Active vibration isolation method for cold atom gravimeter based on neural network sliding mode control

Abstract

The invention provides a cold atom gravimeter active vibration isolation method based on neural network sliding mode control, comprising the following steps: establishing a cold atom gravimeter active vibration isolation model; designing a sliding mode control law; designing a neural network algorithm; designing a Lyapunov function; and designing an adaptive law, which solves the problem that the current control method does not consider the randomness of external disturbances such as ground vibration and model uncertainty. By establishing adaptive neural network sliding mode control, the vibration velocity and vibration displacement of the cold atom gravimeter active vibration isolation system converge rapidly, thereby improving the control accuracy of the cold atom gravimeter active vibration isolation system.

Description

Technical Field

[0001] The invention relates to the technical field of active vibration isolation of cold atom gravimeters, and in particular to an active vibration isolation method of cold atom gravimeters based on neural network sliding mode control. Background Art

[0002] Cold atom gravimeter is a new type of quantum sensor that has developed rapidly in the past two decades. Its function is to use laser cooling, atomic interference and other technologies to achieve high-precision and high-sensitivity gravity acceleration measurement. At present, the measurement accuracy of cold atom gravimeter has reached micro-Gal, which can be used in mineral resource exploration, geological structure research, oil and gas survey, scientific field spectral identification, gravity between materials and other precision engineering measurement fields.

[0003] In actual measurements, the accuracy of atomic gravity measurement is affected by ground vibration noise, Raman optical phase noise and detection noise, among which vibration noise is the most important factor affecting atomic gravimeters. At present, the natural frequency of commercial passive vibration isolation platforms can be adjusted to a minimum of 0.5Hz, which can be used to isolate the impact of ground vibrations above 10Hz on atomic gravimeters. However, atomic gravimeters are more sensitive to vibrations of 0.1-10Hz, 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 show nonlinear effects. The ground vibration near the passive vibration isolation natural frequency is not only not suppressed, but it becomes larger on the basis of the original vibration. Therefore, it is necessary to introduce an active vibration isolation system to suppress the vibration in this frequency band. However, the active vibration isolation system is affected by a large number of uncertain factors, and the current control method does not consider the randomness of external disturbances such as ground vibration and the uncertainty of the model. Summary of the invention

[0004] The present invention discloses a cold atom gravimeter active vibration isolation method based on neural network sliding mode control, which solves the problem that the current control method does not consider the randomness of external disturbances such as ground vibration and model uncertainty. By establishing an adaptive neural network sliding mode control, the vibration velocity and vibration displacement of the cold atom gravimeter active vibration isolation system converge rapidly, thereby improving the control accuracy of the cold atom gravimeter active vibration isolation system.

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

[0006] The present invention discloses a cold atomic gravimeter active vibration isolation method based on neural network sliding mode control, comprising the following steps:

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

[0008] Design sliding mode control law;

[0009] Design neural network algorithms;

[0010] Design Lyapunov functions;

[0011] Design adaptive laws.

[0012] Furthermore, the steps of establishing the active vibration isolation model of the cold atomic gravimeter include:

[0013]

[0014] Among them, ξ 0 is the system damping coefficient, ω 0 is the natural frequency of the system, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman reflector, is the vibration speed of the Raman reflector, is the vibration acceleration of the Raman reflector, y is the ground vibration displacement, is the ground vibration velocity, m is the mass of the Raman reflector;

[0015] Where F is represented by:

[0016] F=K VC Y VC u (2)

[0017] Where u is the controller input, K VC is the voice coil motor current gain coefficient, Y VC is the voltage-to-current gain coefficient;

[0018] Substituting F into formula (1), we get

[0019]

[0020] Let g = K VC Y VC / m,

[0021] Formula (3) can be written as:

[0022]

[0023] Furthermore, the steps of designing the sliding mode control law include:

[0024] Assume that the expected value of the system vibration displacement is x d , is the expected value of vibration displacement x d The first-order derivative of , d is the ground vibration disturbance, |d|≤D, D is the maximum value of the ground vibration disturbance, , then the sliding mode function is:

[0025]

