Active vibration isolation method for mobile cold atom gravimeter based on nonlinear sliding mode differentiator

Abstract

The invention provides a cold atom gravimeter active vibration isolation control method based on a nonlinear sliding mode differentiator, comprising the following steps: establishing an active vibration isolation model of a mobile cold atom gravimeter; designing a second-order nonlinear sliding mode differentiator; designing parameters of the second-order nonlinear sliding mode differentiator; designing a control law of an active vibration isolation system of the mobile cold atom gravimeter, which can accurately describe ground vibrations encountered by the cold atom gravimeter in a mobile measurement process, random vibrations caused by a natural environment, etc., and through the control of the second-order nonlinear sliding mode differentiator, the vibration velocity and vibration displacement of the active vibration isolation system of the mobile cold atom gravimeter converge rapidly, thereby effectively improving the control accuracy of the active vibration isolation system of the mobile cold atom gravimeter.

Description

Technical Field

[0001] The invention relates to the technical field of active vibration isolation of a mobile cold atom gravimeter, and in particular to an active vibration isolation method of a mobile cold atom gravimeter based on a nonlinear sliding mode differentiator. 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. With the rapid development of cold atom gravimeter engineering, the development of mobile, high-precision cold atom gravimeter has become a major development trend. Mobile cold atom gravimeter can be used in basic geological surveys, resource exploration and geophysical research, large submarine detection, underwater navigation and deep space microgravity detection.

[0003] Field mobile gravity measurement installs the cold atom gravimeter on mobile carriers such as vehicles, ships, and aircraft to achieve dynamic measurement while the carrier is in motion. However, environmental vibration and noise seriously affect the accuracy of the cold atom gravimeter during mobile measurement in field environments.

[0004] In actual measurements, interference is common in the controlled system of the mobile cold atom gravimeter. Interference seriously affects the control accuracy of the system and may even cause the control mechanism of the system to fail. Compared with a quiet laboratory, in addition to the influence of ground vibration, high-frequency vibration interference is much greater, and its influence on the cold atom gravimeter cannot be ignored; airflow applied to the active vibration isolation platform will also cause vertical vibration, and the input and output responses show nonlinear random characteristics; the magnetic force generated by the magneto-optical trap of the cold atom gravimeter will also be applied to the platform to cause vibration. The existing methods for controlling environmental noise have many bottlenecks, and passive vibration isolation methods cannot eliminate low-frequency noise; and the existing active vibration isolation methods are mainly aimed at static measurements in laboratories, and their active vibration isolation models cannot accurately describe the influence of multi-source vibration interference, and therefore cannot meet the requirements of changes in the vibration environment. Summary of the invention

[0005] The present invention discloses an active vibration isolation method for a mobile cold atom gravimeter based on a nonlinear sliding mode differentiator, which solves the problem that the existing passive vibration isolation method cannot eliminate low-frequency noise; the existing active vibration isolation method is mainly aimed at static measurement, but cannot accurately describe the multi-source vibration interference, resulting in low control accuracy of the vibration isolation system. The method can accurately describe the ground vibration encountered by the cold atom gravimeter in the mobile measurement process and the random vibration caused by the natural environment. Through the control of the second-order nonlinear sliding mode differentiator, the vibration velocity and vibration displacement of the active vibration isolation system of the mobile cold atom gravimeter converge rapidly, effectively improving the control accuracy of the active vibration isolation system of the mobile cold atom gravimeter.

[0006] To achieve the above object, the technical solution of the present invention is specifically implemented as follows:

[0007] The present invention discloses an active vibration isolation method for a mobile cold atomic gravimeter based on a nonlinear sliding mode differentiator, comprising the following steps:

[0008] Establish an active vibration isolation model for a mobile cold atom gravimeter;

[0009] Design a second-order nonlinear sliding mode differentiator;

[0010] Design parameters of second-order nonlinear sliding mode differentiator;

[0011] Design the control law for the active vibration isolation system of a mobile cold atom gravimeter.

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

[0013]

[0014] 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 mirror, is the vibration acceleration of the Raman reflector, d1 is the ground vibration displacement, is the ground vibration velocity, d2 is the vibration displacement caused by the natural environment, is the vibration velocity caused by the natural environment, m is the mass of the Raman reflector;

[0015] Let F be:

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

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

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

[0019]

[0020] definition:

[0021]

[0022] Then formula (3) can be written as:

[0023]

[0024] Furthermore, the steps of designing a second-order nonlinear sliding mode differentiator include:

[0025]

[0026] Among them, ν1 and ν2 are two state variables, λ and α are two adjustable parameters of the second-order nonlinear sliding mode differentiator, is the first-order derivative of the state variable ν1, is the first-order derivative of the state variable ν2, which can realize ν1 tracking x, is the first-order derivative of the state variable ν2, which can realize ν2 tracking sign is the sign function.

[0027] Furthermore, the design of the parameters of the second-order nonlinear sliding mode differentiator must meet the following constraints:

[0028]

[0029] Wherein, the gain parameter C is the maximum value of the Lipschitz constant of x.

