CN113848721B - Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control - Google Patents

Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control Download PDF

Info

Publication number
CN113848721B
CN113848721B CN202111177535.2A CN202111177535A CN113848721B CN 113848721 B CN113848721 B CN 113848721B CN 202111177535 A CN202111177535 A CN 202111177535A CN 113848721 B CN113848721 B CN 113848721B
Authority
CN
China
Prior art keywords
vibration isolation
gain
active vibration
sliding mode
cold atom
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202111177535.2A
Other languages
Chinese (zh)
Other versions
CN113848721A (en
Inventor
罗东云
邓长寿
张波
彭辉
刘清平
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Jiujiang University
Original Assignee
Jiujiang University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Jiujiang University filed Critical Jiujiang University
Priority to CN202111177535.2A priority Critical patent/CN113848721B/en
Publication of CN113848721A publication Critical patent/CN113848721A/en
Application granted granted Critical
Publication of CN113848721B publication Critical patent/CN113848721B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The invention provides a cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control, which comprises the following steps: establishing an active vibration isolation model of the cold atom gravity meter; designing a high-gain observer of an active vibration isolation system of the cold atom gravity meter, and observing uncertainty of internal parameter change of the active vibration isolation system and uncertain disturbance of external ground vibration; the sliding mode control law of the high-gain observer is designed, the problem that the external disturbance randomness such as ground vibration and the uncertainty of a model are not considered in the existing control method is solved, and the vibration speed and the vibration displacement of the active vibration isolation system of the cold atom gravity meter are rapidly converged by establishing the sliding mode control method of the high-gain observer, so that the control precision of the active vibration isolation system of the cold atom gravity meter is improved.

