CN112520066A - Full-electric stable control method for large-orbit eccentricity multi-body tethered satellite - Google Patents

Full-electric stable control method for large-orbit eccentricity multi-body tethered satellite Download PDF

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CN112520066A
CN112520066A CN202011335416.0A CN202011335416A CN112520066A CN 112520066 A CN112520066 A CN 112520066A CN 202011335416 A CN202011335416 A CN 202011335416A CN 112520066 A CN112520066 A CN 112520066A
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史格非
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Abstract

The invention discloses a full-electric stable control method of a large-orbit eccentricity multi-body tethered satellite, which comprises the following steps: constructing a power model of a space multi-body tether satellite system based on a Lagrange method; obtaining the relation between the rope retracting speed and the stable sinusoidal oscillation according to a space multi-body rope system satellite system power model to obtain the stable retracting rate; and recovering and releasing the tether according to the stable retraction rate. The stable control problem of the multi-body tethered satellite is solved by adjusting the retraction speed of the electric rope shaft mounted on each satellite in the system to the tether. The full-electric stable control method for the large-orbit eccentricity multi-body tethered satellite can be widely applied to the field of satellite control.

Description

Full-electric stable control method for large-orbit eccentricity multi-body tethered satellite
Technical Field
The invention belongs to the field of satellite control, and particularly relates to a full-electric stable control method for a large-orbit eccentricity multi-body tethered satellite.
Background
Space multi-tethered satellite systems typically consist of multiple satellites connected in series by tethers. In order to realize wide-range space observation and atmosphere detection, a space multi-body tethered satellite system is often required to run on an elliptical orbit with large eccentricity. The larger track eccentricity will cause the system to have non-periodic swing motion, and the whole system motion is like a pendulum. The motion state not only brings great negative influence to the stability of the system and even leads to the instability of the turnover of the system, but also is not favorable for the accuracy of space observation. In order to solve this problem, conventional countermeasures are: and a thruster on the exploration satellite is used for carrying out long-term stable control on the system. The control means needs to consume working media, and the working media which can be carried by the satellite are limited, so that the requirement of a long-term detection task cannot be met. In order to realize stable control of a tethered satellite system operating in a large-eccentricity orbit and meet long-term task requirements, a reasonable control method must be adopted to inhibit the swinging of the system, and a control execution mechanism is required to consume only electric energy.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a full-electric stability control method for a large-orbit eccentricity multi-body tethered satellite, which solves the stability control problem of the multi-body tethered satellite by reasonably adjusting the winding and unwinding speeds of electric rope shafts mounted on each satellite in a system to tethers.
The technical scheme adopted by the invention is as follows: a full-electric stable control method for a large-orbit eccentricity multi-body tethered satellite comprises the following steps:
constructing a power model of a space multi-body tether satellite system based on a Lagrange method;
obtaining the relation between the rope retracting speed and the stable sinusoidal oscillation according to a space multi-body rope system satellite system power model to obtain the stable retracting rate;
and recovering and releasing the tether according to the stable retraction rate.
Further, still include:
and judging that a disturbance error exists, and adjusting the control input signal.
Further, the form of the power model of the space multi-body tethered satellite system is as follows:
Figure BDA0002797058180000011
Figure BDA0002797058180000021
Figure BDA0002797058180000022
Figure BDA0002797058180000023
in the above formula, LiRepresenting the tether length between the (i-1) th satellite and the (i) th satellite,
Figure BDA0002797058180000024
representing the true anomaly, T, of the system's dominant stari+1Is the tension of the i +1 th rope, [ theta ]iDenotes a swing angle of the ith satellite, μ ═ (39860044 ± 1) × 107m3/s2Is the coefficient of gravity of the earth, miRepresents the mass of the ith satellite, riRepresents the position vector of the ith satellite in the orbital system, e represents the orbital eccentricity, ri xIndicating the location vector of the ith satellite at erA directional component, ri yIndicating the location vector of the ith satellite
