CN113672002A - Cold atom gravimeter active vibration isolation control method based on nominal model - Google Patents

Cold atom gravimeter active vibration isolation control method based on nominal model Download PDF

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CN113672002A
CN113672002A CN202110969292.XA CN202110969292A CN113672002A CN 113672002 A CN113672002 A CN 113672002A CN 202110969292 A CN202110969292 A CN 202110969292A CN 113672002 A CN113672002 A CN 113672002A
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nominal model
cold atom
vibration isolation
active vibration
gravimeter
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CN113672002B (en
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罗东云
邓长寿
曾伟
樊莉丽
刘清平
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Jiujiang University
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Abstract

The invention provides a cold atom gravimeter active vibration isolation control method based on a nominal model, which comprises the following steps: establishing an active vibration isolation model of a cold atom gravimeter; establishing a nominal model of the real object; designing a control law of the nominal model; the control law of the active vibration isolation system of the cold atom gravimeter is designed, the problems that the randomness of external disturbance such as ground vibration and the like and model uncertainty are not considered in the existing control method are solved, the vibration speed and the vibration displacement of the active vibration isolation system of the cold atom gravimeter are rapidly converged by establishing a nominal model, and the control precision of the active vibration isolation system of the cold atom gravimeter is further improved.

Description

Cold atom gravimeter active vibration isolation control method based on nominal model
Technical Field
The invention relates to the technical field of cold atom gravimeter active vibration isolation, in particular to a cold atom gravimeter active vibration isolation control method based on a nominal model.
Background
The cold atom gravimeter is a novel quantum sensor which is rapidly developed in the last two decades, and the cold atom gravimeter has the function of realizing high-precision and high-sensitivity gravity acceleration measurement by utilizing technologies such as laser cooling, atom interference and the like. At present, the measurement precision of the cold atom gravimeter reaches micro gamma, and the cold atom gravimeter can be used in the precision engineering measurement fields of mineral resource exploration, geological structure research, oil and gas general survey, spectral identification determination in the scientific field, gravity between substances and the like.
In actual measurement, the accuracy of atomic gravity measurement is affected by ground vibration noise, raman optical phase noise, detection noise and the like, wherein the vibration noise is the most important factor affecting the atomic gravimeter. The minimum natural vibration frequency of the conventional commercial passive vibration isolation platform can be adjusted to 0.5Hz, and the passive vibration isolation platform can be used for isolating 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 that the single passive vibration isolation platform cannot meet the vibration isolation requirement of the atomic gravimeter. Although the natural vibration frequency of the whole passive vibration isolation platform can be adjusted, the natural vibration frequency is adjusted too low, the whole system can present a nonlinear effect, the ground vibration near the passive vibration isolation self-frequency is not inhibited, but becomes larger on the basis of the original vibration, so that an active vibration isolation system needs to be introduced to inhibit the vibration of the frequency band, but the active vibration isolation system is influenced by a large number of uncertain factors, and the randomness of external disturbance such as the ground vibration and the uncertainty of a model are not considered in the current control method.
Disclosure of Invention
The invention discloses a cold atom gravimeter active vibration isolation control method based on a nominal model, which solves the problems that the randomness of external disturbance such as ground vibration and the like and model uncertainty are not considered in the conventional control method, and enables the vibration speed and the vibration displacement of a cold atom gravimeter active vibration isolation system to be rapidly converged by establishing the nominal model, thereby improving the control precision of the cold atom gravimeter active vibration isolation system.
In order to achieve the purpose, the technical scheme of the invention is realized as follows:
the invention discloses a cold atom gravimeter active vibration isolation control method based on a nominal model, which comprises the following steps of:
establishing an active vibration isolation model of a cold atom gravimeter;
establishing a nominal model of the real object;
designing a control law of the nominal model;
and designing a control law of the active vibration isolation system of the cold atom gravimeter.
