CN114115315A - Tethered satellite release and recovery control method and system - Google Patents

Tethered satellite release and recovery control method and system Download PDF

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CN114115315A
CN114115315A CN202111430025.1A CN202111430025A CN114115315A CN 114115315 A CN114115315 A CN 114115315A CN 202111430025 A CN202111430025 A CN 202111430025A CN 114115315 A CN114115315 A CN 114115315A
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tethered satellite
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饶海平
王子涵
李锦朝
王任廷
彭维峰
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Dongfanghong Satellite Mobile Communication Co Ltd
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Abstract

The invention provides a method and a system for controlling release and recovery of a tethered satellite, wherein the method comprises the following steps: establishing a dynamic equation of shimmy of the tethered satellite and an orbit equation of mass center of the tethered satellite based on an orbit coordinate system and a body coordinate system of the tethered satellite system; linearizing a kinetic equation of the shimmy of the tethered satellite, and then converting the kinetic equation into a state to obtain a state equation Z after the linearization of the kinetic equation; designing a guaranteed value control law according to a state equation Z after the dynamic equation linearization and system parameter uncertainty caused by the eccentricity of the tethered satellite mass center orbit; and applying the guaranteed value control law to control release and recovery in a tethered satellite system. The invention can stably release and recover the tethered satellite, prevents the tethered satellite from winding in the release and recovery process, and improves the steady-state precision of the release and recovery of the tethered satellite.

Description

Tethered satellite release and recovery control method and system
Technical Field
The invention relates to the technical field of tethered satellites in aerospace engineering, in particular to a tethered satellite release and recovery control method and a tethered satellite release and recovery control system.
Background
Tethered satellites are a very promising project, and have a very large number of applications in space, and are also used to perform a variety of space missions. The earliest application of tethered satellites was assumed to be space elevators, and with the progress of materials, they became a research hotspot today. Another application of tethered satellites, according to the nature of tethered satellites, is assisted orbit transfer, assisted by shearing the tether or changing the tether length. In addition, tethered satellites can assist in pneumatic braking and capture, with the satellite slowing down through interaction of the tether probe with the atmosphere. The tethered satellite can also be used as a space trailer, the trailer carries a flying net system, when the distance between a target and the flying net reaches a certain degree, the flying net moves towards the target, then the target is wrapped, and the required target orbital transfer is realized by connecting the tethered satellite with a platform. Roping is also often used to form flights.
The tethered satellite release recovery is the basic application of tethered satellites, and the uncertainty of a tethered satellite system is very large in the process of controlling the tethered satellite release recovery.
In the releasing and recovering process of the tethered satellite, the eccentricity of the tethered satellite mass center orbit is usually taken as zero, however, under the space interference, the eccentricity of the tethered satellite mass center orbit is not 0 and changes in a small range, which causes uncertainty of system parameters.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method for controlling the release and recovery of a tethered satellite.
In order to achieve the above object of the present invention, the present invention provides a tethered satellite release recovery control method, comprising the steps of:
establishing a dynamic equation of shimmy of the tethered satellite and an orbit equation of mass center of the tethered satellite based on an orbit coordinate system and a body coordinate system of the tethered satellite system;
linearizing a kinetic equation of the shimmy of the tethered satellite, and then converting the kinetic equation into a state to obtain a state equation Z after the linearization of the kinetic equation;
designing a guaranteed value control law according to a state equation Z after the dynamic equation linearization and system parameter uncertainty caused by the eccentricity of the tethered satellite mass center orbit;
and applying the guaranteed value control law to control release and recovery in a tethered satellite system.
