Adaptive model based active vibration isolation method for cold atom gravimeter

Abstract

This invention provides an active vibration isolation method for cold atom gravimeters based on an adaptive model, relating to the field of active vibration isolation technology for cold atom gravimeters. The method includes the following steps: establishing an active vibration isolation reference model for the cold atom gravimeter; designing a proportional-derivative feedback control law; designing a Lyapunov stability function; and designing an adaptive law to address the problems of ground vibration and random vibrations caused by the natural environment encountered by the cold atom gravimeter during measurement. Through the adaptive model-based control method, the vibration velocity and displacement of the active vibration isolation system of the cold atom gravimeter converge rapidly, thereby improving the control accuracy of the active vibration isolation system.

Description

Technical Field

[0001] This invention relates to the field of active vibration isolation technology for cold atom gravimeters, and in particular to an active vibration isolation method for cold atom gravimeters based on an adaptive model. Background Technology

[0002] Cold atom gravimeters are a novel type of quantum sensor that has developed rapidly over the past two decades. They utilize laser cooling, atomic interferometry, and other technologies to achieve high-precision, high-sensitivity measurements of gravitational acceleration. Currently, the measurement accuracy of cold atom gravimeters has reached the microgal level, making them suitable for precision engineering measurements in areas such as mineral resource exploration, geological structure research, oil and gas prospecting, determination of spectroscopic constant brightness in scientific fields, and inter-matter gravitational forces.

[0003] In practical measurements, the accuracy of atomic gravity measurements is affected by ground vibration noise, Raman phase noise, and detection noise, among which vibration noise is the most significant factor affecting atomic gravimeters. Currently, the natural frequency of commercially available passive vibration isolation platforms can be adjusted down to as low as 0.5 Hz, which can be used to isolate the influence of ground vibrations above 10 Hz on atomic gravimeters. However, atomic gravimeters are more sensitive to vibrations in the 0.1-10 Hz range, so a simple passive vibration isolation platform cannot meet the vibration isolation requirements of atomic gravimeters. Although the natural frequency of the entire passive vibration isolation platform can be adjusted, if the natural frequency is adjusted too low, the entire system will exhibit nonlinear effects. Ground vibrations near the passive isolation natural frequency will not only not be suppressed, but will actually increase on top of the original vibration. Therefore, an active vibration isolation system needs to be introduced to suppress vibrations in this frequency band. However, active vibration isolation systems are affected by a large number of uncertainties, and current control methods do not consider the output delay of the active vibration isolation system of cold atomic gravimeters under external disturbances such as ground vibrations. Summary of the Invention

[0004] The present invention discloses an active vibration isolation method for a cold atom gravimeter based on an adaptive model, which solves the problems of current control methods and enables the vibration velocity and vibration displacement of the active vibration isolation system of the cold atom gravimeter to converge rapidly, thereby improving the control accuracy of the active vibration isolation system of the cold atom gravimeter.

[0005] To achieve the above objectives, the technical solution of the present invention is specifically implemented as follows:

[0006] This invention discloses an active vibration isolation method for cold atom gravimeters based on an adaptive model, comprising the following steps:

[0007] Establish an active vibration isolation reference model for a cold atom gravimeter;

[0008] Design a proportional-derivative feedback control law;

[0009] Design a Lyapunov stable function;

[0010] Design adaptive laws.

[0011] Furthermore, the steps for establishing an active vibration isolation model for a cold atom gravimeter include:

[0012]

[0013] Where ξ0 is the system's inherent damping coefficient, ω0 is the system's natural frequency, F is the force generated by the voice coil motor, and x is the vibration displacement of the Raman mirror. Let be the vibration velocity of the Raman mirror. Let y be the vibration acceleration of the Raman mirror, and y be the ground vibration displacement. Let m be the ground vibration velocity, m be the mass of the Raman mirror, u be the controller input, and K be the ground vibration velocity. VC Y is the gain coefficient of the voice coil motor. VC This is the voltage-to-current gain coefficient;

[0014] Let g1 = K VC Y VC / m, g2=-2ξ0ω0, g3=-ω0 2 , Then equation (1) can be expressed as:

[0015]

[0016] The reference model is defined as follows:

[0017]

[0018] Where, x m The output of the model represents the theoretical parameters of the cold atom gravimeter under ideal conditions without vibration interference. For x m The first derivative, For x m The second derivative of , r is the system instruction input; b1, b2, b are known positive real numbers;

[0019] The error signal is defined as:

[0020] e = x m -x (4)

[0021] Subtracting equation (4) from equation (1) yields the error dynamic equation:

[0022]

[0023] definition The error state equation is obtained as follows:

[0024]

[0025] in, Let e ​​be the first derivative of the error signal e. Let be the second derivative of the error signal e.

