Active vibration isolation method for cold atom gravimeter based on adaptive model

Abstract

The invention provides a cold atom gravimeter active vibration isolation method based on an adaptive model, and relates to the technical field of cold atom gravimeter active vibration isolation, and the method comprises the following steps: building a cold atom gravimeter active vibration isolation reference model; designing a proportional differential feedback control law; a Lyapunov stability function is designed; a self-adaptive law is designed, the problems of ground vibration and random vibration caused by the natural environment in the measurement process of the cold atom gravimeter are solved, and the vibration speed and vibration displacement of the active vibration isolation system of the cold atom gravimeter are rapidly converged through a control method based on a self-adaptive model. And the control precision of the active vibration isolation system of the cold atom gravimeter is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of active vibration isolation technology of cold atom gravimeter, and particularly relates to an active vibration isolation method of cold atom gravimeter based on adaptive model. BACKGROUND

[0002] The cold atom gravimeter is a new type of quantum sensor developed rapidly in the past two decades, which realizes high-precision and high-sensitivity gravity acceleration measurement by using laser cooling and atomic interference technology. At present, the measurement precision of the cold atom gravimeter has reached microgal, and can be used in the fields of mineral resource exploration, geological structure research, oil and gas survey, scientific field spectrum identification constant determination, and gravity between materials.

[0003] In actual measurement, the precision of atomic gravity measurement is affected by ground vibration noise, Raman light phase noise and detection noise, among which the vibration noise is the most important factor affecting the atomic gravimeter. The self-vibration frequency of the commercial passive vibration isolation platform can be adjusted to 0.5Hz, which can be used to isolate the influence of ground vibration above 10Hz on the atomic gravimeter, but the atomic gravimeter is more sensitive to vibration of 0.1-10Hz, so the pure passive vibration isolation platform cannot meet the vibration isolation requirements of the atomic gravimeter. Although the self-vibration frequency of the whole passive vibration isolation platform can be adjusted, the self-vibration frequency is too low, the whole system will show nonlinear effect, and the ground vibration near the passive vibration isolation self-frequency is not only not suppressed, but also increased on the basis of the original vibration, so the active vibration isolation system needs to be introduced to suppress the vibration in this frequency band, but the active vibration isolation system is affected by a large number of uncertain factors, and the current control method does not consider the output delay problem of the cold atom gravimeter active vibration isolation system under the influence of ground vibration and other external disturbances. SUMMARY

[0004] The cold atom gravimeter active vibration isolation method based on the adaptive model disclosed in the present application solves the current control method, so that the vibration speed and vibration displacement of the cold atom gravimeter active vibration isolation system converge rapidly, and the control precision of the cold atom gravimeter active vibration isolation system is improved.

[0005] To achieve the above object, the technical scheme of the present application is as follows:

[0006] The present application discloses a cold atom gravimeter active vibration isolation method based on an adaptive model, comprising the following steps:

[0007] Establishing a cold atom gravimeter active vibration isolation reference model;

[0008] Designing a proportional differential feedback control law;

[0009] Designing a Lyapunov stable function;

[0010] Design adaptive law.

[0011] Further, the step of establishing the active vibration isolation model of the cold atom gravimeter comprises:

[0012]

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

[0014] Let g1=K VC Y VC / m, g2=-2ξ0ω0, g3=-ω0 2 , then formula (1) is represented as:

[0015]

[0016] The reference model is defined as:

[0017]

[0018] wherein, x m is the model output, representing the theoretical parameters of the cold atom gravimeter in the ideal state without vibration disturbance; is the first derivative of x m , is the second derivative of x m , r is the system command input; b1, b2, b are known positive real numbers;

[0019] The error signal is defined as:

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

[0021] Subtracting formula (4) from formula (1), the error dynamic equation is obtained as:

[0022]

[0023] Defining the error state equation is obtained as follows:

[0024]

[0025] wherein, is the first derivative of the error signal e, is the second derivative of the error signal e.

[0026] Further, the step of designing the proportional derivative feedback control law comprises:

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

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

[0029] The control term is defined in the form of PD:

[0030] wherein,

[0031] The control law is designed in the form of feedforward plus PD feedback:

[0032] Substitute formula (9) into formula (5), to obtain:

[0033]

[0034] wherein, k0, k1, k2 are gain coefficients.