According to the preferable scheme of the control method for releasing and recovering the tethered satellite, the kinetic equation of the tethered satellite shimmy is as follows:
Figure BDA0003379802550000021
wherein ω isoIs the orbital angular velocity of the tethered satellite system, mu is the gravitational constant, RcCenter of mass orbital radius, FteIs the tether tension, l is the tether length,
Figure BDA0003379802550000022
Figure BDA0003379802550000023
mass of active star is mmTarget star mass is msMass of tether is mtThe mass of the whole system is m ═ mm+ms+mt，Ql，Qα，QβGeneralized force corresponding to generalized coordinates l, alpha and beta;
the motion equation of the mass center orbit of the tethered satellite is as follows:
Figure BDA0003379802550000031
wherein a is a semimajor axis of a mass center orbit of the tethered satellite, e is an orbit eccentricity, omega is a right ascension of a rising intersection point, i is an orbit inclination angle, omega is an amplitude angle of a near place, and theta is a true near point angle. RcIs the centroid orbit radius, p is the orbit radius, fu，fh，frRespectively is the acceleration of the mass center of the tethered satellite in an orbital coordinate system SoThe x-axis, y-axis, and z-axis components,
Figure BDA0003379802550000032
wherein J2Is a constant number, REIs the average equatorial radius of the earth, mu is the gravitational constant, psi is the latitude argument,
Figure BDA0003379802550000033
three-body gravitation of the sun to the tethered satellite in an orbital coordinate system SoThe components in the x-axis, y-axis, z-axis,
Figure BDA0003379802550000034
in an orbital coordinate system S, respectively, the three-body attraction of the moon to the tethered satelliteoThe components on the x-axis, y-axis, and z-axis.
According to the preferable scheme of the control method for releasing and recovering the tethered satellite, the step of linearizing the kinetic equation of the shimmy of the tethered satellite is as follows:
the kinetic equation of the shimmy of the tethered satellite is simplified into the following equation:
Figure BDA0003379802550000041
wherein
Figure BDA0003379802550000042
Obtaining a nonlinear state equation according to the simplified kinetic equation of the shimmy of the tethered satellite, then linearizing the state equation at a zero point, and obtaining the state equation as follows:
Figure BDA0003379802550000043
wherein
Figure BDA0003379802550000044
Figure BDA0003379802550000045
Controlling input quantity
Figure BDA0003379802550000046
Figure BDA0003379802550000047
According to the preferable scheme of the control method for releasing and recovering tethered satellites, a state equation Z after the dynamic equation linearization is substituted into a guaranteed value control law u-R-1BTIn the PZ, u is a control input quantity to obtain a guaranteed value control law of release and recovery of tethered satellites,
wherein Q is a semi-positive definite matrix, R is a positive definite matrix, and P is a matrix satisfying the Riccati equation
Figure BDA0003379802550000048
The positive definite matrix of (a) is,
Figure BDA0003379802550000049
to satisfy the requirement of having any non-zero vector y
Figure BDA00033798025500000410
The matrix of (a) is,
determining items
Figure BDA00033798025500000411
Uncertainty term
Figure BDA00033798025500000412
The application also provides a tethered satellite release and recovery control system, which comprises a processor and a memory, wherein the processor and the memory are in communication connection, the memory is used for storing at least one executable instruction, and the executable instruction enables the processor to execute the operation corresponding to the tethered satellite release and recovery control method.
The invention has the beneficial effects that: the control method used by the invention can stably release and recover the tethered satellite, so that the tethered satellite is not wound in the releasing and recovering process. Compared with a general control method, the method provided by the invention considers that the eccentricity of the tethered satellite mass center orbit is changed in a small range near 0 under space interference for the first time, so that the system parameters of the tethered satellite shimmy equation are uncertain, the robust control law is designed, and the steady-state precision of the tethered satellite release recovery is improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a schematic diagram of a coordinate system used for system modeling;
FIG. 2 shows the change in eccentricity of the tethered satellite's centroid orbit during release;
FIG. 3 shows the rope length change during the release process;
FIG. 4 shows the rope speed change during the release process;
FIG. 5 is a release process in-plane angular change;
FIG. 6 is a graph of the change in angular rate over the release period;
FIG. 7 is a graph of the change in the out-of-plane angle of the release process;
FIG. 8 is a change in out-of-plane angular rate during release;
FIG. 9 shows tether tension change during release;
FIG. 10 shows the change in eccentricity of the tethered satellite centroid orbit during recovery;
FIG. 11 shows the rope length variation during the recovery process;
FIG. 12 shows the rope speed variation during the recovery process;
FIG. 13 is a variation of the in-plane angle during recovery;
FIG. 14 is a graph of the change in corner velocity during recovery;
FIG. 15 is a graph of the change in the out-of-plane angle of the recycling process;
FIG. 16 is a graph of recovery process out-of-plane angular rate variation;
FIG. 17 illustrates tether tension changes during recovery;
FIG. 18 is a flow chart of a method of the present invention.