Further, the step of establishing the active vibration isolation model of the cold atom gravimeter comprises the following steps:
Figure BDA0003225036920000021
wherein ξ0Is the damping coefficient of the system, omega0Is the system natural vibration frequency, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman reflector,
Figure BDA0003225036920000022
is the vibration speed of the raman mirror,
Figure BDA0003225036920000023
is the vibration acceleration of the Raman reflector, y is the ground vibration displacement,
Figure BDA0003225036920000024
the ground vibration speed is adopted, and m is the mass of the Raman reflector;
let F be expressed as:
F＝KVCYVCu (2)
where u is the controller input, KVCIs the current gain coefficient of the voice coil motor, YVCIs a voltage to current gain factor;
bringing F into the formula (1) to obtain
Figure BDA0003225036920000025
(3) Formula both sides remove KVCYVCIs/m to obtain
Figure BDA0003225036920000026
Definition of
Figure BDA0003225036920000027
J＝2ξ0ω0m/KVCYVC，B＝ω0 2m/KVCYVCAnd the formula (4) is substituted, and the obtained cold atom gravimeter active vibration isolation model is as follows:
Figure BDA0003225036920000028
further, the step of establishing a nominal model of the real object comprises:
Figure BDA0003225036920000029
wherein x isnFor the vibrational displacement of the nominal model raman mirror,
Figure BDA00032250369200000210
the vibration velocity of the nominal model raman mirror,
Figure BDA0003225036920000031
vibration acceleration of Raman mirror of nominal model, μ is controller input of nominal model, Jn，BnRespectively are the nominal values of J and B;
defining the expected value of the vibration displacement as xd，
Figure BDA0003225036920000032
For vibration displacement desired value xdThe first derivative of (a) is,
Figure BDA0003225036920000033
for vibration displacement desired value xdThe second derivative of (a);
defining a nominal model with a tracking error of e ═ xn-xdIts first derivative is
Figure BDA0003225036920000034
Second derivative of
Figure BDA0003225036920000035
And substituting it into equation (6):
Figure BDA0003225036920000036
definition of m/KVCYVCAnd (7) substituting the formula to obtain a nominal model of the real object:
Figure BDA0003225036920000037
further, the step of designing a control law of the nominal model comprises:
Figure BDA0003225036920000038
substituting equation (8) into equation (9):
Figure BDA0003225036920000039
wherein h is1,h2Is a positive coefficient and satisfies sigma2+(Jn/C+h2)σ+Bn/C+h1Hurwitz, sigma is Laplace operator;
take (sigma + k)20, k > 0, gives Jn/C+h2＝2k，Bn/C+h1＝k2H is obtained by the value of k1,h2。
Further, the step of establishing a control law of the active vibration isolation system of the cold atom gravimeter comprises the following steps:
defining:
Jm≤J≤JM,Bm≤B≤BM,|d|≤dM (11)
wherein, Jm,JMIs a normal number, respectively lower and upper bound of J, Bm,BMIs a normal number, is the lower and upper bounds of B, dMAn upper bound of d;
defining: e.g. of the typen＝x-xn；
Defining the slip form surface as:
Figure BDA0003225036920000041
wherein λ > 0, and λ ═ Bn/Jn；
Defining:
Ja＝1/2(Jm+JM) (13)
Ba＝1/2(Bm+BM) (14)
obtaining a control law of the active vibration isolation system of the cold atom gravimeter:
Figure BDA0003225036920000042
wherein K and h are positive coefficients.
The beneficial technical effects are as follows:
the invention discloses a cold atom gravimeter active vibration isolation control method based on a nominal model, which comprises the following steps of: establishing an active vibration isolation model of a cold atom gravimeter; establishing a nominal model of the real object; designing a control law of the nominal model; the control law of the active vibration isolation system of the cold atom gravimeter is designed, the problems that the randomness of external disturbance such as ground vibration and the like and model uncertainty are not considered in the existing control method are solved, the vibration speed and the vibration displacement of the active vibration isolation system of the cold atom gravimeter are rapidly converged by establishing a nominal model, and the control precision of the active vibration isolation system of the cold atom gravimeter is further improved.