Description

Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control
Technical Field
The invention relates to the technical field of active vibration isolation of cold atom gravimeters, in particular to an active vibration isolation method of a cold atom gravimeter based on sliding mode control of a high-gain observer.
Background
Cold atom gravity meter is a new type quantum sensor developed rapidly in last twenty years, and its function is to realize high precision and high sensitivity gravity acceleration measurement by using laser cooling, atom interference and other techniques. At present, the measurement precision of the cold atom gravity meter reaches the micro-gamma, and the cold atom gravity meter can be used in the precision engineering measurement fields of mineral resource exploration, geological structure research, oil and gas general investigation, scientific field spectrum identification, inter-substance gravitation and the like.
In actual measurement, the accuracy of atomic gravity measurement receives the influence of ground vibration noise, raman optical phase noise, detection noise and the like, wherein vibration noise is the most important factor influencing an atomic gravity meter. The minimum self-vibration frequency of the current 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 an atomic gravimeter, but the atomic gravimeter is more sensitive to the vibration of 0.1-10Hz, so that the vibration isolation requirement of the atomic gravimeter cannot be met by a pure passive vibration isolation platform. Although the self-vibration frequency of the whole passive vibration isolation platform can be adjusted, the self-vibration frequency is adjusted too low, the whole system can show a nonlinear effect, ground vibration near the self-vibration frequency of the passive vibration isolation platform is not restrained, but rather the ground vibration is enlarged on the basis of original vibration, so that an active vibration isolation system is required to be introduced to restrain the vibration of the frequency band, the active vibration isolation system is influenced by a large number of uncertain factors, and the randomness of external disturbance such as ground vibration and the uncertainty of a model are not considered in the current control method.
Disclosure of Invention
The cold atom gravity meter active vibration isolation method based on the high-gain observer sliding mode control solves the problem that the external disturbance randomness such as ground vibration and the model uncertainty are not considered in the existing control method, and the vibration speed and the vibration displacement of the cold atom gravity meter active vibration isolation system are quickly converged by establishing the high-gain observer sliding mode control, so that the control precision of the cold atom gravity meter active vibration isolation system is improved.
In order to achieve the above purpose, the technical scheme of the invention is specifically realized as follows:
the invention discloses a cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control, which comprises the following steps:
establishing an active vibration isolation model of the cold atom gravity meter;
designing a high-gain observer of an active vibration isolation system of the cold atom gravity meter, and observing uncertainty of internal parameter change of the active vibration isolation system and uncertain disturbance of external ground vibration;
and designing a sliding mode control law of the high-gain observer.
Further, the step of establishing an active vibration isolation model of the cold atom gravity meter comprises the following steps:
Figure BDA0003295889400000021
wherein ,ξ0 Omega is the damping coefficient of the system 0 The self-oscillation frequency of the system is represented by x, the vibration displacement of the Raman reflector,
Figure BDA0003295889400000022
for the vibration speed of the raman mirror, +.>
Figure BDA0003295889400000023
The vibration acceleration of the Raman reflector, y is ground vibration displacement, < >>
Figure BDA0003295889400000024
The ground vibration speed, m is the mass of the Raman reflector, u is the input of the controller, K VC For the current gain coefficient of the voice coil motor, Y VC The gain coefficient is the gain coefficient of voltage to current;
definition:
Figure BDA0003295889400000025
b＝K VC Y VC /m；
k 1 ＝-2ξ 0 ω 0 ；
k 2 ＝-ω 0 2
and bringing the cold atom gravity meter into the formula (1) to obtain an active vibration isolation model of the cold atom gravity meter, wherein the active vibration isolation model is as follows:
Figure BDA0003295889400000026