[0030] Furthermore, the control law of the active vibration isolation system of the mobile cold atom gravimeter is designed as:

[0031] Define the expected value of the vibration displacement as x d , is the expected value of vibration displacement x d The first-order derivative of , the designed controller u is:

[0032]

[0033] Among them, k1 and k2 are gain parameters.

[0034] Beneficial technical effects:

[0035] The invention discloses an active vibration isolation method for a mobile cold atom gravimeter based on a nonlinear sliding mode differentiator, comprising the following steps: establishing an active vibration isolation model of the mobile cold atom gravimeter; designing a second-order nonlinear sliding mode differentiator; designing parameters of the second-order nonlinear sliding mode differentiator; designing a control law of an active vibration isolation system of the mobile cold atom gravimeter, which can accurately describe ground vibrations encountered by the cold atom gravimeter in a mobile measurement process, random vibrations caused by a natural environment, etc., and through the control of the second-order nonlinear sliding mode differentiator, the vibration velocity and vibration displacement of the active vibration isolation system of the mobile cold atom gravimeter converge rapidly, thereby effectively improving the control accuracy of the active vibration isolation system of the mobile cold atom gravimeter. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solution of the present invention, the drawings required for describing the embodiments are briefly introduced below.

[0037] Figure 1 It is a flowchart of the steps of the active vibration isolation method of a mobile cold atom gravimeter based on a second-order nonlinear sliding mode differentiator according to the present invention;

[0038] Figure 2 When the ground vibration frequency is 0.1Hz and the amplitude is a sine wave of 1mm, the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm;

[0039] Figure 3 When the ground vibration frequency is 0.5Hz and the amplitude is a sine wave of 1mm, the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm;

[0040] Figure 4 When the ground vibration frequency is 1Hz and the amplitude is a sine wave of 1mm, the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm;

[0041] Figure 5 When the ground vibration frequency is 5Hz and the amplitude is a sine wave of 1mm, the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm;

[0042] Figure 6 When the ground vibration frequency is 0.1Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration displacement suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0043] Figure 7 When the ground vibration frequency is 0.1Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration velocity suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0044] Figure 8 When the ground vibration frequency is 0.5Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration displacement suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0045] Fig. 9When the ground vibration frequency is 0.5Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration velocity suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0046] Fig.10 When the ground vibration frequency is 1Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration displacement suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0047] Fig.11 When the ground vibration frequency is 1Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration velocity suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0048] Fig.12 When the ground vibration frequency is 5Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration displacement suppression effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator of the present invention is compared with the PID control method;

[0049] Fig.13 When the ground vibration frequency is 5Hz, the amplitude is 1mm of the sine wave, and the external environment vibration interference is a random interference signal with a burr signal amplitude of 0.5mm, the vibration velocity suppression effect of the mobile cold atom gravimeter active vibration isolation method based on nonlinear sliding mode differentiator described in the present invention is compared with that of the PID control method. DETAILED DESCRIPTION

[0050] 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.

[0051] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0052] Unless otherwise specifically stated, the relative arrangement of the parts and steps described in these embodiments, numerical expressions and numerical values ​​do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to ordinary technicians in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be regarded as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0053] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0054] The present invention discloses an active vibration isolation method for a mobile cold atomic gravimeter based on a nonlinear sliding mode differentiator, see Figure 1 , specifically including:

[0055] S1: Establish an active vibration isolation model for a mobile cold atom gravimeter;

[0056] Specifically, the steps of establishing the active vibration isolation model of the mobile cold atom gravimeter include:

[0057]

[0058] 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, d1 is the ground vibration displacement, is the ground vibration velocity, d2 is the vibration displacement caused by the natural environment, is the vibration velocity caused by the natural environment, m is the mass of the Raman reflector;

[0059] Let F be:

[0060] F=KVC Y VC u (2)

[0061] Among them, u is the controller, K VC is the current gain coefficient of the voice coil motor, Y VC is the voltage-to-current gain coefficient;

[0062] Substituting F into formula (1), we get

[0063]

[0064] definition:

[0065]

[0066] Then formula (3) can be written as:

[0067]

[0068] Formula (4) is the expression of the active vibration isolation model of the mobile cold atom gravimeter.

[0069] S2: Design of a second-order nonlinear sliding mode differentiator;

[0070] It is important to understand that the second-order nonlinear sliding mode differentiator can track and accurately derive the input signal and is robust to noise in the input signal.

[0071] Specifically, the steps of designing a second-order nonlinear sliding mode differentiator include:

[0072]

[0073] Among them, ν1 and ν2 are two state variables, λ and α are two adjustable parameters of the second-order nonlinear sliding mode differentiator, is the first-order derivative of the state variable ν1, is the first-order derivative of the state variable ν2, which can realize ν1 tracking x, is the first-order derivative of the state variable ν2, which can realize ν2 tracking sign is the sign function.

[0074] S3: Design parameters of second-order nonlinear sliding mode differentiator;

[0075] Specifically, in order to ensure the tracking effect of the second-order nonlinear sliding mode differentiator, the designed second-order nonlinear sliding mode differentiator parameters must meet the following constraints:

[0076]

[0077] Wherein, the gain parameter C is the maximum value of the Lipschitz constant of x.