Figure BDA0002797058180000025
The directional component, n, represents the track angular velocity,
Figure BDA0002797058180000026
are auxiliary parameters with respect to track eccentricity and true paraxial angle.
Further, the expression of the stable retraction rate is as follows:
Figure BDA0002797058180000027
in the above formula, A represents the amplitude of the sinusoidal oscillation of the system, ω represents the frequency of the sinusoidal oscillation, and θdRepresenting the steady state curve expected for the task.
Further, the control input signal is expressed as follows:
Figure BDA0002797058180000028
in the above formula, the first and second carbon atoms are,
Figure BDA0002797058180000029
f＝[f1,f2...fN]T，
Figure BDA00027970581800000210
θd＝[θ1d,θ2d...θNd]Tb is a control gain diagonal matrix and the ith diagonal parameter is
Figure BDA00027970581800000211
s＝[s1,s2...sN]TShowing the slip form face.
Further, the step of determining that a disturbance error exists and adjusting the control input signal specifically includes:
judging that a disturbance error exists, and bringing the actual swing into the sliding mode surface to obtain a correction control signal of the controller;
and adding the corrected control signal and the stable folding and unfolding law to obtain a control signal required by the actual system.
Further, the control signal expression required by the actual system is as follows:
Figure BDA0002797058180000031
in the above formula, Liki sgn(si) Indicating the modified control signal for the ith controller.
The method and the system have the beneficial effects that: the stability control problem of the multi-body tethered satellite is solved by reasonably adjusting the retraction speed of the electric rope shaft mounted on each satellite in the system to the tether, and the process only consumes electric energy, does not consume chemical energy and working media and has good universality.
Drawings
FIG. 1 is a flow chart of the steps of a full electric stability control method of a large orbit eccentricity multi-body tethered satellite of the present invention;
FIG. 2 is a schematic diagram of a multi-tethered satellite system in accordance with an embodiment of the present invention;
fig. 3 is a graph showing the change in the rope length during the stabilization control of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
As shown in fig. 1, the invention provides a full-electric stable control method for a large-orbit eccentricity multi-body tethered satellite, which comprises the following steps:
s1, constructing a space multi-body tether satellite system power model based on a Lagrange method;
specifically, the system model modeling coordinate system is a geocentric inertial system Oxy and a moving coordinate system
Figure BDA0002797058180000032
Wherein the content of the first and second substances,
Figure BDA0002797058180000033
takes the mother star M as the origin of the moving coordinate system, M-erIs directed outward along the direction from the earth's center to the mother's star,
Figure BDA0002797058180000034
perpendicular to M-erWhole, of
Figure BDA0002797058180000035
The orbit of the mother satellite is not affected by the motion of the child satellites because the mother satellite generally has a mass greater than the other child satellites and has sufficient orbit-maintaining capability.
S2, obtaining the relation between the tether retracting speed and the stable sinusoidal oscillation according to the space multi-tether satellite system power model, and obtaining the stable retracting rate;
and S3, recovering and releasing the tether according to the stable retraction rate.
Further as a preferred embodiment of the present invention, the method further comprises:
and judging that a disturbance error exists, and adjusting the control input signal.
In particular, during the process of executing tasks by the multi-body tethered satellite system, the system is required to have certain robust correction capability for possible external interference.
In addition, the derivation rule in the formula is:
Figure BDA0002797058180000041
further as a preferred embodiment of the method, the form of the power model of the space multi-body tethered satellite system is as follows:
Figure BDA0002797058180000042
Figure BDA0002797058180000043
Figure BDA0002797058180000044
in the above formula, LiThe length of a tether between the (i-1) th satellite and the (i) th satellite is measured by a tether actuating mechanism;
Figure BDA0002797058180000045
representing the true proximal angle of the system main star, which is obtained by real-time orbit determination; t isi+1The tension of the (i + 1) th rope is represented and measured by a rope system actuating mechanism; thetaiThe swing angle of the ith satellite is measured by an observer; μ ═ (39860044 ± 1) × 107m3/s2Is the coefficient of gravity of the earth, miRepresents the mass of the ith satellite, riRepresents the position vector of the ith satellite in the orbital system, and e represents the orbital eccentricityThe rate is obtained by orbit determination design before the task starts; r isi xIndicating the location vector of the ith satellite at erA directional component, ri yIndicating the location vector of the ith satellite