further, the step of designing the high-gain observer of the active vibration isolation system of the cold atom gravity meter comprises the following steps:
formula (2) is represented by:
Figure BDA0003295889400000027
wherein ,
Figure BDA0003295889400000028
C＝[1 0]；/>
Figure BDA0003295889400000029
the I f (t) I is less than or equal to L; l is a normal number, the upper bound of f (t);
the high gain observer is designed to:
Figure BDA0003295889400000031
wherein
Figure BDA0003295889400000032
Alpha, being the observer state value 1 ,α 2 ,α 3 Epsilon is a coefficient, and alpha 1 ＞0,α 2 ＞0,α 3 ＞0,ε＞0；
Definition:
η＝[η 1 η 2 η 3 ] T (5)
as a result of:
Figure BDA0003295889400000033
Figure BDA0003295889400000034
Figure BDA0003295889400000035
wherein
Figure BDA0003295889400000036
For the first derivative of f (t), the observed error state is: />
Figure BDA0003295889400000037
wherein ,
Figure BDA0003295889400000038
matrix array
Figure BDA0003295889400000039
The characteristic equation of (2) is:
Figure BDA00032958894000000310
then there are:
(λ+α 1 )λ 2 +α 2 λ+α 3 ＝0；
and lambda is 3 +α 1 λ 2 +α 2 λ+α 3 ＝0；
Select alpha i (i=1, 2, 3) to matrix
Figure BDA0003295889400000041
Is Hurwitz; then for any given symmetric positive definite matrix Q, there is a symmetric positive definite matrix W that satisfies the Lyapunov equation, namely:
Figure BDA0003295889400000042
the Lyapunov function defining the high gain observer is:
V 0 ＝εU T WU (12)
then:
Figure BDA0003295889400000043
wherein U is the norm of U,
Figure BDA0003295889400000044
is->
Figure BDA0003295889400000045
Is (are) norms of->
Figure BDA0003295889400000046
Is->
Figure BDA0003295889400000047
Is a norm of (1), and:
Figure BDA0003295889400000048
wherein λmin (Q) is the minimum eigenvalue of Q;
from the following components
Figure BDA0003295889400000049
The convergence conditions for the available high gain observer are:
Figure BDA00032958894000000410
further, the step of designing a sliding mode control law of the high gain observer comprises:
designing a sliding mode function:
define the expected value of vibration displacement as x 1d ，
Figure BDA00032958894000000411
Expected value x for vibration displacement d First derivative of>
Figure BDA00032958894000000412
For vibration
Expected value x of dynamic displacement 1d Is a second derivative of (2);
Figure BDA00032958894000000413
wherein c > 0, e=x-x 1d ；
Designing a sliding mode controller based on a dilation observer:
Figure BDA00032958894000000414
wherein ,
Figure BDA0003295889400000051
lyapunov function V of sliding mode controller s ＝1/2s 2 Then:
Figure BDA0003295889400000052
wherein ,
Figure BDA0003295889400000053
taking out
Figure BDA0003295889400000054
Then:
Figure BDA0003295889400000055
taking α=2k g -1,f(t)＝1/2Δ 2 max The solution of the inequality equation is:
Figure BDA0003295889400000056
taking k g > 1/2, then:
Figure BDA0003295889400000057
due to V s (t) is 0 or more, so V at t.fwdarw.infinity s (t)≤1/2(2k g -1)Δ 2 max The convergence speed depends on the gain k of the controller g And observer parameters epsilon.
The beneficial technical effects are as follows:
the invention discloses a cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control, which comprises the following steps: establishing an active vibration isolation model of the cold atom gravity meter; designing a high-gain observer of an active vibration isolation system of the cold atom gravity meter, and observing uncertainty of internal parameter change of the active vibration isolation system and uncertain disturbance of external ground vibration; the control law of the sliding mode of the high-gain observer is designed, the problem that the external disturbance randomness such as ground vibration and the uncertainty of a model are not considered in the existing control method is solved, and the vibration speed and the vibration displacement of the active vibration isolation system of the cold atom gravity meter are rapidly converged by establishing the sliding mode control of the high-gain observer, so that the control precision of the active vibration isolation system of the cold atom gravity meter is improved.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings that are used in the description of the embodiments will be briefly described.
FIG. 1 is a flow chart of the steps of the active vibration isolation method of the cold atomic gravimeter based on the sliding mode control of the high-gain observer;
FIG. 2 shows a comparison of the vibration speed suppression effect of the cold atom gravity meter active vibration isolation method based on the sliding mode control of the high-gain observer and the PID control method according to the invention when the ground vibration frequency is 0.1 Hz;