[0035] Further, the step of designing the Lyapunov stability function comprises:

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

[0037]

[0038] Referring to formula (7), and there is:

[0039]

[0040] Take the derivative of V, then there is:

[0041]

[0042]

[0043] wherein, λ i >0; i=0, 1, 2, is the estimated signal of the error signal e, ε T is the transpose matrix of the error signal ε, is the first derivative of the gain coefficient k0, the first derivative of the gain coefficient k1, the first derivative of the gain coefficient k2.

[0044] Further, the step of designing the adaptive law comprises:

[0045] Let:

[0046]

[0047] Substitute formula (14), formula (15) and formula (16) into formula (13), and then the following formula is obtained:

[0048]

[0049] Beneficial technical effects:

[0050] The application provides a cold atom gravimeter active vibration isolation method based on an adaptive model, comprising the following steps: establishing a cold atom gravimeter active vibration isolation reference model; designing a proportional-derivative feedback control law; designing a Lyapunov stable function; and designing an adaptive law, so as to solve the problems of ground vibration and random vibration caused by natural environment encountered by the cold atom gravimeter in measurement, and make the vibration speed and vibration displacement of the cold atom gravimeter active vibration isolation system rapidly converge through the control method based on the adaptive model, thereby improving the control precision of the cold atom gravimeter active vibration isolation system. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the application, the following will briefly introduce the drawings needed to be used in the embodiment description.

[0052] Figure 1 A step flow chart of the cold atom gravimeter active vibration isolation method based on the proportional-derivative gain adaptive adjustment model reference adaptive control is provided.

[0053] Figure 2 When the ground vibration frequency is 0.1 Hz and the external environmental vibration interference displacement amplitude is a sinusoidal interference signal of 1 mm, the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model is compared with that of the vibration isolation control not implemented.

[0054] Figure 3 When the ground vibration frequency is 0.1 Hz and the external environmental vibration interference speed amplitude is a cosine wave interference signal of 62.8 mm / s, the vibration speed suppression effect of the cold atom gravimeter active vibration isolation method based on the adaptive model is compared with that of the vibration isolation control not implemented.

[0055] Figure 4When the local ground vibration frequency is 0.2 Hz and the external environmental vibration interference displacement amplitude is 1 mm of a sine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration displacement suppression effect than the vibration isolation control without implementation.

[0056] Figure 5 When the local ground vibration frequency is 0.2 Hz and the external environmental vibration interference velocity amplitude is 31.4 mm / s of a cosine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration velocity suppression effect than the vibration isolation control without implementation.

[0057] Figure 6 When the local ground vibration frequency is 0.5 Hz and the external environmental vibration interference displacement amplitude is 1 mm of a sine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration displacement suppression effect than the vibration isolation control without implementation.

[0058] Figure 7 When the local ground vibration frequency is 0.5 Hz and the external environmental vibration interference velocity amplitude is 12.56 mm / s of a cosine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration velocity suppression effect than the vibration isolation control without implementation.

[0059] Figure 8 When the local ground vibration frequency is 1 Hz and the external environmental vibration interference displacement amplitude is 1 mm of a sine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration displacement suppression effect than the vibration isolation control without implementation.

[0060] Figure 9 When the local ground vibration frequency is 1 Hz and the external environmental vibration interference velocity amplitude is 6.28 mm / s of a cosine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration velocity suppression effect than the vibration isolation control without implementation.

[0061] Figure 10 When the local ground vibration frequency is 2 Hz and the external environmental vibration interference displacement amplitude is 1 mm of a sine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration displacement suppression effect than the vibration isolation control without implementation.

[0062] Figure 11 When the local ground vibration frequency is 2 Hz and the external environmental vibration interference velocity amplitude is 3.14 mm / s of a cosine wave interference signal, the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration velocity suppression effect than the vibration isolation control without implementation.

[0063] Figure 12 The random interference signal is a white noise interference signal of external environmental vibration interference.

[0064] Figure 13 The random interference signal is a white noise interference signal of external environmental vibration interference, and the active vibration isolation method of the cold atom gravimeter based on the adaptive model has a better vibration displacement suppression effect than the vibration isolation control without the vibration isolation. DETAILED DESCRIPTION

[0065] Embodiments of the present application are described in detail below with reference to examples shown in the accompanying drawings, in which the same or similar reference numerals represent 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 application and cannot be understood as a limitation of the present application.