Figure BDA0002797058180000046
The direction component, n, represents the track angular velocity, which can be obtained from real-time orbit determination;
Figure BDA0002797058180000047
as an auxiliary parameter with respect to the eccentricity of the track and the true paraxial angle, Ti-1Represents the tension of the i-1 th rope, mi-1Represents the mass of the i-1 th satellite, ri-1Represents the position vector, theta, of the i-1 th satellite in the orbital systemi-1Denotes the swing angle, theta, of the i-1 th satellitei+1Representing the swing angle of the (i + 1) th satellite.
As a further preferred embodiment of the present invention, the expression of the stable retraction ratio is as follows:
Figure BDA0002797058180000048
in the above formula, a represents the amplitude of the sinusoidal oscillation of the system, and ω represents the frequency of the sinusoidal oscillation, which are determined by the user; n denotes track angular velocity, thetadAnd the steady state curve representing the task expectation is set by a user.
Specifically, as long as each sub-satellite and the electric rope shaft installed on the main satellite in the system recover/release the tether according to the rule of the formula, the system can keep stable sine swing, the swing amplitude and the frequency can be realized by changing A and omega, and the A can be set to be 0 under the working condition that the swing is not generated at all.
Further as a preferred embodiment of the present invention, the control input signal expression is as follows:
Figure BDA0002797058180000051
for a multi-tethered satellite system with N sub-satellites and a main satellite,
Figure BDA0002797058180000052
the ith row and ith column elements in the matrix B are
Figure BDA0002797058180000053
The other matrix elements are all 0; f ═ f1,f2...fN]TSelf-designing; wherein:
Figure BDA0002797058180000054
c is an N-order diagonal matrix, and each diagonal element is a control parameter and can be selected by self; thetad＝[θ1d,θ2d...θNd]TThe elements are as follows:
Figure BDA0002797058180000055
θ＝[θ1,θ2...θN]T(ii) a K is an N-order diagonal matrix, and each diagonal element is a control parameter and can be selected by self; sgn(s) ═ sign(s)1),...,sign(sN)]T(ii) a Sliding form surface s ═ s1,s2...sN]T；
Figure BDA0002797058180000056
Steady state curve of mission expectations
Figure BDA0002797058180000057
As a further preferred embodiment of the present invention, the step of determining that there is a disturbance error and adjusting the control input signal further includes:
judging that a disturbance error exists, and bringing the actual swing into the sliding mode surface to obtain a correction control signal of the controller;
in particular, the actual oscillation will beThe angle is brought into the sliding mode surface to obtain: s ═ s1,s2...sN]T，
Figure BDA0002797058180000058
And further obtaining a correction control signal of the ith controller: l isiki sgn(si)。
And adding the corrected control signal and the stable folding and unfolding law to obtain a control signal required by the actual system.
Further as a preferred embodiment of the present invention, the control signal required by the actual system is expressed as follows:
Figure BDA0002797058180000059
in the above formula, Liki sgn(si) A correction control signal representing the ith controller;
specifically, under control of this signal, the system swing will gradually converge towards the set task desired stability curve and eventually coincide.
The following is a description with specific parameter examples:
referring to fig. 2, setting of system parameters and initial parameters: n is 2, L1(0)＝10000m，L2(0)＝10000m，
Figure BDA0002797058180000061
Figure BDA0002797058180000062
m1＝500kg，m2＝500kg，e＝0.2，θ1(0)＝0.1rad，θ2(0)＝0。
The selection control parameters are:
Figure BDA0002797058180000063
the control inputs are:
Figure BDA0002797058180000064
Figure BDA0002797058180000065
wherein the content of the first and second substances,
Figure BDA0002797058180000066
in the first half of the track, the wobble angle is larger than ideal due to the presence of the initial perturbations. By the end of the first orbit, the balance motion of each sub-satellite tends to be ideal, as shown in fig. 3. After the first orbit period, the tether retraction speed follows a periodic motion, indicating that the system motion has already trended toward the ideal periodic motion, and by the end of the first orbit, the total tether length of the system smoothly varies periodically, around 0.9. This illustrates that periodic adjustments to tether length are required in order for three satellites that are tethered to maintain a line and periodically oscillate. After a sharp change in the first trajectory, the control input tends to move periodically. Although buffeting still exists in each cycle, its amplitude is very small and bounded.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (7)

