Modeling and bandwidth extension design method for SERF atomic spin gyroscope

Abstract

The invention relates to a modeling and bandwidth extension design method for an SERF atomic spin gyroscope, which comprises the following steps of: 1, ignoring a second-order minimal quantity, and establishing an open-loop transfer function model of the SERF atomic spin gyroscope; 2, adding a zero-pole compensation controller in a modulation-demodulation output signal of the SERF atomic spin gyroscope; and 3, after the SERF atomic spin gyroscope passes through the zero-pole compensation controller on a rotating speed response signal, outputting a voltage signal which is proportional to an input angular rate through a sampling resistor for a system to use. The compensation method for bandwidth expansion of the SERF atomic spin gyroscope solves the problem that an existing SERF atomic spin gyroscope cannot give consideration to static sensitivity and working bandwidth at the same time.

Description

Technical Field

[0001] The present invention belongs to the field of quantum precision measurement technology, belongs to gyroscope dynamic control technology, and specifically relates to a SERF atomic spin gyroscope modeling and bandwidth expansion design method. Background Art

[0002] The atomic spin gyroscope based on spin-exchange relaxation-free (SERF) has an ultra-high theoretical angular velocity measurement sensitivity, and its theoretical accuracy can reach 10 -8 ° / h level, with a theoretical limit accuracy far exceeding that of other types of gyroscopes. It is one of the important development directions for ultra-high precision inertial navigation for the new generation of moving carriers.

[0003] At present, although the SERF atomic spin gyroscope has achieved high sensitivity, its bandwidth is very low, which greatly limits the application prospects of the SERF atomic spin gyroscope. However, the existing research on the bandwidth and dynamic performance of the SERF atomic spin gyroscope is very limited. How to improve the bandwidth and dynamic performance of the SERF atomic spin gyroscope has become an urgent problem to be solved. Summary of the invention

[0004] In view of the deficiencies of the prior art, the present invention proposes a modeling and bandwidth expansion design method for a SERF atomic spin gyroscope.

[0005] The above-mentioned object of the present invention is achieved by the following technical solutions:

[0006] A method for modeling and bandwidth extension design of a SERF atomic spin gyroscope comprises the following steps:

[0007] Step 1, ignoring the second-order tiny quantity, establish the open-loop transfer function model of SERF atomic spin gyroscope;

[0008] Step 2: Based on the model established in step 1, a zero-pole compensation controller is added to the modulation and demodulation output signal of the SERF atomic spin gyroscope:

[0009] Step 3: After the SERF atomic spin gyroscope passes through the zero-pole compensation controller, the speed response signal is output through the sampling resistor as a voltage signal proportional to the input angular rate for use by the system.

[0010] Furthermore, step 1 includes:

[0011] The Bloch equations are used to establish the dynamic equations of the SERF atomic spin gyroscope:

[0012]

[0013] In formula (A1), Ω represents the input angular velocity, P e and P n are the electron spin polarizability of alkali metal atoms / nuclear spin polarizability of noble gas atoms, λM e and λM n represent the electron spin of alkali metal atoms / nuclear spin magnetic moment of inert gas atoms, B represents the ambient magnetic field, R p It represents the optical pumping rate of the pumping laser, reflecting the polarization effect of the pumping laser on the electron spin, S p The direction of angular momentum transfer of pump laser photons, R se en It represents the nuclear spin pumping rate, reflecting the polarization effect of the inert gas atomic nuclear spin on the alkali metal atomic electron spin. tot e and R tot n are the total relaxation rates of alkali metal electrons / inert gas nuclei spins, γ e and γ n They represent the spin magnetic ratio of the electron spin of the alkali metal atom to the nuclear spin of the inert gas atom, L represents the light displacement felt by the electron spin of the alkali metal atom, Q represents the slowing factor, and R represents the deceleration factor. m It represents the optical pumping rate of the detection laser, reflecting the polarization effect of the detection laser on the electron spin, S m Detect the direction of the photon angular momentum transfer of the laser, R se ne It represents the electron spin pumping rate, reflecting the polarization effect of the electron spin of alkali metal atoms on the nuclear spin of inert gas atoms.