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In order to more clearly illustrate the technical solution of the present invention, the drawings used in the description of the embodiments will be briefly described below.
FIG. 1 is a flow chart illustrating steps of a cold atom gravimeter active vibration isolation control method based on a nominal model according to the present invention;
FIG. 2 is a diagram illustrating a structure of a control system in the active vibration isolation control method for a cold atom gravimeter based on a nominal model according to the present invention;
FIG. 3 is a diagram showing the comparison of vibration displacement after the cold atom gravimeter active vibration isolation control method based on a nominal model is controlled and the PID control method is controlled according to the invention;
FIG. 4 is a diagram comparing the vibration speed of a cold atom gravimeter according to the present invention after being controlled by a nominal model based active vibration isolation control method and a PID control method;
fig. 5 is a graph comparing the influence of the vibration on the gravity measurement phase angle of the cold atomic gravimeter after being controlled by the cold atomic gravimeter active vibration isolation control method based on the nominal model and the PID control method according to the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The invention discloses a cold atom gravimeter active vibration isolation control method based on a nominal model, which specifically comprises the following steps of:
s1: establishing an active vibration isolation model of a cold atom gravimeter;
specifically, the step of establishing the active vibration isolation model of the cold atom gravimeter comprises the following steps:
Figure BDA0003225036920000051
wherein ξ0Is the damping coefficient of the system, omega0Is the system natural vibration frequency, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman reflector,
Figure BDA0003225036920000052
is the vibration speed of the raman mirror,
Figure BDA0003225036920000053
is the vibration acceleration of the Raman reflector, y is the ground vibration displacement,
Figure BDA0003225036920000054
the ground vibration speed is adopted, and m is the mass of the Raman reflector;
let F be expressed as:
F＝KVCYVCu (2)
where u is the controller input, KVCIs the current gain coefficient of the voice coil motor, YVCIs a voltage to current gain factor;
bringing F into the formula (1) to obtain
Figure BDA0003225036920000055
(3) Formula both sides remove KVCYVCIs/m to obtain
Figure BDA0003225036920000056
Definition of
Figure BDA0003225036920000061
J＝2ξ0ω0m/KVCYVC，B＝ω0 2m/KVCYVCAnd the formula (4) is substituted, and the obtained cold atom gravimeter active vibration isolation model is as follows:
Figure BDA0003225036920000062
s2: establishing a nominal model of the real object;
specifically, the step of establishing a nominal model of the real object comprises:
Figure BDA0003225036920000063
wherein x isnFor the vibrational displacement of the nominal model raman mirror,
Figure BDA0003225036920000064
the vibration velocity of the nominal model raman mirror,
Figure BDA0003225036920000065
vibration acceleration of Raman mirror of nominal model, μ is controller input of nominal model, Jn，BnRespectively are the nominal values of J and B;
defining the expected value of the vibration displacement as xd，
Figure BDA0003225036920000066
For vibration displacement desired value xdThe first derivative of (a) is,
Figure BDA0003225036920000067
for vibration displacement desired value xdThe second derivative of (a);
defining a nominal model with a tracking error of e ═ xn-xdIts first derivative is
Figure BDA0003225036920000068
Second derivative of
Figure BDA0003225036920000069
And substituting it into equation (6):
Figure BDA00032250369200000610
definition of m/KVCYVCAnd (7) substituting the formula to obtain a nominal model of the real object:
Figure BDA00032250369200000611
s3: designing a control law of a nominal model;
specifically, the step of designing the control law of the nominal model comprises the following steps:
Figure BDA00032250369200000612
substituting equation (8) into equation (9):
Figure BDA00032250369200000613
wherein h is1,h2Is a positive coefficient and satisfies sigma2+(Jn/C+h2)σ+Bn/C+h1Hurwitz, sigma is Laplace operator;
take (sigma + k)20, k > 0, gives Jn/C+h2＝2k，Bn/C+h1＝k2H is obtained by the value of k1,h2。
S4: and designing a control law of the active vibration isolation system of the cold atom gravimeter.