The reference numbers and symbols in the figures are explained as follows:
o is the center of mass of the tethered satellite system, xoAs a track coordinate system xoAxis, yoAs an orbital coordinate system yoAxis, zoAs an orbital coordinate system zoAxis, xbFor systems of tethered satellite systemsbAxis, ybFor the system of tethered satellite systemsbAxis, zbZ for tethered satellite system body systemsbA shaft.
Earth, RoThe distance between the center of the earth and the center of mass of the tethered satellite system. Alpha is the system in-plane tilt angle and beta is the system out-of-plane tilt angle.
X is the X axis of the earth equator inertial coordinate system, Y is the Y axis of the earth equator inertial coordinate system, and Z is the Z axis of the terrain equator inertial coordinate system.
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.
In the description of the present invention, unless otherwise specified and limited, it is to be noted that the terms "mounted," "connected," and "connected" are to be interpreted broadly, and may be, for example, a mechanical connection or an electrical connection, a communication between two elements, a direct connection, or an indirect connection via an intermediate medium, and specific meanings of the terms may be understood by those skilled in the art according to specific situations.
As shown in fig. 1, the invention provides a tethered satellite release and recovery control method based on uncertain system parameters, which comprises the steps of firstly making necessary assumptions on a tethered satellite system, and performing dynamic modeling on the tethered satellite system; then, a dynamic equation of the shimmy of the tethered satellite and a mass center orbit perturbation equation of the tethered satellite are deduced; then, carrying out stability analysis on the swing vibration mechanical equation of the tethered satellite, and linearizing the swing vibration mechanical equation of the tethered satellite; then considering the uncertainty of system parameters, designing a guaranteed value control law; applying the guaranteed value control law to control release and recovery in a tethered satellite system; robustness and stability of the designed control law are analyzed, and the fact that the tethered satellite can be stably released and recovered under the condition that system parameters are uncertain is analyzed; finally, the model obtained by performing the dynamic modeling on the tethered satellite system is combined with the designed control law to perform numerical simulation to verify the accuracy of the control method, as shown in fig. 18.
As described in detail below.
The tethered satellite system comprises a main satellite with a propelling device, a sub satellite and a main body, wherein the main satellite and the sub satellite are elastically connected with a tether and are respectively positioned at two ends of the tether; to describe the shimmy of the tether, the following assumptions are made:
1) the satellites at the rope ends are respectively called a main satellite and a sub-satellite, and the main satellite and the sub-satellite are respectively taken as the mass mmAnd msThe main star is provided with a tether take-up and pay-off device;
2) the tied rope is regarded as a rigid rod and can only bear tension, and the mass of the tied rope is uniformly distributed;
3) besides the action of the spherical gravitational field, the influence of generalized perturbation forces such as the term J2 of the earth and the gravity of the sun and the moon is considered;
4) neglecting the difference between the mass center and the gravity center of the tethered satellite, the motion of the tethered satellite is decomposed into orbital motion of the mass center and shimmy motion around the mass center.
The method guarantees the value control law by considering the uncertain design of the mass center eccentricity of the tethered satellite. The method comprises the following specific steps:
firstly, performing dynamic modeling on a tethered satellite system by adopting an orbit coordinate system and a body coordinate system of the tethered satellite system, and establishing a dynamic equation of shimmy of the tethered satellite and an orbit motion equation of the mass center of the tethered satellite.
Specifically, a kinetic equation of the shimmy of the tethered satellite is firstly deduced, and an orbit coordinate system and a body coordinate system of the tethered satellite system are adopted for modeling. As shown in fig. 1, an orbital coordinate system oxoyozoMiddle zoThe axis being oriented from the center of the earth to the center of mass, y, of the tethered satellite systemoThe axis is perpendicular to the plane of the track. The orbit coordinate system rotates by adopting a y-x rotation sequence and then is in contact with a body coordinate system ox of the tethered satellite systembybzbSuperposing, wherein the two obtained included angles alpha and beta are an in-plane swing angle in the track plane and an out-of-plane swing angle vertical to the track plane respectively; the lagrangian equation can then be used to derive the kinetic equation for the tether shimmy motion as follows:
Figure BDA0003379802550000081
wherein ω isoIs the orbital angular velocity of the tethered satellite system,
Figure BDA0003379802550000082
is omegaoFirst derivative with respect to time, mu is the gravitational constant, RcCenter of mass orbital radius, FteIs the tether tension, l is the tether length,
Figure BDA0003379802550000083
is the first derivative of/with respect to time,
Figure BDA0003379802550000084
is the second derivative of l and is,
Figure BDA0003379802550000085
is the first derivative of a with respect to time,
Figure BDA0003379802550000086
is the second derivative of a and is,
Figure BDA0003379802550000087
is the first derivative of beta with respect to time,
Figure BDA0003379802550000088
is the second derivative of beta, with a dominant star mass of mmThe mass of the child star is msIs a system ofMass of the rope is mtThe mass of the whole system is m ═ mm+ms+mtFor the simplification of the equation, two parameters are introduced, respectively
Figure BDA0003379802550000089
Ql，Qα，QβThe generalized force corresponding to generalized coordinates l, alpha and beta is composed of a main satellite thrust, an earth J2 term and a sun-moon attraction.