[0014] By solving equation (A1) and setting Available and The steady-state value of:

[0015]

[0016] Among them, the subscripts x, y, and z represent the coordinate axis positions corresponding to the variables;

[0017] make but:

[0018]

[0019] Ignoring the transient terms, the steady-state solution can be obtained:

[0020]

[0021] make There are the following expressions:

[0022]

[0023] After simplification, equation (A1) can be described by the following 4×4 matrix:

[0024]

[0025] Make the following transformation but:

[0026]

[0027] Define as follows:

[0028]

[0029] Equations (A12) and (A13) can be simplified to

[0030]

[0031] Eliminate from equation (A16) Then, through Laplace transformation, it is transformed into The second-order equation is:

[0032]

[0033] The two characteristic roots of the equation are:

[0034]

[0035] λ 1,2 =aa 1,2 +bb 1,2 i (A20)

[0036] These two characteristic roots determine the dynamic behavior of the SERF atomic spin gyroscope:

[0037] make The transfer function of the SERF atomic spin gyroscope to the y-axis speed input can be written as:

[0038]

[0039] Simplify (A21) to (A22)

[0040]

[0041] Among them, p 1 and p 2 , p 3 and p 4 are two pairs of conjugate poles in the SERF atomic spin gyroscope; 1 and z 2 are two pairs of conjugate zero points of the SERF atomic spin gyroscope, K0 is the gain factor from the system to the output;

[0042] Furthermore, step 2 includes:

[0043] First, a first-level zero-pole compensation controller is added to the detection loop of the SERF atomic spin gyroscope, and the zero-pole compensation controller includes a proportional link, a zero-point generation link and a pole generation link; the output signal of the SERF atomic spin gyroscope in response to the y-axis speed is demodulated by a phase-locked amplifier and then enters the zero-pole compensation controller, the input end of the zero-pole generation link is connected to the output end of the phase-locked amplifier demodulation, the output end of the zero-pole generation link is connected to the input end of the proportional link, and the output end of the proportional link is connected to the input end of the sampling circuit;

[0044] Assume the transfer function of the zero-pole compensation controller is:

[0045]

[0046] In formula (A23): G C (s) is the transfer function of the zero-pole compensation controller; K Gain is the gain of the dipole compensation controller; the gain of the zero-pole compensation controller is generated by the proportional link; z C1 、z C2 are the two conjugate zeros of the zero-pole compensation controller; p C1 、p C2 are two poles of the zero-pole compensation controller; the two conjugate zeros and poles of the zero-pole compensation controller are generated by the zero-pole generation link;

[0047] After adding the zero-pole compensation controller to the loop, the transfer function of the SERF atomic spin gyroscope to the y-axis speed input becomes the product of equation (A22) and equation (A23):

[0048]

[0049] The two conjugate zeros of the zero-pole compensation controller are designed so that the two conjugate zeros of the zero-pole compensation controller and the two conjugate poles that affect the dynamic performance of the SERF atomic spin gyroscope form a zero-pole cancellation:

[0050] z C1 =p 1 ,z C2 =p 2 (A25)

[0051] The relevant parameters of the SERF atomic spin gyroscope are brought in to draw the Bode plot of the closed-loop system. The 3 dB drop in the curve corresponds to the gyroscope bandwidth. If the one-stage zero-pole compensation controller cannot meet the bandwidth requirements of the SERF atomic spin gyroscope, a two-stage zero-pole compensation controller is used, and the transfer function of the ERF atomic spin gyroscope to the y-axis speed input becomes:

[0052]

[0053] The four conjugate zeros of the zero-pole compensation controller are designed so that the four conjugate zeros of the zero-pole compensation controller and the four conjugate poles that affect the dynamic performance of the SERF atomic spin gyroscope form a zero-pole cancellation, and the four conjugate poles of the zero-pole compensation controller are configured to the desired bandwidth position:

[0054] z C1 =p 1 ,z C2 =p 2 ,z C3 =p 3 ,z C4 =p 4 (A27)

[0055] The advantages and positive effects of the present invention are:

[0056] 1. Based on the Bloch equations, the present invention neglects the second-order micro-quantity and establishes an open-loop transfer function model of the SERF atomic spin gyroscope to the speed input. Based on the model, a zero-pole compensation controller is added to the modulation and demodulation output signal of the SERF atomic spin gyroscope; the zero-pole compensation controller includes a proportional link, a zero point generation link and a pole generation link. The present invention solves the problem that the existing SERF atomic spin gyroscope cannot take into account both static sensitivity and working bandwidth, and is a compensation method for bandwidth expansion of the SERF atomic spin gyroscope. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 The block diagram of the control loop of the SERF atomic spin gyroscope including the zero-pole compensation controller of the present invention;

[0058] Figure 2 It is a transfer function block diagram of the zero-pole compensation controller of the present invention;

[0059] Figure 3 is a Bode diagram of an uncompensated SERF gyroscope according to an embodiment of the present invention;

[0060] Figure 4 1 is a Bode diagram of the SERF gyroscope after compensation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The structure of the present invention is further described below with reference to the accompanying drawings and by way of examples. It should be noted that the present examples are descriptive rather than restrictive.

[0062] A method for modeling and bandwidth extension design of SERF atomic spin gyroscopes, see Figure 1-2 , the invention point is: comprising the following steps:

[0063] Step 1: Use the Bloch equations to establish the dynamic equations of the SERF atomic spin gyroscope.

[0064]

[0065] In formula (A1), Ω represents the input angular velocity, P e and P n are the electron spin polarizability of alkali metal atoms / nuclear spin polarizability of noble gas atoms, λM e and λM n represent the electron spin of alkali metal atoms / nuclear spin magnetic moment of inert gas atoms, B represents the ambient magnetic field, R p It represents the optical pumping rate of the pumping laser, reflecting the polarization effect of the pumping laser on the electron spin, S p The direction of angular momentum transfer of pump laser photons, R se en It represents the nuclear spin pumping rate, reflecting the polarization effect of the inert gas atomic nuclear spin on the alkali metal atomic electron spin. tot e and R tot n are the total relaxation rates of alkali metal electrons / inert gas nuclei spins, γ e and γ n They represent the spin magnetic ratio of the electron spin of the alkali metal atom to the nuclear spin of the inert gas atom, L represents the light displacement felt by the electron spin of the alkali metal atom, Q represents the slowing factor, and R represents the deceleration factor. m It represents the optical pumping rate of the detection laser, reflecting the polarization effect of the detection laser on the electron spin, S m Detect the direction of the photon angular momentum transfer of the laser, R se ne It represents the electron spin pumping rate, reflecting the polarization effect of the electron spin of alkali metal atoms on the nuclear spin of inert gas atoms.

[0066] By solving equation (A1) and setting Available and steady-state value.

[0067]

[0068] The subscripts x, y, and z represent the coordinate axis positions of the variables. have

[0069]

[0070]

[0071] Ignoring the transient terms, the steady-state solution can be obtained:

[0072]

[0073] make There are the following expressions:

[0074]

[0075] After simplification, equation (A1) can be described by the following 4×4 matrix:

[0076]

[0077] Make the following transformation have

[0078]

[0079] To simplify the formula, we define

[0080]

[0081] Equations (A12) and (A13) can be simplified to

[0082]

[0083] Eliminate from equation (A16) Then, through Laplace transformation, it is transformed into The second-order equation is:

[0084]

[0085] The two characteristic roots of the equation are

[0086]

[0087] λ 1,2 =aa 1,2 +bb 1,2 i (A20)

[0088] These two characteristic roots determine the dynamic behavior of the SERF atomic spin gyroscope

[0089] make The transfer function of the SERF atomic spin gyroscope to the y-axis speed input can be written as:

[0090]

[0091] For ease of analysis, (A21) is simplified to (A22)

[0092]

[0093] Among them, p 1 and p 2 , p 3 and p 4 are two pairs of conjugate poles in the SERF atomic spin gyroscope; 1 and z 2 are two pairs of conjugate zero points of the SERF atomic spin gyroscope, K 0 is the gain coefficient from the system to the output. All poles of the SERF atomic spin gyroscope system are located in the left half of the s-plane, indicating that the system is always in a stable state, but the poles close to the zero axis limit the bandwidth and dynamic response speed of the system.