[0026] Furthermore, the steps for designing a proportional-derivative feedback control law include:

[0027] By designing b1 and b2 such that the eigenvalues ​​of matrix A have negative real parts, there exist symmetric positive definite matrices P and Q such that the following equation holds:

[0028] A T P + PA = -Q (7)

[0029] Define the control item in PD form as follows:

[0030] In the formula,

[0031] The control rate of the feedforward plus PD feedback design is:

[0032] Substituting equation (9) into equation (5), we get:

[0033]

[0034] Where k0, k1, and k2 are gain coefficients.

[0035] Furthermore, the steps for designing the Lyapunov stable function include:

[0036] In equation (10), to ensure ε→0, the Lyapunov stability function is designed as follows:

[0037]

[0038] Refer to equation (7), and we have:

[0039]

[0040] Taking the derivative with respect to V, we have:

[0041]

[0042] Where, λ i >0; i = 0, 1, 2, Let ε be the estimated signal of the error signal e. T Let be the transpose matrix of the error signal ε. The first derivative of the gain coefficient k0 The first derivative of the gain coefficient k1 It is the first derivative of the gain coefficient k2.

[0043] Furthermore, the steps for designing an adaptive law include:

[0044] make:

[0045]

[0046] Substituting equations (14), (15), and (16) into equation (13), we get:

[0047]

[0048] Beneficial technical effects:

[0049] This invention provides an active vibration isolation method for cold atom gravimeters based on an adaptive model, comprising the following steps: establishing an active vibration isolation reference model for the cold atom gravimeter; designing a proportional-derivative feedback control law; designing a Lyapunov stability function; and designing an adaptive law to address the problems of ground vibration and random vibration caused by the natural environment encountered by the cold atom gravimeter during measurement. Through the control method based on the adaptive model, the vibration velocity and vibration displacement of the active vibration isolation system of the cold atom gravimeter converge rapidly, thereby improving the control accuracy of the active vibration isolation system of the cold atom gravimeter. Attached Figure Description

[0050] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below.

[0051] Figure 1 This is a flowchart of the steps of the active vibration isolation method for cold atom gravimeters based on proportional-derivative gain adaptive adjustment model reference adaptive control as described in this invention;

[0052] Figure 2 When the ground vibration frequency is 0.1Hz and the external environmental vibration interference displacement amplitude is 1mm, the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model described in this invention is compared with that of vibration displacement suppression without vibration isolation control.

[0053] Figure 3 When the ground vibration frequency is 0.1Hz and the external environmental vibration interference signal has a vibration velocity amplitude of 62.8mm / s, the active vibration isolation method of the cold atom gravimeter based on the adaptive model described in this invention is compared with the vibration velocity suppression effect of no vibration isolation control.

[0054] Figure 4When the ground vibration frequency is 0.2Hz and the external environmental vibration interference displacement amplitude is 1mm, the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model described in this invention is compared with that of vibration displacement suppression without vibration isolation control.

[0055] Figure 5 When the ground vibration frequency is 0.2Hz and the external environmental vibration interference signal has a vibration velocity amplitude of 31.4mm / s, the active vibration isolation method of the cold atom gravimeter based on the adaptive model described in this invention is compared with the vibration velocity suppression effect of no vibration isolation control.

[0056] Figure 6 When the ground vibration frequency is 0.5Hz and the external environmental vibration interference displacement amplitude is 1mm, the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model described in this invention is compared with that of vibration displacement suppression without vibration isolation control.

[0057] Figure 7 When the ground vibration frequency is 0.5Hz and the external environmental vibration interference signal has a vibration velocity amplitude of 12.56mm / s, the active vibration isolation method of the cold atom gravimeter based on the adaptive model described in this invention is compared with the vibration velocity suppression effect of no vibration isolation control.

[0058] Figure 8 When the ground vibration frequency is 1Hz and the external environmental vibration interference displacement amplitude is 1mm, the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model described in this invention is compared with that of vibration displacement suppression without vibration isolation control.

[0059] Figure 9 When the ground vibration frequency is 1Hz and the external environmental vibration interference signal has a vibration velocity amplitude of 6.28mm / s, the active vibration isolation method of the cold atom gravimeter based on the adaptive model described in this invention is compared with the vibration velocity suppression effect of no vibration isolation control.