[0078] S4: Design the control law for the active vibration isolation system of a mobile cold atom gravimeter.

[0079] Specifically, the control law of the active vibration isolation system of the mobile cold atom gravimeter is designed as:

[0080] Define the expected value of the vibration displacement as x d , is the expected value of vibration displacement x d The first-order derivative of , the designed controller u is:

[0081]

[0082] Among them, k1 and k2 are gain parameters.

[0083] As an embodiment of the present invention, the experimental simulation parameters of the active vibration isolation method of a mobile cold atom gravimeter based on a nonlinear sliding mode differentiator disclosed in the present invention are set as follows:

[0084] Set the system damping coefficient ξ0 = 0.1N·s·m -1 , system self-oscillation frequency ω0 = 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 gain parameter C = 1 of the second-order nonlinear sliding mode differentiator, the adjustable parameter λ = 10 of the second-order nonlinear sliding mode differentiator, the adjustable parameter α = 15 of the second-order nonlinear sliding mode differentiator, the gain parameter k1 = 10, and the gain parameter k2 = 0.5.

[0085] Compared with the traditional PID control method, the PID control law parameters of the cold atomic gravimeter active vibration isolation system are: proportional coefficient P = 10, integral time T i =20 and differential time T d =20.

[0086] The active vibration isolation method for a mobile cold atom gravimeter based on a nonlinear sliding mode differentiator disclosed in the present invention enables the vibration velocity and vibration displacement of the active vibration isolation system of the mobile cold atom gravimeter to converge rapidly, thereby greatly improving the control accuracy of the active vibration isolation system of the mobile cold atom gravimeter. Figure 6-Figure 13, respectively showing 0.1Hz frequency, 1mm amplitude ground vibration and 0.5mm amplitude external environment interference burr signal vibration, 0.5Hz frequency, 1mm amplitude ground vibration and 0.5mm amplitude external environment interference burr signal vibration, 1Hz frequency, 1mm amplitude ground vibration and 0.5mm amplitude external environment interference burr signal vibration, 5Hz frequency, 1mm amplitude ground vibration and 0.5mm amplitude external environment interference burr signal vibration, the results of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator disclosed in the present invention are compared with the traditional PID control method after control. It can be seen from the figure that the vibration displacement of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator disclosed in the present invention after control is much smaller than the vibration displacement of the PID control method, and the vibration speed of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator disclosed in the present invention after control is much smaller than the vibration speed of the PID control method; from the above, it can be seen that the control effect of the mobile cold atom gravimeter active vibration isolation method based on the nonlinear sliding mode differentiator disclosed in the present invention is far superior to the traditional PID control method.

[0087] The present invention discloses an active vibration isolation method for a mobile cold atom gravimeter based on a nonlinear sliding mode differentiator, which solves the problem that the current passive vibration isolation method cannot eliminate low-frequency noise. The existing active vibration isolation method is mainly aimed at static measurement, but cannot accurately describe multi-source vibration interference, resulting in low control accuracy of the vibration isolation system. The present invention can accurately describe the ground vibration encountered by the cold atom gravimeter during mobile measurement, random vibration caused by the natural environment, etc. Through the control of a second-order nonlinear sliding mode differentiator, the vibration velocity and vibration displacement of the active vibration isolation system of the mobile cold atom gravimeter converge rapidly, effectively improving the control accuracy of the active vibration isolation system of the mobile cold atom gravimeter.

[0088] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0089] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0090] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0091] 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.

[0092] 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. Active vibration isolation method for mobile cold atom gravimeter based on nonlinear sliding mode differentiator, characterized in that: The following steps are involved: Establish an active vibration isolation model for a mobile cold atom gravimeter; Design a second-order nonlinear sliding mode differentiator; Design parameters of second-order nonlinear sliding mode differentiator; Design the control law of the active vibration isolation system of the mobile cold atom gravimeter; The steps to establish the active vibration isolation model of the mobile cold atom 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, d1 is the ground vibration displacement, is the ground vibration velocity, d2 is the vibration displacement caused by the natural environment, is the vibration velocity caused by the natural environment, m is the mass of the Raman reflector; Let F be: F=K VC Y VC u(2) Among them, u is the controller, 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 definition: Then formula (3) can be written as: The steps to design a second-order nonlinear sliding mode differentiator include: Among them, v1 and v2 are two state variables, λ and α are two adjustable parameters of the second-order nonlinear sliding mode differentiator, is the first-order derivative of the state variable v1, is the first-order derivative of the state variable v2, which can realize v1 tracking x. is the first-order derivative of the state variable v2, which can realize v2 tracking sign is the sign function; The design of the parameters of the second-order nonlinear sliding mode differentiator must meet the following constraints: Wherein, the gain parameter C is the maximum value of the Lipschitz constant of x; The control law of the active vibration isolation system of the mobile cold atom gravimeter is designed as follows: Define the expected value of the vibration displacement as x d , is the expected value of vibration displacement x d The first-order derivative of , the designed controller u is: Among them, k1 and k2 are gain parameters.

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