[0066] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0067] The present application discloses an active vibration isolation method of a cold atom gravimeter based on an adaptive model, referring to Figure 1 , specifically comprising the following steps:

[0068] S1: establishing an active vibration isolation reference model of a cold atom gravimeter;

[0069] Specifically, the step of establishing the active vibration isolation model of the cold atom gravimeter comprises:

[0070]

[0071] wherein, ξ0 is the inherent damping coefficient of the system, ω0 is the inherent natural frequency of the system, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman mirror, is the vibration speed of the Raman mirror, is the vibration acceleration of the Raman mirror, y is the ground vibration displacement, is the ground vibration speed, m is the mass of the Raman mirror, u is the input of the controller, K VC is the gain coefficient of the voice coil motor, Y VC is the voltage-to-current gain coefficient;

[0072] Let g1=K VC Y VC / m, g2=-2ξ0ω0, g3=-ω0 2 , Then formula (1) is represented as:

[0073]

[0074] The reference model is defined as:

[0075]

[0076] wherein x m is the model output, representing the theoretical parameter of the cold atom gravimeter in the ideal state without vibration interference; is the first derivative of x m , is the second derivative of x m , and r is the system command input; b1, b2, b are known positive real numbers;

[0077] Define the error signal as:

[0078] e = x m -x (4)

[0079] Subtracting equation (4) from equation (1), the error dynamic equation is obtained as:

[0080] Define The error state equation is obtained as follows:

[0081]

[0082] wherein, is the first derivative of the error signal e, is the second derivative of the error signal e.

[0083] S2: Design a proportional-derivative feedback control law;

[0084] Specifically, the steps of designing a proportional-derivative feedback control law include:

[0085] By designing b1 and b2, the eigenvalues of the matrix A have negative real parts, and there exist symmetric positive definite matrices P and Q such that the following equation is established:

[0086] A T P+PA=-Q (7)

[0087] Define the control term in the PD form as:

[0088] wherein,

[0089] The control law is designed in the form of feedforward plus PD feedback as:

[0090] Substitute equation (9) into equation (5) to obtain:

[0091]

[0092] wherein k0, k1, k2 are gain coefficients.

[0093] S3: design Lyapunov stability function;

[0094] Specifically, the step of designing the Lyapunov stability function comprises:

[0095] In formula (10), in order to ensure that ε→0, the Lyapunov stability function is designed as:

[0096]

[0097] Referring to formula (7), and has:

[0098]

[0099] Taking the derivative of V, then has:

[0100]

[0101] Wherein, λ i >0; i=0, 1, 2, is an estimated signal of the error signal e, and ε T is a transpose matrix of the error signal ε, is a first-order derivative of the gain coefficient k0, is a first-order derivative of the gain coefficient k1, is a first-order derivative of the gain coefficient k2.

[0102] S4: design adaptive law.

[0103] The step of designing the adaptive law comprises:

[0104] Let:

[0105]

[0106] Substituting formula (14), formula (15) and formula (16) into formula (13), then:

[0107]

[0108] When and only when ε=0, that is, when , ε≡0, according to the LaSalle invariance principle, the closed-loop system is asymptotically stable; when t→∞, ε→0, that is, e→0, The convergence speed of the system depends on Q.

[0109] As an embodiment of the present application, the experimental simulation parameters of the active vibration isolation method of a cold atom gravimeter based on an adaptive model disclosed by the present application are set as follows:

[0110] The system damping coefficient ξ0 is set as 0.1 N·s·m-1 System natural frequency ω0=4.396 rad, voice coil motor current gain coefficient K VC =0.1 V·A -1 Voltage to current gain coefficient Y VC =7.6 N·A -1 Mass of the Raman mirror m=10 kg; gain parameter b1=0.8792, gain parameter b2=19.3248, gain parameter b=0.76, and initial values of adaptive parameters k0, k1, and k2 are

[000] for the active vibration isolation method of the cold atom gravimeter based on the proportional-derivative gain adaptive adjustment model reference adaptive control.

[0111] It should be noted that, in order to better describe the observation effect, Figure 2 、 Figure 4 、 Figure 6 、 Figure 8 and Figure 10 , a double coordinate representation method is adopted, the left coordinate is a displacement representation coordinate without vibration isolation control, and the right coordinate is a displacement representation coordinate of the active vibration isolation method of the cold atom gravimeter based on the adaptive model. Figure 3 、 Figure 5 、 Figure 7 and Figure 9 , a double coordinate representation method is adopted, the left coordinate is a displacement representation coordinate without vibration isolation control, and the right coordinate is a velocity representation coordinate of the active vibration isolation method of the cold atom gravimeter based on the adaptive model.