FIG. 3 shows a comparison of the vibration displacement suppression effect of the cold atom gravity meter active vibration isolation method based on the sliding mode control of the high-gain observer and the PID control method according to the invention when the ground vibration frequency is 0.1 Hz;
FIG. 4 shows a comparison of vibration displacement inhibition effects of the cold atom gravity meter active vibration isolation method based on the sliding mode control of the high-gain observer and the PID control method according to the invention when the ground vibration frequency is 10 Hz;
FIG. 5 shows the comparison of the vibration speed inhibition effect of the cold atom gravity meter active vibration isolation method based on the sliding mode control of the high-gain observer and the PID control method according to the invention when the ground vibration frequency is 10 Hz;
FIG. 6 shows a comparison of vibration displacement inhibition effects of the cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control and the PID control method according to the invention when the ground vibration frequency is 1 Hz;
fig. 7 is a comparison of vibration speed inhibition effect of the active vibration isolation method of the cold atom gravity meter based on the sliding mode control of the high-gain observer and the PID control method when the ground vibration frequency is 1 Hz.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
The invention discloses a cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control, which is shown in fig. 1 and specifically comprises the following steps:
s1: establishing an active vibration isolation model of the cold atom gravity meter;
specifically, the step of establishing an active vibration isolation model of the cold atom gravimeter comprises the following steps:
Figure BDA0003295889400000071
wherein ,ξ0 Omega is the damping coefficient of the system 0 The self-oscillation frequency of the system is represented by x, the vibration displacement of the Raman reflector,
Figure BDA0003295889400000072
for the vibration speed of the raman mirror, +.>
Figure BDA0003295889400000073
The vibration acceleration of the Raman reflector, y is ground vibration displacement, < >>
Figure BDA0003295889400000074
For the ground vibration speed, m is the mass u of the Raman reflector and is input by the controller, K VC For the current gain coefficient of the voice coil motor, Y VC The gain coefficient is the gain coefficient of voltage to current;
definition:
Figure BDA0003295889400000075
b＝K VC Y VC /m；
k 1 ＝-2ξ 0 ω 0 ；
k 2 ＝-ω 0 2
and bringing the cold atom gravity meter into the formula (1) to obtain an active vibration isolation model of the cold atom gravity meter, wherein the active vibration isolation model is as follows:
Figure BDA0003295889400000076
s2: designing a high-gain observer of an active vibration isolation system of the cold atom gravity meter, and observing uncertainty of internal parameter change of the active vibration isolation system and uncertain disturbance of external ground vibration;
specifically, the step of designing a high-gain observer of an active vibration isolation system of the cold atom gravity meter comprises the following steps:
formula (2) is represented by:
Figure BDA0003295889400000077
wherein ,
Figure BDA0003295889400000078
C＝[1 0]；/>
Figure BDA0003295889400000079
the I f (t) I is less than or equal to L; l is a normal number, the upper bound of f (t);
the high gain observer is designed to:
Figure BDA0003295889400000081
wherein
Figure BDA0003295889400000082
Alpha, being the observer state value 1 ,α 2 ,α 3 Epsilon is a coefficient, and alpha 1 ＞0,α 2 ＞0,α 3 ＞0,ε＞0；
Definition:
η＝[η 1 η 2 η 3 ] T (5)
as a result of:
Figure BDA0003295889400000083
Figure BDA0003295889400000084
Figure BDA0003295889400000085
wherein
Figure BDA0003295889400000086
For the first derivative of f (t), the observed error state is:
Figure BDA0003295889400000087
wherein ,
Figure BDA0003295889400000088
matrix array
Figure BDA0003295889400000089
The characteristic equation of (2) is:
Figure BDA00032958894000000810
then there are:
(λ+α 1 )λ 2 +α 2 λ+α 3 ＝0；
and lambda is 3 +α 1 λ 2 +α 2 λ+α 3 ＝0；
Select alpha i (i=1, 2, 3) to matrix
Figure BDA0003295889400000091
Is Hurwitz; then for any given symmetric positive definite matrix Q, there is a symmetric positive definite matrix W that satisfies the Lyapunov equation, namely:
Figure BDA0003295889400000092
the Lyapunov function defining the high gain observer is:
V 0 ＝εU T WU (12)
then:
Figure BDA0003295889400000093
wherein U is the norm of U,
Figure BDA0003295889400000094
is->
Figure BDA0003295889400000095
Is (are) norms of->