Then based on the Gaussian perturbation equation, a tethered satellite mass center orbital kinematics equation can be obtained:
Figure BDA0003379802550000091
wherein a is a semimajor axis of a mass center orbit of the tethered satellite, e is an orbit eccentricity, omega is a right ascension of a rising intersection point, i is an orbit inclination angle, omega is an amplitude angle of a near place, theta is a true near point angle, RcIs the centroid orbit radius, p is the orbit radius, fu，fh，frRespectively is the acceleration of the mass center of the tethered satellite in an orbital coordinate system SoThe components on the x axis, the y axis and the z axis, which comprise the main satellite thrust, the earth J2 term, the sun and moon gravity and the like, act on the mass center of the tethered satellite, and the expressions are as follows:
Figure BDA0003379802550000092
wherein Fx，Fy，FzRefer to the components of satellite thrust in the x, y, and z axes, J, respectively2Is a constant number, REIs the average equatorial radius of the earth, mu is the gravitational constant, psi is the latitude argument, which is the sum of the argument of the perigee and the true perigee,
Figure BDA0003379802550000093
Figure BDA0003379802550000094
three-body gravitation of the sun to the tethered satellite in an orbital coordinate system SoThe components in the x-axis, y-axis, z-axis,
Figure BDA0003379802550000095
in an orbital coordinate system S, respectively, the three-body attraction of the moon to the tethered satelliteoThe components on the x-axis, y-axis, and z-axis.
And step two, linearizing the kinetic equation of the shimmy of the tethered satellite, and then converting the state of the tethered satellite to obtain a state equation Z after the linearization of the kinetic equation.
Specifically, the stability of the system in the release and recovery process of the tethered satellite is firstly analyzed, small angle hypothesis is made and the mass m of the tether is consideredtAnd (3) the value is approximately equal to 0, the external interference and the high-order term of the angle are ignored, and the dynamic equation of the shimmy of the tethered satellite is simplified into the following equation:
Figure BDA0003379802550000101
it can be seen that the release process is when uncontrolled
Figure BDA0003379802550000102
The in-plane motion and the out-of-plane motion are in damping states, the system is stable, and the recovery process is carried out
Figure BDA0003379802550000103
In-plane motion and out-of-plane motion are negative damping states, and the system is unstable. OmegaoIs the orbital eccentricity of the system's centroid, RcFor centroid orbit radii, their expressions are as follows:
Figure BDA0003379802550000104
wherein p is the track radius, thus defining
Figure BDA0003379802550000105
The dimensionless time tau is selected to be omega t, the track eccentricity in the text is near 0, so that the track eccentricity can be ignored
Figure BDA0003379802550000106
And (3) the simplified dynamics equation of the shimmy of the tethered satellite is expressed as the following expression G:
Figure BDA0003379802550000107
wherein L ismFor the length of the task rope in the releasing and recovering process of the tethered satellite, lambda is equal to L/Lmλ ' represents the first derivative of λ with respect to dimensionless time τ, λ "represents the second derivative of λ with respect to dimensionless time τ, α ' represents the first derivative of α with respect to dimensionless time τ, α" represents the first derivative of α with respect to dimensionless time τ, β ' represents the first derivative of β with respect to dimensionless time τ, and β "represents the first derivative of β with respect to dimensionless time τ. A state equation refers to an expression that describes the relationship between system inputs and states, including z1、z2、z3、z4、z5、z6Defining: z is a radical of1＝λ-q，z2＝λ′，z3＝α，z4＝α′，z5＝β，z6β', the expression is G into a state equation, which is expressed as follows:
Figure BDA0003379802550000111
z 'is the derivative of z to dimensionless time, z'1,z′2,z′3,z′4,z′5,z′6Are each z1＝λ-q，z2＝λ′，z3＝α，z4＝α′，z5＝β，z6Beta' derivative to dimensionless time, the equation of state is normalized by the tethered satellite kinetic equation with small angle assumptions, now assume z1And z2For small quantities, neglecting the state high-order quantity and eccentricity high-order quantity, a linearized state equation of the state equation in the (0,0,0,0,0,0) expansion can be obtained