[0026] Among them, the gain coefficient c of the sliding mode function is greater than 0, then the derivative of the sliding mode function is;

[0027]

[0028] Assuming that f and g are both known, the designed control law is:

[0029]

[0030] in, is the expected value of vibration displacement x d The second-order derivative of sgn(s), sgn(s) is the sign function, η is the gain coefficient of the sign function, and substituting (7) into (6) yields:

[0031]

[0032] If η≥D, then

[0033]

[0034] Furthermore, the steps of designing a neural network algorithm include:

[0035] The neural network algorithm is:

[0036]

[0037] f=W T h+ε (11)

[0038] Among them, j is the jth network input of the hidden layer, is the input of the neural network, c j is the center vector value of the jth node, b j is the basis width value vector of the Gaussian basis function of the jth node, h is the output of the Gaussian basis function, W is the network weight vector, ε is the neural network approximation error, ε≤ε N , ε N is the maximum value of the neural network approximation error;

[0039] Then the approximation function of f is

[0040]

[0041] in, Estimate the weight vector for the network, and its control law is:

[0042]

[0043] Substituting (13) into (6), we can obtain:

[0044]

[0045] Furthermore, the steps of designing the Lyapunov function include:

[0046] Define the Lyapunov function as:

[0047]

[0048] Where, the gain coefficient γ>0, and combining equation (13) and equation (14) we can get:

[0049]

[0050] Furthermore, the steps of designing the adaptive law include:

[0051] The designed adaptive law is:

[0052]

[0053] Then we have:

[0054]

[0055] Beneficial technical effects:

[0056] The invention discloses a cold atom gravimeter active vibration isolation method based on neural network sliding mode control, comprising the following steps: establishing a cold atom gravimeter active vibration isolation model; designing a sliding mode control law; designing a neural network algorithm; designing a Lyapunov function and designing an adaptive law, which solves the problem that the current control method does not consider the randomness of external disturbances such as ground vibration and model uncertainty, and by establishing an adaptive neural network sliding mode control, the vibration velocity and vibration displacement of the cold atom gravimeter active vibration isolation system converge rapidly, thereby improving the control accuracy of the cold atom gravimeter active vibration isolation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solution of the present invention, the drawings required for describing the embodiments are briefly introduced below.

[0058] Figure 1 This is a flow chart of the steps of a cold atom gravimeter active vibration isolation method based on neural network sliding mode control according to the present invention;

[0059] Figure 2 It is a structural schematic diagram of an active vibration isolation control system of a cold atom gravimeter based on neural network sliding mode control according to the present invention;

[0060] Figure 3This is a comparison diagram of the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 0.1 Hz;

[0061] Figure 4 This is a comparison diagram of the vibration velocity suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 0.1 Hz;

[0062] Figure 5 This is a comparison diagram of the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 0.2 Hz;

[0063] Figure 6 This is a comparison diagram of the vibration velocity suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 0.2 Hz;

[0064] Figure 7 This is a comparison diagram of the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 0.5 Hz;

[0065] Figure 8 This is a comparison diagram of the vibration velocity suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 0.5 Hz;

[0066] Fig. 9 This is a comparison diagram of the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 1 Hz;

[0067] Fig.10 This is a comparison diagram of the vibration velocity suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 1 Hz;

[0068] Fig.11 This is a comparison diagram of the vibration displacement suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 2 Hz;

[0069] Fig.12This is a comparison diagram of the vibration velocity suppression effect of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequency is 2 Hz;

[0070] Fig.13 This is a comparison diagram of the influence of vibration controlled by the active vibration isolation control method of a cold atom gravimeter based on neural network sliding mode control described in the present invention on the gravity measurement phase angle of the cold atom gravimeter and the influence of vibration controlled by the traditional PID control method on the gravity measurement phase angle of the cold atom gravimeter. DETAILED DESCRIPTION

[0071] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be understood as limiting the present invention.