[0060] Figure 10 When the ground vibration frequency is 2Hz and the external environmental vibration interference displacement amplitude is 1mm, the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model described in this invention is compared with that of vibration displacement suppression without vibration isolation control.

[0061] Figure 11 When the ground vibration frequency is 2Hz and the external environmental vibration interference signal has a vibration velocity amplitude of 3.14mm / s, the active vibration isolation method of the cold atom gravimeter based on the adaptive model described in this invention is compared with the vibration velocity suppression effect of no vibration isolation control.

[0062] Figure 12 The external environmental vibration interference is a random interference signal that is white noise;

[0063] Figure 13 The method for active vibration isolation of a cold atom gravimeter based on an adaptive model, as described in this invention, is compared with the vibration displacement suppression effect of a method without vibration isolation control, where the external environmental vibration interference is a random interference signal of white noise. Detailed Implementation

[0064] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0065] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0066] This invention discloses an active vibration isolation method for cold atom gravimeters based on an adaptive model. See [link to relevant documentation]. Figure 1 Specifically, it includes the following steps:

[0067] S1: Establish an active vibration isolation reference model for a cold atom gravimeter;

[0068] Specifically, the steps for establishing an active vibration isolation model for a cold atom gravimeter include:

[0069]

[0070] Where ξ0 is the system's inherent damping coefficient, ω0 is the system's natural frequency, F is the force generated by the voice coil motor, and x is the vibration displacement of the Raman mirror. Let be the vibration velocity of the Raman mirror. Let y be the vibration acceleration of the Raman mirror, and y be the ground vibration displacement. Let m be the ground vibration velocity, m be the mass of the Raman mirror, u be the controller input, and K be the ground vibration velocity. VC Y is the gain coefficient of the voice coil motor. VC This is the voltage-to-current gain coefficient;

[0071] Let g1 = K VC Y VC / m, g2=-2ξ0ω0, g3=-ω0 2 , Then equation (1) can be expressed as:

[0072]

[0073] The reference model is defined as follows:

[0074]

[0075] Where, x m The output of the model represents the theoretical parameters of the cold atom gravimeter under ideal conditions without vibration interference. For x m The first derivative, For x m The second derivative of , r is the system instruction input; b1, b2, b are known positive real numbers;

[0076] The error signal is defined as:

[0077] e = x m -x (4)

[0078] Subtracting equation (4) from equation (1) yields the error dynamic equation:

[0079] definition The error state equation is obtained as follows:

[0080]

[0081] in, Let e ​​be the first derivative of the error signal e. Let be the second derivative of the error signal e.

[0082] S2: Design proportional-derivative feedback control law;

[0083] Specifically, the steps for designing a proportional-derivative feedback control law include:

[0084] By designing b1 and b2 such that the eigenvalues ​​of matrix A have negative real parts, there exist symmetric positive definite matrices P and Q such that the following equation holds:

[0085] A T P + PA = -Q (7)

[0086] Define the control item in PD form as follows:

[0087] In the formula,

[0088] The control rate of the feedforward plus PD feedback design is:

[0089] Substituting equation (9) into equation (5), we get:

[0090]

[0091] Where k0, k1, and k2 are gain coefficients.

[0092] S3: Design a Lyapunov stable function;

[0093] Specifically, the steps for designing a Lyapunov stable function include:

[0094] In equation (10), to ensure ε→0, the Lyapunov stability function is designed as follows:

[0095]

[0096] Refer to equation (7), and we have:

[0097]

[0098] Taking the derivative with respect to V, we have:

[0099]

[0100] Where, λ i >0; i = 0, 1, 2, Let ε be the estimated signal of the error signal e. T Let be the transpose matrix of the error signal ε. The first derivative of the gain coefficient k0 The first derivative of the gain coefficient k1 It is the first derivative of the gain coefficient k2.

[0101] S4: Design Adaptive Law.

[0102] The steps involved in designing an adaptive law include:

[0103] make:

[0104]

[0105] Substituting equations (14), (15), and (16) into equation (13), we get:

[0106]

[0107] If and only if ε = 0 That is when When t→∞, ε≡0, and according to the LaSalle invariance principle, the closed-loop system is asymptotically stable; when t→∞, ε→0, that is, when e→0, The convergence rate of the system depends on Q.