Figure BDA0003379802550000112
Wherein
Figure BDA0003379802550000113
Figure BDA0003379802550000114
Controlling input quantity
Figure BDA0003379802550000115
Figure BDA0003379802550000116
As can be seen from the state equation after linearization, the out-of-plane motion and the in-plane motion are decoupled, and the in-plane motion can be considered independently; the rope length movement and the out-of-plane movement are decoupled, so that the change of the rope length has small influence on the out-of-plane movement, but if the rope length is too small, the change of the rope length influences the out-of-plane movement through a high-order term during recovery to cause the divergence of the out-of-plane movement, so the rope length during recovery cannot be too small, otherwise, the control force is added to control the out-of-plane movement.
And step three, designing a guaranteed value control law according to a state equation Z after the dynamic equation linearization.
Under the interference of space, the eccentricity of the tethered satellite mass center orbit changes in a small range near 0, the change of the orbit eccentricity causes system parameters to have uncertain items, the item containing the orbit eccentricity e in the system parameters is determined as an uncertain item, the following expression is obtained, and the certain item
Figure BDA0003379802550000121
Then the linearized equation of state uncertainty
Figure BDA0003379802550000122
The following linear uncertainty system can be considered: z ═ a + Δ a) Z + Bu, Z (t)0)＝Z0The value function is
Figure BDA0003379802550000123
Wherein Q is a semi-positive definite matrix and R is a positive definite matrix, and if there is a unique positive definite matrix P satisfying the following Riccati equation:
Figure BDA0003379802550000124
wherein
Figure BDA0003379802550000125
Satisfy the condition of having any non-zero vector y
Figure BDA0003379802550000126
Then there is a guaranteed value control rate u ═ R-1BTPZ, u are control input quantities such that the cost function satisfies the following conditions
Figure BDA0003379802550000127
Wherein
Figure BDA0003379802550000128
To guarantee the guaranteed value of the value control law.
To prove the above conclusion, the lyapunov function is defined as follows: V-1/2ZTPZ, so that the following equation can be obtained
Figure BDA0003379802550000129
Converting Z' ═ A + DeltaA) Z + Bu, Z (t)0)＝Z0Substituted therein, the following equation can be obtained
Figure BDA00033798025500001210
Substituting the guaranteed value control law into this equation yields the following equation
Figure BDA00033798025500001211
By
Figure BDA00033798025500001212
Can be defined by the following inequality
Figure BDA0003379802550000131
Will be provided with
Figure BDA0003379802550000132
Substituted therein, the following inequality can be obtained
Figure BDA0003379802550000133
For the inequalityThe integral of two sides of the formula can obtain the following inequality
Figure BDA0003379802550000134
Since P is a positive definite matrix, V (∞) ≧ 0, so the inequality
Figure BDA0003379802550000135
This is true.
And step four, controlling the release and recovery by applying the guaranteed value control law in the tethered satellite system.
The stability of the control laws is analyzed below.
Since Q is a semi-positive definite matrix and R is a positive definite matrix, the following relationship Z is satisfiedTQZ+uTRu is more than or equal to 0, and the guaranteed value of the control law meets the relation that P is a positive definite matrix
Figure BDA0003379802550000136
Whereinλ(P) represents the minimum eigenvalue of P,
Figure BDA0003379802550000137
representing the maximum eigenvalue of P. Since the initial conditions are uncertain, i.e. Z0Is indeterminate, but Z0The control law is bounded, so that the guaranteed value of the control law is bounded, and the value function is bounded, so that when the time t tends to be infinite, the state Z approaches 0, and the stability of the linear uncertain system under the uncertain initial conditions is guaranteed.