[0072] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0073] The present invention discloses a cold atomic gravimeter active vibration isolation method based on neural network sliding mode control, see Figure 1 , specifically including the following steps:

[0074] S1: Establish the active vibration isolation model of cold atom gravimeter;

[0075] Specifically, the steps of establishing the active vibration isolation model of the cold atomic gravimeter include:

[0076]

[0077] Among them, ξ 0 is the system damping coefficient, ω 0 is the natural frequency of the system, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman reflector, is the vibration speed of the Raman reflector, is the vibration acceleration of the Raman reflector, y is the ground vibration displacement, is the ground vibration velocity, m is the mass of the Raman reflector;

[0078] Where F is represented by:

[0079] F=K VC Y VC u (2)

[0080] Where u is the controller input, K VC is the voice coil motor current gain coefficient, Y VC is the voltage-to-current gain coefficient;

[0081] Substituting F into formula (1), we get

[0082]

[0083] Let g = K VC Y VC / m,

[0084] Formula (3) can be written as:

[0085]

[0086] S2: Design sliding mode control law;

[0087] Specifically, the steps of designing the sliding mode control law include:

[0088] Assume that the expected value of the system vibration displacement is x d , is the expected value of vibration displacement x d The first-order derivative of , d is the ground vibration disturbance, |d|≤D, D is the maximum value of the ground vibration disturbance, then the sliding mode function is:

[0089]

[0090] Among them, the gain coefficient c of the sliding mode function is greater than 0, then the derivative of the sliding mode function is;

[0091]

[0092] Assuming that f and g are both known, the designed control law is:

[0093]

[0094] in, is the expected value of vibration displacement x d The second-order derivative of sgn(s), sgn(s) is the sign function, η is the gain coefficient of the sign function, and substituting (7) into (6) yields:

[0095]

[0096] If η≥D, then

[0097]

[0098] S3: Design neural network algorithms;

[0099] Specifically, the steps of designing a neural network algorithm include:

[0100] The neural network algorithm is:

[0101]

[0102] f=W T h+ε (11)

[0103] Among them, j is the jth network input of the hidden layer, is the input of the neural network, c j is the center vector value of the jth node, b j is the basis width value vector of the Gaussian basis function of the jth node, h is the output of the Gaussian basis function, W is the network weight vector, ε is the neural network approximation error, ε≤ε N , ε N is the maximum value of the neural network approximation error;

[0104] Then the approximation function of f is

[0105]

[0106] in, Estimate the weight vector for the network, and its control law is:

[0107]

[0108] Substituting (13) into (6), we can obtain:

[0109]

[0110] S4: Design Lyapunov function.

[0111] Define the Lyapunov function as:

[0112]

[0113] Where, the gain coefficient γ>0, and combining equation (13) and equation (14) we can get:

[0114]

[0115] S5: Design adaptive laws.

[0116] The designed adaptive law is:

[0117]

[0118] Then we have:

[0119]

[0120] Since the neural network approximation error ε is a very small positive real number, as long as η ≥ ε N +D, then

[0121] The structural schematic diagram of the cold atom gravimeter active vibration isolation system based on neural network sliding mode control disclosed in the present invention is shown in Figure 2 The control system includes an adaptive neural network sliding mode controller and a cold atom gravimeter vibration isolation model for the actual system. The principle of the control system is simply to achieve x→x d and

[0122] As an embodiment of the present invention, the experimental simulation parameters of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention are set as follows:

[0123] Set the system damping coefficient ξ 0 =0.1N·s·m -1 , the system natural frequency ω 0 =4.396rad, voice coil motor current gain coefficient K VC =0.1V·A -1 , voltage to current gain coefficient Y VC =7.6N·A -1 , the mass of the Raman reflector m = 10 kg; the base width value vector b of the Gaussian basis function j =0.05, center vector value The gain coefficient η of the sign function is 5, the coefficient γ is 0.015, and the gain coefficient c of the sliding mode function is 5000.

[0124] In the traditional PID control method used as the comparison group, the PID control law parameters are set as follows: proportional coefficient P = 10, integral time T i =20, integration time T d =20.

