlling the transverse magnetic field compensation of noble gas nuclear spins under angular velocity input, comprising the following steps: Step 1, constructing a linear non-autonomous system model of alkali metal-noble gas atomic spin ensemble, taking the transverse magnetic field as the input term and the unknown transverse angular velocity as the disturbance term; Step 2, constructing a high-gain state observer to observe the transverse nuclear spin polarization intensity; Step 3, based on the high-gain state observer constructed in Step 2, measuring the magnetization density constant; Step 4, designing a compensation controller to generate a transverse magnetic field applied to the system to compensate for the transverse magnetic field generated by the nuclear spin under angular velocity input.

[0039] The linear non-autonomous system model in Step 1 adopts the following expression:

[0040]

[0041] y = Cx

[0042]

[0043] u = [B x , B y ] T

[0044] Ω = [Ω x , Ω y ] T

[0045]

[0046] where is the first derivative of x, x is the state quantity, u is the transverse magnetic field input term, i.e., the output quantity of the compensation controller, Ω is the transverse angular velocity disturbance term, y is the output quantity of the system model, A, B, and W are matrices related to system parameters and , is the z-axis alkali metal electron spin polarization intensity, is the non-autonomous term, C is a fourth-order unit matrix, and are the x-axis and y-axis alkali metal electron spin polarization intensities, and are the x-axis and y-axis noble gas nuclear spin polarization intensities, Bx is the applied x-axis magnetic field, By is the applied y-axis magnetic field, Ωx is the x-axis angular velocity, and Ωy is the y-axis angular velocity.

[0047] The high-gain state observer in Step 2 adopts the following expression:

[0048]

[0049]

[0050] is an estimate of x, is a first derivative of is an estimate of y, H is an observer gain matrix, is the x-axis nuclear spin polarization intensity, is the y-axis nuclear spin polarization intensity.

[0051] The measured magnetization density constant in step 3 includes the following steps: step 3.1, working the atomic ensemble at the magnetic compensation point; step 3.2, applying a step magnetic field B y0 to the y-axis; step 3.3, recording the observed y-axis nuclear spin polarization intensity step 3.4, the magnetization density constant λM n is represented by the following formula:

[0052] The expression of the compensation controller output u in step 4 is as follows:

[0053]

[0054] where K is a proportional coefficient.

[0055] The application discloses a method for compensating a transverse magnetic field of nuclear spin of inert gas under angular velocity input. The method first constructs a linear non-autonomous system model of the system, takes the transverse magnetic field as an input term, and takes unknown transverse angular velocity as a disturbance term; then constructs a high-gain state observer to observe the transverse nuclear spin polarization intensity; then measures the magnetization density constant by using the constructed high-gain state observer; finally, a controller is designed, and the observed transverse nuclear spin polarization intensity is used to generate a transverse magnetic field applied to the system to compensate for the transverse magnetic field generated by the nuclear spin under the angular velocity input. The method realizes real-time measurement and compensation control of the transverse magnetic field of the nuclear spin of inert gas, is easy to implement in engineering, and is suitable for the field of atomic spin inertial measurement device atomic ensemble magnetic field measurement and control.

[0056] Referring to the flow in Figure 1 , a method for compensating a transverse magnetic field of nuclear spin of inert gas under angular velocity input includes the following steps:

[0057] Step one, constructing a linear non-autonomous system model of an alkali metal-inert gas atomic spin ensemble, wherein the transverse magnetic field is taken as an input term, and unknown transverse angular velocity is taken as a disturbance term, as shown below:

[0058]

[0059] y=Cx

[0060] wherein is a state variable, wherein and are the alkali metal electron spin polarization intensities, and are the x-axis and y-axis noble gas nuclear spin polarization intensities, respectively; denotes the first derivative of x; u = [Bx, B y ] T is the input control variable, where B x is the applied x-axis magnetic field, B y is the applied y-axis magnetic field; Ω = [Ω x , Ω y ] T is the input angular velocity, which is considered as a disturbance variable, where Ω x is the x-axis angular velocity, Ω y is the y-axis angular velocity; is the output variable; A, B and W are matrices related to system parameters and longitudinal electron spin polarization intensities , where is a non-autonomous term; C is a fourth-order unit matrix.

[0061] Step two, construct a high-gain state observer to observe the transverse nuclear spin polarization intensity. The constructed high-gain observer has the following form:

[0062]

[0063]

[0064] where is the estimate of x, is the first derivative of , is the estimate of y, and H is the observer gain matrix.

[0065] Define the error as Then, subtract the constructed high-gain observer from the aforementioned linear non-autonomous system model, is the first derivative of e, the following equation can be obtained:

[0066]

[0067] Further, the transfer function G Ω (s) from the disturbance term Ω(s) to the error term e(s) is obtained:

[0068]

[0069] where I is the unit matrix, s is the Laplace operator, and the observer gain matrix H is selected to make the matrix A-HC have a negative real part and the influence of the disturbance term on the system is minimized.

[0070] Step three, based on the high gain state observer constructed in step two, measure the magnetization constant, the steps are:

[0071] 1) First, the atomic ensemble works at the magnetic compensation point;

[0072] 2) Apply a step magnetic field B y0 to the y-axis;

[0073] 3) Record the observed y-axis nuclear spin polarization intensity at steady state

[0074] 4) The magnetization constant λM n is represented by the following formula:

[0075] Step four, design a controller to generate a transverse magnetic field applied to the system to compensate for the transverse magnetic field generated by the nuclear spin under angular velocity input. The output of the compensation controller is the proportional coefficient K multiplied by the x-axis and y-axis magnetic fields of the nuclear spin. The x-axis and y-axis magnetic fields of the nuclear spin can be represented as the magnetization constant λM n multiplied by the observed x-axis nuclear spin polarization intensity and the y-axis nuclear spin polarization intensity The final output of the controller u can be represented as:

[0076]

[0077] Reference Figure 2 algorithm control, where the longitudinal electron spin polarization is assigned in real time to the constructed linear non-autonomous system model and high gain observer, Ω is the unknown input transverse angular velocity.

[0078] The contents not described in detail in the specification of the present invention belong to the prior art known to those skilled in the art. It is pointed out that the above description is helpful for those skilled in the art to understand the present invention, but does not limit the protection scope of the present invention. Any equivalent replacement, modification, improvement and / or deletion of the above description without departing from the essential content of the present invention falls within the protection scope of the present invention.

Claims

1. A method for inert gas nuclear spin transverse magnetic field compensation control under angular velocity input, characterized by, The method comprises the following steps: Step 1, constructing a linear non-autonomous system model of alkali metal-inert gas atomic spin ensemble, taking the transverse magnetic field as an input term and the unknown transverse angular velocity as a disturbance term; Step 2, constructing a high-gain state observer to observe the transverse nuclear spin polarization intensity; Step 3, measuring the magnetization density constant based on the high-gain state observer constructed in step 2; Step 4, designing a compensation controller to generate a transverse magnetic field applied to the system to compensate for the transverse magnetic field generated by the nuclear spin under the angular velocity input; The linear non-autonomous system model in step 1 adopts the following expression: y = Cx u = [B x ,B y ] T Ω = [Ω x , Ω y ] T wherein is the first derivative of x, x is the state variable, u is the transverse magnetic field input, i.e., the output of the compensation controller, Ω is the transverse angular velocity disturbance term, y is the system model output, A, B, and W are matrices related to system parameters and , is the alkali electron spin polarization strength of the z-axis, is a non-autonomous term, C is a fourth-order identity matrix, and are the alkali electron spin polarization strengths of the x-axis and y-axis, respectively, and are the noble gas nuclear spin polarization strengths of the x-axis and y-axis, respectively, Bx is the applied x-axis magnetic field, By is the applied y-axis magnetic field, Ωx is the x-axis angular velocity, and Ωy is the y-axis angular velocity. The measurement of the magnetization density constant in step 3 comprises the following steps: Step 3.1, working the atomic ensemble at the magnetic compensation point; Step 3.2, applying a step magnetic field B on the y-axis y0 ; Step 3.3, record the y-axis nuclear spin polarisation strength observed at steady state Step 3.4, magnetization density constant λM n is represented by the following equation: The expression of the compensation controller output u in step 4 is as follows: where K is a proportionality coefficient, is the x-axis nuclear spin polarization strength, is the y-axis nuclear spin polarization strength.

2. The method of claim 1, wherein, The high-gain state observer in step 2 adopts the following expression: is an estimate of x, is a first derivative of is an estimate of y, H is an observer gain matrix.

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