[0108] As an embodiment of the present invention, the experimental simulation parameters for the active vibration isolation method for a cold atom gravimeter based on an adaptive model disclosed in the present invention are set as follows:

[0109] Set the system damping coefficient ξ0 = 0.1 N·s·m-1 The system's natural frequency ω0 = 4.396 rad, and the voice coil motor current gain coefficient K VC =0.1V·A -1 Voltage-to-current gain coefficient Y VC =7.6 N·A -1 The mass of the Raman mirror is m = 10 kg; the gain parameter b1 = 0.8792, the gain parameter b2 = 19.3248, the gain parameter b = 0.76, and the initial values ​​of the adaptive parameters k0, k1, k2 are

[000] .

[0110] It should be noted that, in order to better describe the observation results, Figure 2 , Figure 4 , Figure 6 , Figure 8 and Figure 10 The image uses a dual-coordinate representation method. The left coordinate represents the displacement without vibration isolation control, while the right coordinate represents the displacement of the cold atom gravimeter with active vibration isolation based on an adaptive model. Figure 3 , Figure 5 , Figure 7 and Figure 9 The image uses a dual-coordinate representation method. The left coordinate represents the displacement without vibration isolation control, while the right coordinate represents the velocity of the active vibration isolation method of the cold atom gravimeter based on an adaptive model.

[0111] This invention discloses an active vibration isolation method for cold atom gravimeters based on an adaptive model, which enables the vibration velocity and displacement of the active vibration isolation system of the cold atom gravimeter to converge rapidly, greatly improving the control accuracy of the active vibration isolation system of the cold atom gravimeter. Figures 2-11 The results show that the active vibration isolation method for cold atom gravimeters based on adaptive models disclosed in this invention is much smaller than that without vibration isolation control. The vibration displacement of the cold atom gravimeter after active vibration isolation control based on adaptive models is much smaller than that without vibration isolation control. The vibration velocity of the cold atom gravimeter after active vibration isolation control based on adaptive models is much smaller than that without vibration isolation control.

[0112] Figures 12-13 The results show that the vibration displacement suppression effect of the active vibration isolation method for cold atom gravimeters based on the adaptive model disclosed in this invention is much smaller than that of the method without vibration isolation control. This demonstrates that the active vibration isolation method for cold atom gravimeters based on the adaptive model disclosed in this invention has significant advantages.

[0113] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0114] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An active vibration isolation method for a cold atom gravimeter based on an adaptive model, characterized in that, Includes the following steps: Establish an active vibration isolation reference model for a cold atom gravimeter; The steps for establishing an active vibration isolation model for a cold atom gravimeter include: （1） wherein, is a system inherent damping coefficient, is a system inherent natural frequency, is a vibration displacement of the Raman mirror, is a vibration velocity of the Raman mirror, is a vibration acceleration of the Raman mirror, is a ground vibration displacement, is a ground vibration velocity, is a mass of the Raman mirror, is a controller input, is a voice coil motor gain coefficient, is a voltage-to-current gain coefficient; make , , , Then equation (1) can be expressed as: （2） The reference model is defined as follows: （3） in, The output of the model represents the theoretical parameters of the cold atom gravimeter under ideal conditions without vibration interference. for The first derivative, for The second derivative, For system System command input; , , Given a positive real number; The error signal is defined as: （4） Subtracting equation (4) from equation (1) yields the error dynamic equation: （5） definition The error state equation is obtained as follows: （6） in, , Error signal The first derivative, Error signal The second derivative; Design a proportional-derivative feedback control law; The steps involved in designing a proportional-derivative feedback control law include: Through design and , make the matrix If the eigenvalues ​​have negative real parts, then there exists a symmetric positive definite matrix. and This makes the following equation true: （7） Define the control item in PD form as follows: （8） In the formula, ; The control rate of the feedforward plus PD feedback design is: （9） Substituting equation (9) into equation (5), we get: （10）； in, This is the gain coefficient; Design a Lyapunov stable function; The steps involved in designing a Lyapunov stable function include: In equation (10), to ensure The Lyapunov stable function is designed as follows: （11） Refer to equation (7), and we have: （12） right Taking the derivative, we have: （13） in, , Error signal The estimated signal, Error signal The transpose of the matrix, Gain coefficient The first derivative, Gain coefficient The first derivative, Gain coefficient The first derivative; Design an adaptive law; The steps involved in designing an adaptive law include: make: （14） （15） （16） Substituting equations (14), (15), and (16) into equation (13), we get: （17）。

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