Specifically, the step of establishing the control law of the active vibration isolation system of the cold atom gravimeter comprises the following steps:
defining:
Jm≤J≤JM,Bm≤B≤BM,|d|≤dM (11)
wherein, Jm,JMIs a normal number, respectively lower and upper bound of J, Bm,BMIs a normal number, is the lower and upper bounds of B, dMAn upper bound of d;
defining: e.g. of the typen＝x-xn；
Defining the slip form surface as:
Figure BDA0003225036920000071
wherein λ > 0, and λ ═ Bn/Jn；
Defining:
Ja＝1/2(Jm+JM) (13)
Ba＝1/2(Bm+BM) (14)
obtaining a control law of the active vibration isolation system of the cold atom gravimeter:
Figure BDA0003225036920000072
wherein K and h are positive coefficients.
The invention discloses a structure of an active vibration isolation control system based on a nominal model cold atom gravimeter, which is shown in figure 2, wherein the control system comprises two controllers, one of the controllers is a controller for an actual system and is used for realizing x → xnAnd
Figure BDA0003225036920000073
and the other controller is a controller for a nominal model to implement xn→xdAnd
Figure BDA0003225036920000074
thus the entire control system implements x → xdAnd
Figure BDA0003225036920000075
as an embodiment of the present invention, the experimental simulation parameters of the cold atom gravimeter active vibration isolation control method based on the nominal model disclosed in the present invention are set as follows:
damping system of setting systemXi number0＝0.1N·s·m-1Frequency of natural vibration of system omega04.396rad, current gain coefficient K of voice coil motorVC＝0.1V·A-1Voltage to current gain coefficient YVC＝7.6N·A-1Mass m of the Raman reflector is 10 kg; gain parameter k is 100, coefficient h110000, factor h2200, nominal value Jn11.6 nominal value Bn254: gain parameter K is 200, h is 0.00005, λ is 30; coefficient h is 0.00005, coefficient λ is 30, and lower bound value J of JmUpper bound of J11.1M12.1, lower bound of Bm253.9, upper bound value of BM＝254.1。
Compared with the traditional PID control method, the PID control law parameters of the cold atom gravimeter active vibration isolation system are as follows: proportional coefficient P10, integral time T i20 and a differential time Td＝20。
The invention discloses a cold atom gravimeter active vibration isolation control method based on a nominal model, which enables the vibration speed and the vibration displacement of a cold atom gravimeter active vibration isolation system to be rapidly converged and greatly improves the control precision of the cold atom gravimeter active vibration isolation system, and figures 3-5 show the comparison result of the cold atom gravimeter active vibration isolation control method based on the nominal model disclosed by the embodiment of the invention and a PID control method, and the vibration displacement after being controlled by the control method based on the nominal model is far smaller than the vibration displacement after being controlled by the PID control method; the vibration speed controlled by the control method based on the nominal model is far less than that controlled by the PID control method; the influence of the vibration based on the nominal model control method on the gravity measurement phase angle of the cold atom gravimeter is far smaller than the influence of the vibration controlled by the PID control method on the gravity measurement phase angle of the cold atom gravimeter, so that the advantage of the cold atom gravimeter active vibration isolation control method based on the nominal model disclosed by the invention is far superior to that of other control methods.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The above examples are only for describing the preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and various modifications and improvements made to the technical solution of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims (5)

1. A cold atom gravimeter active vibration isolation control method based on a nominal model is characterized by comprising the following steps:
establishing an active vibration isolation model of a cold atom gravimeter;
establishing a nominal model of the real object;
designing a control law of the nominal model;
and designing a control law of the active vibration isolation system of the cold atom gravimeter.