Final determination
Figure BDA0003379802550000138
If the uncertainty Δ A element is bounded, | Δ A | ≦ D, based on
Figure BDA0003379802550000139
Is preferably defined as
Figure BDA00033798025500001310
Wherein
Figure BDA00033798025500001311
For the maximum eigenvalue of matrix D, it is next demonstrated that any non-zero vector y has
Figure BDA00033798025500001312
It is verified by the inverse syndrome method that the following condition is satisfied assuming that there exists a non-zero vector h
Figure BDA00033798025500001313
Then there is a positive definite matrix Q satisfy
Figure BDA00033798025500001314
Therefore, it is not only easy to use
Figure BDA00033798025500001315
Since the matrices Q and P are positive definite matrices, so
Figure BDA00033798025500001316
Is the Lyapunov equation, so the matrix
Figure BDA00033798025500001317
The eigenvalues are all negative and do not accord with the assumption that | delta A | ≦ D, so the assumption is not true, and the evidence is obtained.
Numerical simulation verification
The compiling platform of the numerical simulation software of the embodiment is a matrix laboratory platform (namely a Matlab platform), Matlab series products are widely applied in the field of aerospace engineering, and the Matlab series products are very reliable numerical simulation software in the development and development process of dynamics and control related problems. By combining the invention content, a dynamic model method and a control system method are compiled, numerical simulation is carried out on given parameters, and the correctness of a designed control method is verified.
The balance point parameter q of the release process is 1, the initial conditions and system parameters of the tethered satellite are shown in table 1, and the control parameters of the guaranteed-value controller are shown in table 2.
TABLE 1 tethered satellite initial conditions and System parameters
Figure BDA0003379802550000141
TABLE 2 guaranteed value controller parameters
Parameter(s) Numerical value
Positive definite weighting matrix Q diag{[1,1,1,1]}
Positive definite weighting matrix R 1
Consideration of the maximum value e of eccentricitymaxThe guaranteed value control law of 0.1 controls the release process of the tethered satellite, and the release process is compared with the LQR controller with the same controller parameters as the control law, so that the simulation results are shown in fig. 2 to 9. From the comparison of the two simulation results, the two control laws can control the release process of the tethered satellite and can stably release the tethered satellite, but the tension required by the two control laws is in a time period less than 0, and the main satellite thrust is required to make up for the lack of tension in the time period when the tension is less than 0; the guarantee control law of uncertain design of system parameters is considered, so that after the release of the tethered satellite is finished, the steady-state precision of the tether length is higher, the variation amplitude is smaller, the steady-state precision of the in-plane angle is higher, the in-plane swing is smaller, and the method has certain engineering significance.
The recovery process balance point parameter q is 0.125, the initial conditions and system parameters of tethered satellites are shown in table 3, and the guaranteed value controller control parameters are shown in table 4.
TABLE 3 tethered satellite initial conditions and System parameters
Figure BDA0003379802550000151
Figure BDA0003379802550000161
TABLE 4 guaranteed value controller parameters
Figure BDA0003379802550000162
Consideration of the maximum value e of eccentricitymaxThe guaranteed value control law of 0.01 controls the recovery process of the tethered satellite, and the simulation results are shown in fig. 10 to 17 by comparing the recovered process with the LQR controller having the same controller parameters as the control law. From the comparison of the two simulation results, the guaranteed value control law considering the uncertain design is faster in recovery process and larger in change amplitude of the inner angle and the outer angle of the surface compared with the LQR control law not considering the uncertain design, but after recovery is completed, the stable-state precision of the rope length and the inner angle of the surface is higher.
Combining the shimmy kinematic equation of the tethered satellite derived in the step one with the control rate obtained in the step three to obtain a method for controlling the release and recovery of the tethered satellite; the tethered satellite mass center orbital motion equation obtained in the step one describes orbital motion of the tethered satellite mass center in an uncontrolled state; fifthly, numerical simulation is carried out, and feasibility and accuracy of the control system are verified; the guarantee value control law designed by the method can effectively control the releasing and recovering process of the tethered satellite, so that the releasing and recovering process of the tethered satellite is stable and has higher steady-state precision.