1. A full-electric stable control method for a large-orbit eccentricity multi-body tethered satellite is characterized by comprising the following steps:
constructing a power model of a space multi-body tether satellite system based on a Lagrange method;
obtaining the relation between the rope retracting speed and the stable sinusoidal oscillation according to a space multi-body rope system satellite system power model to obtain the stable retracting rate;
and recovering and releasing the tether according to the stable retraction rate.
2. The method for fully electrically controlling the stability of a large-orbital-eccentricity multi-body tethered satellite according to claim 1 further comprising:
and judging that a disturbance error exists, and adjusting the control input signal.
3. The full-electric stability control method for the large-orbit eccentricity multi-body tethered satellite according to claim 2 wherein the spatial multi-body tethered satellite system power model is of the form:
Figure FDA0002797058170000011
Figure FDA0002797058170000012
Figure FDA0002797058170000013
Figure FDA0002797058170000014
in the above formula, LiRepresenting the tether length between the (i-1) th satellite and the (i) th satellite,
Figure FDA0002797058170000015
representing the true anomaly, T, of the system's dominant stari+1Is the tension of the i +1 th rope, [ theta ]iDenotes a swing angle of the ith satellite, μ ═ (39860044 ± 1) × 107m3/s2Is the coefficient of gravity of the earth, miRepresents the mass of the ith satellite, riRepresents the position vector of the ith satellite in the orbital system, e represents the orbital eccentricity, ri xIs shown asi satellite position vectors at erA directional component, ri yIndicating the location vector of the ith satellite
Figure FDA0002797058170000016
The directional component, n, represents the track angular velocity,
Figure FDA0002797058170000017
are auxiliary parameters with respect to track eccentricity and true paraxial angle.
4. The full-electric stability control method for the large-orbit eccentricity multi-body tethered satellite according to claim 3, wherein the stable retraction and extension rate is expressed as follows:
Figure FDA0002797058170000021
in the above formula, A represents the amplitude of the sinusoidal oscillation of the system, ω represents the frequency of the sinusoidal oscillation, and θdRepresenting the steady state curve expected for the task.
5. The method according to claim 4, wherein the control input signal is expressed as follows:
Figure FDA0002797058170000022
in the above formula, the first and second carbon atoms are,
Figure FDA0002797058170000023
f＝[f1,f2...fN]T，
Figure FDA0002797058170000024
θd＝[θ1d,θ2d...θNd]Tb is a control gain diagonal matrix and the ith diagonal parameter is
Figure FDA0002797058170000025
s＝[s1,s2...sN]TShowing the slip form face.
6. The method according to claim 5, wherein the step of determining that a disturbance error exists and adjusting the control input signal further comprises:
judging that a disturbance error exists, and bringing the actual swing into the sliding mode surface to obtain a correction control signal of the controller;
and adding the corrected control signal and the stable folding and unfolding law to obtain a control signal required by the actual system.
7. The method for fully electrically controlling the stability of the large-orbit eccentricity multi-body tethered satellite according to claim 6, wherein the control signal required by the actual system is expressed as follows:
Figure FDA0002797058170000026
wherein L isiki sgn(si) Indicating the modified control signal for the ith controller.
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CN113734476A (en) * 2021-09-07 2021-12-03 北京控制工程研究所 Method and system for controlling swing angle under boundary trigger constant thrust

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CN113734476B (en) * 2021-09-07 2023-03-14 北京控制工程研究所 Method and system for controlling swing angle under boundary trigger constant thrust

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