Figure BDA0003295889400000096
Is->
Figure BDA0003295889400000097
Is a norm of (1), and:
Figure BDA0003295889400000098
wherein λmin (Q) is the minimum eigenvalue of Q;
from the following components
Figure BDA0003295889400000099
The convergence conditions for the available high gain observer are:
Figure BDA00032958894000000910
s3: designing a sliding mode control law of a high-gain observer;
specifically, the step of designing a sliding mode control law of the high gain observer includes:
designing a sliding mode function:
define the expected value of vibration displacement as x 1d ，
Figure BDA00032958894000000911
Expected value x for vibration displacement 1d First derivative of>
Figure BDA00032958894000000912
Expected value x for vibration displacement 1d Is a second derivative of (2);
Figure BDA00032958894000000913
wherein c > 0, e=x-x 1d ；
Designing a sliding mode controller based on a dilation observer:
Figure BDA00032958894000000914
wherein ,
Figure BDA0003295889400000101
lyapunov function V of sliding mode controller s ＝1/2s 2 Then:
Figure BDA0003295889400000102
/>
wherein ,
Figure BDA0003295889400000103
taking out
Figure BDA0003295889400000104
Then:
Figure BDA0003295889400000105
taking α=2k g -1,f(t)＝1/2Δ 2 max The solution of the inequality equation is:
Figure BDA0003295889400000106
taking k g > 1/2, then:
Figure BDA0003295889400000107
due to V s (t) is 0 or more, so V at t.fwdarw.infinity s (t)≤1/2(2k g -1)Δ 2 max The convergence speed depends on the gain k of the controller g And observer parameters epsilon; considering the closed loop system of the high gain observer and the controller comprehensively, the Lyapunov function is:
V＝V s +V 0 (22)
take k large enough g And epsilon small enough to ensure V.ltoreq.0, i.e. convergence speed dependent on the controller gain k g And observer parameters epsilon.
As one embodiment of the invention, experimental simulation parameters of the cold atom gravity meter active vibration isolation method based on the high-gain observer sliding mode control disclosed by the invention are set as follows:
setting a system damping coefficient xi 0 ＝0.1N·s·m -1 System self-oscillation frequency omega 0 4.396rad, the current gain factor K of the voice coil motor VC ＝0.1V·A -1 Gain factor Y of voltage-to-current VC ＝7.6N·A -1 The mass of the raman mirror m=10kg; gain parameter alpha 1 =6, gain parameter α 2 =11, gain parameter α 3 =6, coefficient c=50, coefficient d=10, controller gain k g Observer parameter epsilon=0.01, =1000.
As a conventional PID control method of the comparison group, PID control law parameters are set: proportional coefficient p=10, integration time T i =20 and differential time T d ＝20。
The invention discloses a cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control, which adopts high-gain error feedback to improve the dynamic performance of an observer, namely the dynamic performance is equivalent to a fast-changing subsystem in a system, so that the fast convergence of an observation error and high estimation precision are ensured, and usable vibration displacement and speed signals are provided for feedback, so that the vibration speed and vibration displacement of the cold atom gravity meter active vibration isolation system are fast converged, the control precision of the cold atom gravity meter active vibration isolation system is greatly improved, and figures 2-7 show the comparison result of the cold atom gravity meter active vibration isolation control method based on the high-gain observer sliding mode control disclosed by the invention and the traditional PID control method when the ground vibration frequency is 0.1Hz, 10Hz and 1Hz respectively; the vibration speed after the control based on the sliding mode method of the high-gain observer is far smaller than the vibration speed after the control based on the PID control method, so that the advantage of the active vibration isolation method of the cold atom gravity meter based on the sliding mode control of the high-gain observer disclosed by the invention is far superior to that of other control methods.
It will be appreciated by those skilled in the art that 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 flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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 of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means 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 present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. 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 illustrative of 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 by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the design of the present invention.