[0125] The cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention enables the vibration velocity and vibration displacement of the cold atom gravimeter active vibration isolation system to converge rapidly, greatly improving the control accuracy of the cold atom gravimeter active vibration isolation system. Figure 3-Figure 12 , showing the comparison results of the cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention and the traditional PID control method when the ground vibration frequencies are 0.1Hz, 0.2Hz, 0.5Hz, 1Hz and 2Hz respectively. Fig.13It can be seen that the vibration displacement after control by the active vibration isolation method of the cold atom gravimeter based on the neural network sliding mode control disclosed in the present invention is much smaller than the vibration displacement after control by the PID control method; the vibration speed after control by the active vibration isolation method of the cold atom gravimeter based on the neural network sliding mode control disclosed in the present invention is much smaller than the vibration speed after control by the PID control method; the influence of the vibration after control by the active vibration isolation method of the cold atom gravimeter based on the neural network sliding mode control disclosed in the present invention on the gravity measurement phase angle of the cold atom gravimeter is much smaller than the influence of the vibration after control by the traditional PID control method on the gravity measurement phase angle of the cold atom gravimeter; from the above, it can be seen that the control effect of the active vibration isolation method of the cold atom gravimeter based on the neural network sliding mode control disclosed in the present invention is far superior to the traditional PID control method.

[0126] The cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention solves the problem that the current control method does not consider the randomness of external disturbances such as ground vibration and model uncertainty. By designing an adaptive law, the method is essentially an adaptive neural network sliding mode control. The cold atom gravimeter active vibration isolation method based on neural network sliding mode control disclosed in the present invention enables the vibration velocity and vibration displacement of the cold atom gravimeter active vibration isolation system to converge rapidly, thereby improving the control accuracy of the cold atom gravimeter active vibration isolation system.

[0127] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0128] The above embodiments are only descriptions of the preferred implementation modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary engineering and technical personnel in the field should fall within the protection scope determined by the claims of the present invention.

Claims

1. A cold atom gravimeter active vibration isolation method based on neural network sliding mode control, characterized in that: The following steps are involved: Establish an active vibration isolation model for cold atom gravimeter; The steps to establish the active vibration isolation model of the cold atomic gravimeter include: Among them, ξ0 is the system damping coefficient, ω0 is the system natural frequency, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman reflector, is the vibration speed of the Raman reflector, is the vibration acceleration of the Raman reflector, y is the ground vibration displacement, is the ground vibration velocity, m is the mass of the Raman reflector; Where F is represented by: F=K VC Y VC u (2) Where u is the controller input, K VC is the voice coil motor current gain coefficient, Y VC is the voltage-to-current gain coefficient; Substituting F into formula (1), we get Let g = K VC Y VC / m, Then (3) can be written as: Design sliding mode control law; The steps to design a sliding mode control law include: Assume that the expected value of the system vibration displacement is x d , is the expected value of vibration displacement x d The first-order derivative of , d is the ground vibration disturbance, |d|≤D, D is the maximum value of the ground vibration disturbance, then the sliding mode function is: Among them, the gain coefficient c of the sliding mode function is greater than 0, then the derivative of the sliding mode function is; Assuming that f and g are both known, the designed control law is: in, is the expected value of vibration displacement x d The second-order derivative of sgn(s), sgn(s) is the sign function, η is the gain coefficient of the sign function, and substituting (7) into (6) yields: If η≥D, then Design neural network algorithms; The steps in designing a neural network algorithm include: The neural network algorithm is: f=W T h+ε (11) Among them, j is the jth network input of the hidden layer, is the input of the neural network, c j is the center vector value of the jth node, b j is the basis width value vector of the Gaussian basis function of the jth node, h is the output of the Gaussian basis function, W is the network weight vector, ε is the neural network approximation error, ε≤ε N , ε N is the maximum value of the neural network approximation error; Then the approximation function of f is in, Estimate the weight vector for the network, and its control law is: Substituting (13) into (6), we can obtain: Design Lyapunov functions; The steps to design a Lyapunov function include: Define the Lyapunov function as: Where, the gain coefficient γ>0, and combining equation (13) and equation (14) we can get: Design adaptive laws; The steps to design an adaptive law include: The adaptive law is taken as: Then we have:

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