2. The cold atom gravimeter active vibration isolation control method based on the nominal model according to claim 1, wherein the step of establishing the cold atom gravimeter active vibration isolation model includes:
Figure FDA0003225036910000011
wherein ξ0Is the damping coefficient of the system, omega0Is the system natural vibration frequency, F is the force generated by the voice coil motor, x is the vibration displacement of the Raman reflector,
Figure FDA0003225036910000012
is a Raman reflectorThe speed of vibration of the vibration means (c),
Figure FDA0003225036910000013
is the vibration acceleration of the Raman reflector, y is the ground vibration displacement,
Figure FDA0003225036910000014
the ground vibration speed is adopted, and m is the mass of the Raman reflector;
let F be expressed as:
F＝KVCYVCu (2)
where u is the controller input, KVCIs the current gain coefficient of the voice coil motor, YVCIs a voltage to current gain factor;
bringing F into the formula (1) to obtain
Figure FDA0003225036910000015
(3) Formula both sides remove KVCYVCIs/m to obtain
Figure FDA0003225036910000016
Definition of
Figure FDA0003225036910000017
J＝2ξ0ω0m/KVCYVC，B＝ω0 2m/KVCYVCAnd the formula (4) is substituted, and the obtained cold atom gravimeter active vibration isolation model is as follows:
Figure FDA0003225036910000018
。
3. the cold atom gravimeter active vibration isolation control based on nominal model as set forth in claim 2
A method, characterized in that the step of establishing a nominal model of the real object comprises:
Figure FDA0003225036910000021
wherein x isnFor the vibrational displacement of the nominal model raman mirror,
Figure FDA0003225036910000022
the vibration velocity of the nominal model raman mirror,
Figure FDA0003225036910000023
vibration acceleration of Raman mirror of nominal model, μ is controller input of nominal model, Jn，BnRespectively are the nominal values of J and B;
defining the expected value of the vibration displacement as xd，
Figure FDA0003225036910000024
For vibration displacement desired value xdThe first derivative of (a) is,
Figure FDA0003225036910000025
for vibration displacement desired value xdThe second derivative of (a);
defining a nominal model with a tracking error of e ═ xn-xdIts first derivative is
Figure FDA0003225036910000026
Second derivative of
Figure FDA0003225036910000027
And substituting it into equation (6):
Figure FDA0003225036910000028
definition of m/KVCYVCAnd (7) substituting the formula to obtain a nominal model of the real object:
Figure FDA0003225036910000029
。
4. the active vibration isolation control method for the cold atom gravimeter based on the nominal model as claimed in claim 3, wherein the step of designing the control law of the nominal model comprises:
Figure FDA00032250369100000210
substituting equation (8) into equation (9):
Figure FDA00032250369100000211
wherein h is1,h2Is a positive coefficient and satisfies sigma2+(Jn/C+h2)σ+Bn/C+h1Hurwitz, sigma is Laplace operator;
take (sigma + k)20, k > 0, gives Jn/C+h2＝2k，Bn/C+h1＝k2H is obtained by the value of k1,h2。
5. The cold atom gravimeter active vibration isolation control method based on the nominal model according to claim 4, wherein the step of establishing a control law of the cold atom gravimeter active vibration isolation system includes:
defining:
Jm≤J≤JM,Bm≤B≤BM,|d|≤dM (11)
wherein, Jm,JMIs a normal number, respectively lower and upper bound of J, Bm,BMIs aConstants, lower and upper bounds of B, dMAn upper bound of d;
defining: e.g. of the typen＝x-xn；
Defining the slip form surface as:
Figure FDA0003225036910000031
wherein λ > 0, and λ ═ Bn/Jn；
Defining:
Ja＝1/2(Jm+JM) (13)
Ba＝1/2(Bm+BM) (14)
obtaining a control law of the active vibration isolation system of the cold atom gravimeter:
Figure FDA0003225036910000032
wherein K and h are positive coefficients.
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