The invention also provides an embodiment of the tethered satellite release and recovery control system, which comprises a processor and a memory, wherein the processor and the memory are mutually connected in a communication manner, and the memory is used for storing at least one executable instruction, and the executable instruction enables the processor to execute the corresponding operation of the tethered satellite release and recovery control method.
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.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims (5)

1. A method for controlling release and recovery of tethered satellites is characterized by comprising the following steps:
establishing a dynamic equation of shimmy of the tethered satellite and an orbit equation of mass center of the tethered satellite based on an orbit coordinate system and a body coordinate system of the tethered satellite system;
linearizing a kinetic equation of the shimmy of the tethered satellite, and then converting the kinetic equation into a state to obtain a state equation Z after the linearization of the kinetic equation;
designing a guaranteed value control law according to a state equation Z after the dynamic equation linearization and system parameter uncertainty caused by the eccentricity of the tethered satellite mass center orbit;
and applying the guaranteed value control law to control release and recovery in a tethered satellite system.
2. The tethered satellite release and recovery control method of claim 1, wherein the kinetic equation for tethered satellite shimmy is:
Figure FDA0003379802540000011
wherein ω isoIs the orbital angular velocity of the tethered satellite system, mu is the gravitational constant, RcCenter of mass orbital radius, FteIs the tether tension, l is the tether length,
Figure FDA0003379802540000012
Figure FDA0003379802540000013
mass of active star is mmTarget star mass is msMass of tether is mtThe mass of the whole system is m ═ mm+ms+mt，Ql，Qα，QβGeneralized force corresponding to generalized coordinates l, alpha and beta;
the motion equation of the mass center orbit of the tethered satellite is as follows:
Figure FDA0003379802540000021
wherein a is a semimajor axis of a mass center orbit of the tethered satellite, e is an orbit eccentricity, omega is a right ascension of a rising intersection point, i is an orbit inclination angle, omega is an amplitude angle of a near place, and theta is a true near point angle. RcIs the centroid orbit radius, p is the orbit radius, fu，fh，frRespectively is the acceleration of the mass center of the tethered satellite in an orbital coordinate system SoThe x-axis, y-axis, and z-axis components,
Figure FDA0003379802540000022
wherein J2Is a constant number, REIs the average equatorial radius of the earth, mu is the gravitational constant, psi is the latitude argument,
Figure FDA0003379802540000023
three-body gravitation of the sun to the tethered satellite in an orbital coordinate system SoThe components in the x-axis, y-axis, z-axis,
Figure FDA0003379802540000024
in an orbital coordinate system S, respectively, the three-body attraction of the moon to the tethered satelliteoThe components on the x-axis, y-axis, and z-axis.
3. The tethered satellite release recovery control method of claim 2, wherein the step of linearizing the equations of dynamics of tethered satellite shimmy comprises:
the kinetic equation of the shimmy of the tethered satellite is simplified into the following equation:
Figure FDA0003379802540000031
wherein
Figure FDA0003379802540000032
Obtaining a nonlinear state equation of the system according to the simplified kinetic equation of the shimmy of the tethered satellite, then linearizing the state equation at a zero point, and obtaining the state equation as follows:
Figure FDA0003379802540000033
wherein
Figure FDA0003379802540000034
Figure FDA0003379802540000035
Controlling input quantity
Figure FDA0003379802540000036
Figure FDA0003379802540000037
4. The tethered satellite release and recovery control method of claim 2, wherein the state equation Z after the dynamic equation linearization is substituted into the guaranteed value control law u-R-1BTIn the PZ, u is a control input quantity to obtain a guaranteed value control law of release and recovery of tethered satellites,
wherein Q is a semi-positive definite matrix, R is a positive definite matrix, and P is a matrix satisfying the Riccati equation
Figure FDA0003379802540000038
The positive definite matrix of (a) is,
Figure FDA0003379802540000039
to satisfy the requirement of having any non-zero vector y
Figure FDA00033798025400000312
The matrix of (a) is,
determining items
Figure FDA00033798025400000310
Uncertainty term
Figure FDA00033798025400000311
5. Tethered satellite release recovery control system, characterized in that it comprises a processor and a memory, said processor and memory being communicatively connected to each other, said memory being intended to store at least one executable instruction that causes said processor to perform operations corresponding to the tethered satellite release recovery control method according to any of the claims 1 to 4.
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