[0112] The active vibration isolation method of the cold atom gravimeter based on the adaptive model disclosed in the present application makes the vibration velocity and vibration displacement of the active vibration isolation system of the cold atom gravimeter converge rapidly, greatly improves the control precision of the active vibration isolation system of the cold atom gravimeter, Figures 2-11 The comparison results of the active vibration isolation method of the cold atom gravimeter based on the adaptive model disclosed in the present application and the vibration isolation control without implementation are shown, and the vibration displacement after the active vibration isolation control of the cold atom gravimeter based on the adaptive model is far less than the vibration displacement after the vibration isolation control without implementation; the vibration velocity after the active vibration isolation control of the cold atom gravimeter based on the adaptive model is far less than the vibration velocity after the vibration isolation control without implementation.

[0113] Figures 12-13 The comparison results of the active vibration isolation method of the cold atom gravimeter based on the adaptive model disclosed in the present application and the vibration isolation control without implementation are shown, and the vibration displacement after the active vibration isolation control of the cold atom gravimeter based on the adaptive model is far less than the vibration displacement after the vibration isolation control without implementation; the vibration velocity after the active vibration isolation control of the cold atom gravimeter based on the adaptive model is far less than the vibration velocity after the vibration isolation control without implementation.

[0114] 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.

[0115] 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, The method comprises the following steps: establishing a reference model of active vibration isolation of a cold atom gravimeter; designing a proportional differential feedback control law; designing a Lyapunov stability function; designing an adaptive law.

2. The active vibration isolation method of a cold atom gravimeter based on a proportional derivative delayed observer according to claim 1, characterized in that, The step of establishing the reference model of active vibration isolation of the cold atom gravimeter comprises: wherein ξ0 is a system inherent damping coefficient, ω0 is a system inherent natural frequency, F is a force generated by a voice coil motor, x is a vibration displacement of a Raman mirror, is a vibration velocity of the Raman mirror, is a vibration acceleration of the Raman mirror, y is a ground vibration displacement, is a ground vibration velocity, m is a mass of the Raman mirror, u is a controller input, K VC is a voice coil motor gain coefficient, Y VC is a voltage-to-current gain coefficient; Let g1= K VC Y VC / m, g2 = -2ξ0ω0, g3 = -ω0 2 , Equation (1) is then expressed as: the reference model is defined as: where x m is the model output, representing the theoretical parameters of the cold atom gravimeter in the ideal state without vibration interference; is the first derivative of x m , is the second derivative of x m , and r is the system command input; b1, b2, and b are known positive real numbers; an error signal is defined as: e = x m - x (4) subtracting equation (4) from equation (1) to obtain an error dynamic equation: Definitions The error state equation is obtained as follows: wherein is the first derivative of the error signal e, is the second derivative of the error signal e.

3. The active vibration isolation method for a cold atom gravimeter based on an adaptive model according to claim 2, characterized in that, The step of designing the proportional differential feedback control law comprises: by designing b1 and b2, eigenvalues of the matrix A have negative real parts, so that there exist symmetric positive definite matrices P and Q, and the following equation is established: A T P+PA=-Q (7) the control term is defined in a PD form as: In the formulae, the control rate is designed in a feedforward plus PD feedback form as: equation (9) is substituted into equation (5) to obtain: where k0, k1 and k2 are gain coefficients.

4. The active vibration isolation method of claim 3, wherein, The step of designing the Lyapunov stability function comprises: in equation (10), to ensure that ε→0, the Lyapunov stability function is designed as: reference is made to equation (7), and there are: the derivative of V is taken, and the following equation is obtained: where λ > 0; i = 0, 1, 2, i > 0; i = 0, 1, 2, is an estimated signal of the error signal e, ε T is a transposed matrix of the error signal ε, is a first derivative of the gain coefficient k0, is a first derivative of the gain coefficient k1, is a first derivative of the gain coefficient k2.

5. The active vibration isolation method of a cold atom gravimeter based on an adaptive model according to claim 4, characterized in that, The step of designing the adaptive law comprises: letting: equations (14), (15) and (16) are substituted into equation (13), and the following equation is obtained:

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