Claims (1)

1. The cold atom gravity meter active vibration isolation method based on the sliding mode control of the high-gain observer is characterized by comprising the following steps of:
establishing an active vibration isolation model of the cold atom gravity meter;
designing a high-gain observer of an active vibration isolation system of the cold atom gravity meter, and observing uncertainty of internal parameter change of the active vibration isolation system and uncertain disturbance of external ground vibration;
designing a sliding mode control law of a high-gain observer;
the step of establishing the cold atom gravity meter active vibration isolation model comprises the following steps:
Figure FDA0004150204080000011
wherein ,ξ0 Omega is the damping coefficient of the system 0 The self-oscillation frequency of the system is represented by x, the vibration displacement of the Raman reflector,
Figure FDA0004150204080000012
for the vibration speed of the raman mirror, +.>
Figure FDA0004150204080000013
The vibration acceleration of the Raman reflector, y is ground vibration displacement, < >>
Figure FDA0004150204080000014
The ground vibration speed, m is the mass of the Raman reflector, u is the input of the controller, K VC For the current gain coefficient of the voice coil motor, Y VC The gain coefficient is the gain coefficient of voltage to current;
definition:
Figure FDA0004150204080000015
b＝K VC Y VC /m；
k 1 ＝-2ξ 0 ω 0 ；
k 2 ＝-ω 0 2
substituting the model into the formula (1) to obtain the active vibration isolation model of the cold atom gravimeter, wherein the active vibration isolation model is as follows:
Figure FDA0004150204080000016
the method for designing the high-gain observer of the active vibration isolation system of the cold atom gravity meter comprises the following steps of:
formula (2) is represented by:
Figure FDA0004150204080000017
wherein ,
Figure FDA0004150204080000018
C＝[1 0]；/>
Figure FDA0004150204080000019
the I f (t) I is less than or equal to L; l is a normal number, the upper bound of f (t);
the high gain observer is designed to:
Figure FDA0004150204080000021
wherein
Figure FDA0004150204080000022
Alpha, being the observer state value 1 ,α 2 ,α 3 Epsilon is a coefficient, and alpha 1 ＞0,α 2 ＞0,α 3 ＞0,ε＞0；
Definition:
η＝[η 1 η 2 η 3 ] T (5)
as a result of:
Figure FDA0004150204080000023
Figure FDA0004150204080000024
Figure FDA0004150204080000025
wherein
Figure FDA0004150204080000026
For the first derivative of f (t), the observed error state is:
Figure FDA0004150204080000027
wherein ,
Figure FDA0004150204080000028
matrix array
Figure FDA0004150204080000029
Is of (1)The sign equation is:
Figure FDA00041502040800000210
then there are:
(λ+α 1 )λ 2 +α 2 λ+α 3 ＝0；
and lambda is 3 +α 1 λ 2 +α 2 λ+α 3 ＝0；
Select alpha i (i=1, 2, 3) to matrix
Figure FDA0004150204080000031
Is Hurwitz; then for any given symmetric positive definite matrix Q, there is a symmetric positive definite matrix W that satisfies the Lyapunov equation, namely:
Figure FDA0004150204080000032
the Lyapunov function defining the high gain observer is:
V 0 ＝εU T WU (12)
then:
Figure FDA0004150204080000033
wherein U is the norm of U,
Figure FDA0004150204080000034
is->
Figure FDA0004150204080000035
Is (are) norms of->
Figure FDA0004150204080000036
Is->
Figure FDA0004150204080000037
Is a norm of (1), and:
Figure FDA0004150204080000038
wherein λmin (Q) is the minimum eigenvalue of Q;
from the following components
Figure FDA0004150204080000039
The convergence conditions for the available high gain observer are:
Figure FDA00041502040800000310
the step of designing the sliding mode control law of the high-gain observer comprises the following steps:
designing a sliding mode function:
define the expected value of vibration displacement as x 1d ，
Figure FDA00041502040800000311
Expected value x for vibration displacement 1d First derivative of>
Figure FDA00041502040800000312
Expected value x for vibration displacement 1d Is a second derivative of (2);
Figure FDA00041502040800000313
wherein c > 0, e=x-x 1d ；
Designing a sliding mode controller based on a dilation observer:
Figure FDA00041502040800000314
wherein ,
Figure FDA0004150204080000041
lyapunov function V of sliding mode controller s ＝1/2s 2 Then:
Figure FDA0004150204080000042
wherein ,
Figure FDA0004150204080000043
get->
Figure FDA0004150204080000044
Then:
Figure FDA0004150204080000045
taking α=2k g -1,f(t)＝1/2Δ 2 max The solution of the inequality equation is:
Figure FDA0004150204080000046
taking k g > 1/2, then:
Figure FDA0004150204080000047
due to V s (t) is 0 or more, so V at t.fwdarw.infinity s (t)≤1/2(2k g -1)Δ 2 max The convergence speed depends on the gain k of the controller g And observer parameters epsilon.
CN202111177535.2A 2021-10-09 2021-10-09 Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control Active CN113848721B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111177535.2A CN113848721B (en) 2021-10-09 2021-10-09 Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111177535.2A CN113848721B (en) 2021-10-09 2021-10-09 Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control