[0094] Step 2, adding a first-level zero-pole compensation controller in the detection loop of the SERF atomic spin gyroscope; the output signal of the SERF atomic spin gyroscope in response to the y-axis speed is demodulated by the phase-locked amplifier and enters the zero-pole compensation controller. The zero-pole compensation controller includes a zero-pole generation link and a proportional link; the input end of the zero-pole generation link is connected to the output end of the phase-locked amplifier demodulation, the output end of the zero-pole generation link is connected to the input end of the proportional link, and the output end of the proportional link is connected to the input end of the sampling circuit;

[0095] Assume the transfer function of the zero-pole compensation controller is:

[0096]

[0097] In formula (A23): G C (s) is the transfer function of the zero-pole compensation controller; K Gain is the gain of the dipole compensation controller; the gain of the zero-pole compensation controller is generated by the proportional link; z C1 、z C2 are the two conjugate zeros of the zero-pole compensation controller; p C1 、p C2 are two poles of the zero-pole compensation controller; the two conjugate zeros and poles of the zero-pole compensation controller are generated by the zero-pole generation link;

[0098] After adding the zero-pole compensation controller to the loop, the transfer function of the SERF atomic spin gyroscope to the y-axis speed input becomes the product of equation (A22) and equation (A23):

[0099]

[0100] The two conjugate zeros of the zero-pole compensation controller are designed so that the two conjugate zeros of the zero-pole compensation controller and the two conjugate poles that affect the dynamic performance of the SERF atomic spin gyroscope form a zero-pole cancellation:

[0101] z C1 =p 1 ,z C2 =p 2 (A25)

[0102] 3) If it is still difficult to meet the bandwidth requirements of the SERF atomic spin gyroscope, a two-stage zero-pole compensation controller can be used, and the transfer function of the ERF atomic spin gyroscope to the y-axis speed input becomes:

[0103]

[0104] The four conjugate zeros of the zero-pole compensation controller are designed so that the four conjugate zeros of the zero-pole compensation controller and the four conjugate poles that affect the dynamic performance of the SERF atomic spin gyroscope form a zero-pole cancellation, and the four conjugate poles of the zero-pole compensation controller are configured to the desired bandwidth position:

[0105] z C1 =p 1 ,z C2 =p 2 ,z C3 =p 3 ,z C4 =p 4 (A27)

[0106] According to equations (A24) and (A26), by configuring the poles and gains of the zero-pole compensation controller, the transfer function of the SERF atomic spin gyroscope is no longer restricted by the pole position, thereby greatly improving the bandwidth and dynamic performance of the SERF atomic spin gyroscope.

[0107] Step 3: After the SERF atomic spin gyroscope passes through the zero-pole compensation controller, the speed response signal is output through the sampling resistor as a voltage signal proportional to the input angular rate for use by the system.

[0108] Although the embodiments and drawings of the invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the scope of the invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for modeling and bandwidth extension design of a SERF atomic spin gyroscope, characterized in that: The following steps are involved: Step 1, ignoring the second-order tiny quantity, establish the open-loop transfer function model of SERF atomic spin gyroscope; Step 2: Add a zero-pole compensation controller to the modulation and demodulation output signal of the SERF atomic spin gyroscope: Step 3: After the SERF atomic spin gyroscope passes through the zero-pole compensation controller, the speed response signal is output through the sampling resistor as a voltage signal proportional to the input angular rate for use by the system.

2. The SERF atomic spin gyroscope modeling and bandwidth extension design method according to claim 1, characterized in that: Step 1 includes: The Bloch equations are used to establish the dynamic equations of the SERF atomic spin gyroscope: In formula (A1), Ω represents the input angular velocity, P e and P n are the electron spin polarizability of alkali metal atoms / nuclear spin polarizability of noble gas atoms, λM e and λM n represent the electron spin of alkali metal atoms / nuclear spin magnetic moment of inert gas atoms, B represents the ambient magnetic field, R p It represents the optical pumping rate of the pumping laser, reflecting the polarization effect of the pumping laser on the electron spin, S p The direction of angular momentum transfer of pump laser photons, R se en It represents the nuclear spin pumping rate, reflecting the polarization effect of the inert gas atomic nuclear spin on the alkali metal atomic electron spin. tot e and R tot n are the total relaxation rates of alkali metal electrons / inert gas nuclei spins, γ e and γ n They represent the spin magnetic ratio of the electron spin of the alkali metal atom to the nuclear spin of the inert gas atom, L represents the light displacement felt by the electron spin of the alkali metal atom, Q represents the slowing factor, and R represents the deceleration factor. m It represents the optical pumping rate of the detection laser, reflecting the polarization effect of the detection laser on the electron spin, S m Detect the direction of the photon angular momentum transfer of the laser, R se ne It represents the electron spin pumping rate, reflecting the polarization effect of the electron spin of the alkali metal atom on the nuclear spin of the inert gas atom; By solving equation (A1) and setting Available and The steady-state value of: Among them, the subscripts x, y, and z represent the coordinate axis positions corresponding to the variables; make b1=R se ne ,b2=R tot n +R se ne ,but: Ignoring the transient terms, the steady-state solution can be obtained: make d2=γ n λM e , we have the following expression: After simplification, equation (A1) can be described by the following 4×4 matrix: Make the following transformation but: Define as follows: Equations (A12) and (A13) can be simplified to Eliminate from equation (A16) Then, through Laplace transformation, it is transformed into The second-order equation is: The two characteristic roots of the equation are: λ 1,2 =aa 1,2 +bb 1,2 i (A20) These two characteristic roots determine the dynamic behavior of the SERF atomic spin gyroscope: make The transfer function of the SERF atomic spin gyroscope to the y-axis speed input can be written as: Simplify (A21) to (A22) Among them, p1 and p2, p3 and p4 are two pairs of conjugate poles in the SERF atomic spin gyroscope; z1 and z2 are two pairs of conjugate zeros in the SERF atomic spin gyroscope, and K0 is the gain coefficient from the system to the output.

3. The SERF atomic spin gyroscope modeling and bandwidth extension design method according to claim 2, characterized in that: Based on the transfer function expression (A22) of the SERF atomic spin gyroscope to the y-axis speed input obtained in step 1, bandwidth expansion design is performed. Step 2 includes: First, a first-level zero-pole compensation controller is added to the detection loop of the SERF atomic spin gyroscope, and the zero-pole compensation controller includes a proportional link, a zero-point generation link and a pole generation link; the output signal of the SERF atomic spin gyroscope in response to the y-axis speed is demodulated by a phase-locked amplifier and then enters the zero-pole compensation controller, the input end of the zero-pole generation link is connected to the output end of the phase-locked amplifier demodulation, the output end of the zero-pole generation link is connected to the input end of the proportional link, and the output end of the proportional link is connected to the input end of the sampling circuit; Assume the transfer function of the zero-pole compensation controller is: In formula (A23): G C (s) is the transfer function of the zero-pole compensation controller; K Gain is the gain of the dipole compensation controller; the gain of the zero-pole compensation controller is generated by the proportional link; z C1 、z C2 are the two conjugate zeros of the zero-pole compensation controller; p C1 、p C2 are two poles of the zero-pole compensation controller; the two conjugate zeros and poles of the zero-pole compensation controller are generated by the zero-pole generation link; After adding the zero-pole compensation controller to the loop, the transfer function of the SERF atomic spin gyroscope to the y-axis speed input becomes the product of equation (A22) and equation (A23): The two conjugate zeros of the zero-pole compensation controller are designed so that the two conjugate zeros of the zero-pole compensation controller and the two conjugate poles that affect the dynamic performance of the SERF atomic spin gyroscope form a zero-pole cancellation: With C1 =p1,z C2 =p2 (A25) The relevant parameters of the SERF atomic spin gyroscope are brought in to draw the Bode plot of the closed-loop system. The 3 dB drop in the curve corresponds to the gyroscope bandwidth. If the one-stage zero-pole compensation controller cannot meet the bandwidth requirements of the SERF atomic spin gyroscope, a two-stage zero-pole compensation controller is used, and the transfer function of the ERF atomic spin gyroscope to the y-axis speed input becomes: The four conjugate zeros of the zero-pole compensation controller are designed so that the four conjugate zeros of the zero-pole compensation controller and the four conjugate poles that affect the dynamic performance of the SERF atomic spin gyroscope form a zero-pole cancellation, and the four conjugate poles of the zero-pole compensation controller are configured to the desired bandwidth position: from C1 =p1,z C2 =p2,z C3 =p3,z C4 =p4 (A27).

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