Publications (2)

Publication Number Publication Date
CN113848721A CN113848721A (en) 2021-12-28
CN113848721B true CN113848721B (en) 2023-05-16

Family

ID=78977924

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111177535.2A Active CN113848721B (en) 2021-10-09 2021-10-09 Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control

Country Status (1)

Country Link
CN (1) CN113848721B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115013473B (en) * 2022-05-31 2023-03-31 九江学院 Cold atom gravimeter active vibration isolation method based on self-adaptive fuzzy sliding mode control

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2006153129A (en) * 2004-11-29 2006-06-15 Hitachi High-Technologies Corp Active vibration-free method and its device
CN106067747A (en) * 2016-06-01 2016-11-02 哈尔滨工业大学 A kind of method for designing of the sliding formwork disturbance observer for servo system control
CN107607102A (en) * 2017-11-05 2018-01-19 西北工业大学 MEMS gyro sliding formwork based on interference observer buffets suppressing method

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104793488B (en) * 2015-01-06 2019-11-15 中国人民解放军装备学院 A kind of superfluid gyroscope Control System Design method based on automatic disturbance rejection controller
CN106406086B (en) * 2016-05-26 2019-05-07 北京航空航天大学 A kind of flexible spacecraft interference compensation method based on sliding formwork interference observer
CN106054615B (en) * 2016-07-22 2019-04-09 浙江工业大学 Ultralow frequency vein of the earth vibration atom interferometer vibration isolating method
CN106647926B (en) * 2016-11-18 2023-08-08 浙江工业大学 DDS frequency hopping device for laser time sequence control of cold atom interferometer
WO2019179882A1 (en) * 2018-03-23 2019-09-26 Fnv Ip B.V. Automated tuning of an estimator
CN111175838A (en) * 2018-11-13 2020-05-19 北京自动化控制设备研究所 High-precision modeling control method for temperature control system of inertial platform type gravimeter
DE102019006594A1 (en) * 2019-09-19 2021-03-25 Manfred Alexander Gregor Combination absolute gravimeter
CN112835294B (en) * 2021-01-07 2022-08-12 九江学院 Control method for active vibration isolation system of cold atom gravimeter

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2006153129A (en) * 2004-11-29 2006-06-15 Hitachi High-Technologies Corp Active vibration-free method and its device
CN106067747A (en) * 2016-06-01 2016-11-02 哈尔滨工业大学 A kind of method for designing of the sliding formwork disturbance observer for servo system control
CN107607102A (en) * 2017-11-05 2018-01-19 西北工业大学 MEMS gyro sliding formwork based on interference observer buffets suppressing method

Also Published As

Publication number Publication date
CN113848721A (en) 2021-12-28

Similar Documents

Publication Publication Date Title
Nakata Acceleration trajectory tracking control for earthquake simulators
Mitrovica et al. Glaciation‐induced perturbations in the Earth's rotation: A new appraisal
CN110749337B (en) MIMU error compensation method based on deep neural network
Zhang et al. Coupled microvibration analysis of a reaction wheel assembly including gyroscopic effects in its accelerance
CN113848721B (en) Cold atom gravity meter active vibration isolation method based on high-gain observer sliding mode control
CN111290015B (en) Fractional order self-sustaining type electromechanical seismograph system acceleration stability control method with constraint
Polichtchouk et al. Intercomparison of general circulation models for hot extrasolar planets
Collette et al. Sensor fusion methods for high performance active vibration isolation systems
Wen et al. A high‐order accurate explicit time integration method based on cubic b‐spline interpolation and weighted residual technique for structural dynamics
Zavershinskii et al. Mixed properties of slow magnetoacoustic and entropy waves in a plasma with heating/cooling misbalance
Leleu et al. Stability of the co-orbital resonance under dissipation-Application to its evolution in protoplanetary discs
CN112835294B (en) Control method for active vibration isolation system of cold atom gravimeter
Setiawan et al. Synchronous sensor runout and unbalance compensation in active magnetic bearings using bias current excitation
CN114879507A (en) Cold atom gravimeter active vibration isolation method based on neural network sliding mode control
CN113672002B (en) Cold atom gravimeter active vibration isolation control method based on nominal model
Cui et al. Harmonic current suppression of active-passive magnetically suspended control moment gyro based on variable-step-size FBLMS
CN106054615B (en) Ultralow frequency vein of the earth vibration atom interferometer vibration isolating method
Balik et al. Vibration control using a dedicated inertial sensor
Shapiro et al. Selection of important parameters using uncertainty and sensitivity analysis
Liang et al. The temperature compensation method for the laser gyro based on the relevance vector machine
Bhardwaj et al. Allan variance the stability analysis algorithm for MEMS based inertial sensors stochastic error
Fan et al. Stability analyses and numerical simulations of the single degree of freedom spring-slider system obeying the revised rate-and state-dependent friction law
Zhang et al. Artificial specimen damping for substructure real-time hybrid simulation
CN115013473B (en) Cold atom gravimeter active vibration isolation method based on self-adaptive fuzzy sliding mode control
Arias-Montiel et al. Finite element modeling and unbalance compensation for a two disks asymmetrical rotor system

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant