CN114115315B - Method and system for controlling release and recovery of tethered satellites - Google Patents
Method and system for controlling release and recovery of tethered satellites Download PDFInfo
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Abstract
The invention provides a tethered satellite release recovery control method and a tethered satellite release recovery control system, wherein the method comprises the following steps: establishing a dynamic equation of the shimmy of the tethered satellite and an orbital motion equation of the mass center of the tethered satellite based on an orbit coordinate system and a body coordinate system of the tethered satellite system; linearizing a dynamic equation of the shimmy of the tethered satellite, and then converting the dynamic equation to obtain a state equation Z after linearization of the dynamic equation; according to the system parameter uncertainty caused by the linear state equation Z of the dynamic equation and the orbit eccentricity of the mass center of the tethered satellite, designing a value control law; the release recovery is controlled in a tethered satellite system using the guaranteed value control law. The invention can ensure that the tethered satellite is stably released and recovered, so that the tethered satellite can not be wound in the releasing and recovering process, and the steady-state precision of the releasing and recovering of the tethered satellite is improved.
Description
Technical Field
The invention relates to the technical field of tethered satellites in aerospace engineering, in particular to a tethered satellite release recovery control method and system.
Background
Tethered satellites are a very promising item, with a very large number of applications in space, and are also used to perform a variety of space tasks. The earliest application of tethered satellites was envisaged as space elevators, which became the focus of research today with advances in materials. Another application of tethered satellites is in assisting orbit transfer by cutting off the tether or changing the tether length, depending on the characteristics of the tethered satellite. In addition, tethered satellites can assist in pneumatic braking and acquisition, and the satellites are decelerated by the interaction of the tethered detectors 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 the 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 orbit change is realized through the tether connection with the platform. Tether structures are also often used to train flights.
The release and recovery of the tethered satellites is a basic application of the tethered satellites, and the uncertainty of a tethered satellite system is very large in the process of controlling the release and recovery of the tethered satellites.
In the process of releasing and recovering the tethered satellites, the mass center orbit eccentricity of the tethered satellites is usually regarded as zero, however, under the condition of space interference, the mass center orbit eccentricity of the tethered satellites is not 0 and changes in a small range, so that the system parameters are uncertain.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a tethered satellite release recovery control method.
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 the shimmy of the tethered satellite and an orbital motion equation of the mass center of the tethered satellite based on an orbit coordinate system and a body coordinate system of the tethered satellite system;
linearizing a dynamic equation of the shimmy of the tethered satellite, and then converting the dynamic equation to obtain a state equation Z after linearization of the dynamic equation;
according to the system parameter uncertainty caused by the linear state equation Z of the dynamic equation and the orbit eccentricity of the mass center of the tethered satellite, designing a value control law;
the release recovery is controlled in a tethered satellite system using the guaranteed value control law.
The optimal scheme of the tethered satellite release recovery control method is that the dynamic equation of the tethered satellite shimmy is as follows:
wherein omega o Is the orbital angular velocity of the tethered satellite system, mu is the gravitational constant, R c Centroid orbit radius, F te For tether tension, l is the tether length, the mass of the active star is m m The mass of the target star is m s The mass of the tether is m t The mass of the whole system is m=m m +m s +m t ，Q l ，Q α ，Q β The generalized force corresponding to the generalized coordinates l, alpha and beta;
the mass center orbit motion equation of the tethered satellite is as follows:
wherein a is the semi-long axis of the mass center orbit of the tethered satellite, e is the orbit eccentricity, Ω is the right ascent and intersection point, i is the orbit inclination angle, ω is the near-point amplitude angle, and θ is the true near-point angle. R is R c Is the radius of the centroid orbit, p is the orbit semi-diameter, f u ，f h ，f r The mass center acceleration of the tethered satellites is respectively in an orbit coordinate system S o Components in the x-axis, y-axis, z-axis,wherein J 2 Is constant, R E The average equatorial radius of the earth, mu is the constant of gravitational force, psi is the latitude amplitude angle,/>Three-body gravitation of solar pair tethered satellite in orbit coordinate system S o The components on the x-axis, y-axis, z-axis of the middle,/->Three-body gravitation of lunar pair tethered satellites in orbit coordinate system S o Components in the x, y, z axes.
The optimal scheme of the tethered satellite release recovery control method comprises the following steps of:
the dynamic equation of the tethered satellite shimmy is simplified to the following equation:
wherein->
Obtaining a nonlinear state equation according to the simplified dynamic equation of the shimmy of the tethered satellite, and linearizing the state equation at a zero point to obtain the state equation:
wherein the method comprises the steps of
Control input quantity->
The optimal scheme of the tethered satellite release recovery control method brings the state equation Z with the linearized dynamic equation into the guaranteed value control law u= -R -1 B T In PZ, u is the control input quantity, and the control law of the guarantee value of the release and recovery of the tethered satellite is obtained,
wherein Q is a semi-positive definite matrix, R is a positive definite matrix, and P is a matrix satisfying the Li-Ka equationPositive definite matrix, < >>To satisfy +.>Is a matrix of the (c) in the matrix,
determining itemsUncertain item->
The application also provides a tethered satellite release 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 recovery control method.
The beneficial effects of the invention are as follows: the control method used by the invention can ensure that the tethered satellite is released and recovered stably, so that the tethered satellite can not be wound in the releasing and recovering process. Compared with a general control method, the method considers that the mass center orbit eccentricity of the tethered satellite 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, a robust control law is designed, and the steady-state precision of the release and recovery of the tethered satellite 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.
Drawings
The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a schematic diagram of a coordinate system employed in system modeling;
FIG. 2 is a graph showing the change in mass center orbit eccentricity of a tethered satellite during release;
FIG. 3 is a graph showing the rope length change during release;
FIG. 4 is a graph showing rope speed variation during release;
FIG. 5 is a graph showing the change in the internal angle of the release process;
FIG. 6 is a graph of in-plane angle rate change during release;
FIG. 7 is a release process out-of-plane angle variation;
FIG. 8 is a graph of out-of-plane angular rate change during release;
FIG. 9 is a change in tether tension during release;
FIG. 10 is a graph showing the change in mass center orbit eccentricity of a tethered satellite during recovery;
FIG. 11 is a graph showing the change in rope length during recovery;
FIG. 12 is a graph showing rope speed variation during recovery;
FIG. 13 is a graph showing the change in the internal angle of the recycling process;
FIG. 14 is a graph showing the in-plane angular rate change during recovery;
FIG. 15 is a plot of recovery process out-of-plane angle variation;
FIG. 16 is a graph of recovery process out-of-plane angular rate variation;
FIG. 17 is a change in tether tension during recovery;
fig. 18 is a flow chart of the method of the present invention.
The reference numerals and symbols in the drawings are as follows:
o is the mass center of the tethered satellite system and x o Is an orbit coordinate system x o Axis, y o Is the track coordinate system y o Axis, z o Is an orbital coordinate system z o Axis, x b X being the system body of tethered satellite system b Axis, y b Y being the system body of the tethered satellite system b Axis, z b Z of the system body of the tethered satellite system b A shaft.
Earth is Earth R o Is the distance between the center of the earth and the center of mass of the tethered satellite system. Alpha is the system in-plane pendulum angle and beta is the system out-of-plane pendulumAnd (5) corners.
X is the X axis of the earth equatorial inertial coordinate system, Y is the Y axis of the earth equatorial inertial coordinate system, and Z is the Z axis of the terrain equatorial inertial coordinate system.
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.
In the description of the present invention, unless otherwise specified and defined, it should be noted that the terms "mounted," "connected," and "coupled" are to be construed broadly, and may be, for example, mechanical or electrical, or may be in communication with each other between two elements, directly or indirectly through intermediaries, as would be understood by those skilled in the art, in view of the specific meaning of the terms described above.
As shown in fig. 1, the invention provides a tethered satellite release recovery control method based on uncertain system parameters, which comprises the steps of firstly carrying out necessary assumption on a tethered satellite system and carrying out dynamic modeling on the tethered satellite system; then deducing a dynamic equation of the shimmy of the tethered satellite and a mass center orbit perturbation equation of the tethered satellite; then, stability analysis is carried out on the dynamic equation of the satellite shimmy of the tethered satellite, and the dynamic equation of the satellite shimmy of the tethered satellite is linearized; then consider the uncertainty of system parameter, design and guarantee the value control law; the control law of the guaranteed value is applied to a tethered satellite system to control release and recovery; the robustness and stability of the designed control law are analyzed, and the fact that the tethered satellites can be stably released and recovered under the condition that the system parameters are uncertain is analyzed; finally, the model obtained by dynamically modeling the tethered satellite system is combined with the designed control law, and the accuracy of the control method is verified by numerical simulation, as shown in fig. 18.
The following is a detailed description.
The tethered satellite system comprises a main body with a propulsion device, a main star, a sub star and an elastic connection tether, wherein the main star and the sub star 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 star and a sub star, and the main star and the sub star are respectively regarded as the mass m m And m s The main star is provided with a tether retraction device;
2) The tether is regarded as a rigid rod, only can bear tensile force, and the tether mass is uniformly distributed;
3) Besides the spherical gravitational field effect, consider the influence of generalized perturbation forces such as J2 term of the earth, the gravity of the sun and the moon and the like;
4) Ignoring 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 ensures a value control law by considering uncertainty design of mass center and eccentricity of the tethered satellites. The method comprises the following specific steps:
and firstly, carrying out dynamic modeling on the 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 tethered satellite shimmy and a mass center orbit motion equation of the tethered satellite.
Specifically, a dynamic 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 ox o y o z o Middle z o The direction of the axis is from the center of the earth to the centroid of the tethered satellite system, y o The axis is perpendicular to the plane of the track. The orbit coordinate system rotates in a y-x rotation sequence and then is in a body coordinate system ox of the tethered satellite system b y b z b The two included angles alpha and beta are respectively an in-plane swing angle in the track plane and an out-of-plane swing angle perpendicular to the track plane; the Lagrangian equation can then be used to derive a kinetic equation for the tie-line shimmy motion as follows:
wherein omega o For the orbital angular velocity of the tethered satellite system, < +.>Is omega o The first derivative of time, μ is the gravitational constant, R c Centroid orbit radius, F te For tether tension, l is tether length, < ->Is the first derivative of l with respect to time, +.>Is the second derivative of l>Is the first derivative of alpha with respect to time, < >>Is the second derivative of alpha,/-, and>is the first derivative of β with respect to time, +.>Is the second derivative of beta, and the mass of the main star is m m The mass of the son star is m s The mass of the tether is m t The mass of the whole system is m=m m +m s +m t To simplify the equation, two parameters are introduced, respectively +.>Q l ，Q α ，Q β The generalized force corresponding to the generalized coordinates l, alpha and beta consists of a main star thrust, an earth J2 term and a lunar attraction.
Based on the Gaussian perturbation equation, a tethered satellite centroid orbit kinematics equation can be obtained:
wherein a is the semi-long axis of the mass center orbit of the tethered satellite, e is the orbit eccentricity, Ω is the right ascent intersection point, i is the orbit inclination angle, ω is the near-point amplitude angle, θ is the true near-point angle, R c Is the radius of the centroid orbit, p is the orbit semi-diameter, f u ，f h ，f r The mass center acceleration of the tethered satellites is respectively in an orbit coordinate system S o The components in the x-axis, y-axis and z-axis of the system, which contain the effects of main satellite thrust, earth J2 term, and lunar attraction on the mass center of the tethered satellite, are expressed as follows:
wherein F is x ，F y ，F z Respectively refers to the components of satellite thrust in the x axis, the y axis and the z axis, J 2 Is constant, R E For the mean equatorial radius of the earth, μ is the gravitational constant, ψ is the latitude argument which is the sum of the perigee argument and the true perigee, +.> Three-body gravitation of solar pair tethered satellite in orbit coordinate system S o The components on the x-axis, y-axis, z-axis of the middle,/->Three-body gravitation of lunar pair tethered satellites in orbit coordinate system S o Components in the x, y, z axes.
And step two, linearizing a dynamic equation of the shimmy of the tethered satellite, and then converting the dynamic equation to obtain a state equation Z after linearization of the dynamic equation.
Specifically, the stability of the system during the release and recovery of the tethered satellites is first analyzed, a small angle assumption is made and the mass m of the tether is considered t About 0, neglecting external interference and angle higher-order terms, and shimmy the tethered satelliteThe kinetic equation is reduced to the following equation:it can be seen that in the uncontrolled state the release process +.>The in-plane motion and the out-of-plane motion are in damping state, the system is stable, and the recovery process is +.>The in-plane motion and the out-of-plane motion are in a negative damping state, and the system is unstable. Omega o For the eccentricity of the system centroid orbit, R c For centroid orbit radii, their expressions are as follows:wherein p is the track half-diameter, thus defining +.>The dimensionless time τ=Ω t is chosen, in this context the track eccentricity is around 0, so that +.>The simplified dynamics of the satellite tie is expressed as the following expression G:
wherein L is m For mission rope length in tethered satellite release recovery process, λ=l/L m λ ' represents the first derivative of λ with respect to the dimensionless time τ, λ "represents the second derivative of λ with respect to the dimensionless time τ, α ' represents the first derivative of α with respect to the dimensionless time τ, α" represents the first derivative of α with respect to the dimensionless time τ, β ' represents the first derivative of β with respect to the dimensionless time τ, and β "represents the first derivative of β with respect to the dimensionless time τ. The state equation refers to an expression that characterizes the system input and state relationships, the stateThe state includes z 1 、z 2 、z 3 、z 4 、z 5 、z 6 Definition: z 1 ＝λ-q，z 2 ＝λ′，z 3 ＝α，z 4 ＝α′，z 5 ＝β，z 6 =β', the expression G is converted to a state equation, the expression of which is as follows:
z 'is the derivative of z with respect to dimensionless time, z' 1 ,z′ 2 ,z′ 3 ,z′ 4 ,z′ 5 ,z′ 6 Z is respectively 1 ＝λ-q，z 2 ＝λ′，z 3 ＝α，z 4 ＝α′，z 5 ＝β，z 6 The derivative of =β' with respect to dimensionless time, which is obtained by normalization of the tethered satellite dynamics equation after making a small angle assumption, now assuming z 1 And z 2 To be small, the state higher order quantity and the eccentricity higher order quantity are ignored, and a linearized state equation of the state equation after (0, 0) expansion can be obtained>Wherein the method comprises the steps of Control input quantity-> As can be seen from the linearized state equation, the out-of-plane motion is decoupled from the in-plane motion, which can be considered alone; the rope length motion and the out-of-plane motion are decoupled, so that the rope length change has less influence on the out-of-plane, but if the rope length is too small, the rope length change is influenced by a higher-order term during recoveryOut-of-plane motion causes the out-of-plane motion to diverge so that the rope length must not be too small for retrieval, otherwise control the out-of-plane motion with the addition of control forces.
And thirdly, designing a guarantee value control law according to a state equation Z after linearization of a dynamics equation.
Under the interference of space, the orbital eccentricity of the mass center of the tethered satellite changes within a small range around 0, and the state equation shows that the change of the orbital eccentricity causes uncertain items of system parameters, the items containing the orbital eccentricity e in the system parameters are determined as uncertain items, the following expression is obtained, and the items are determined
Then the linearized state equation uncertainty termThe following linear uncertainty system can be considered: z' = (a+Δa) z+bu, Z (t) 0 )＝Z 0 The cost function is->Where Q is a semi-positive definite matrix and R is a positive definite matrix, if there is a unique positive definite matrix P satisfying the following Li-Card equation: />Wherein->Satisfy the requirement of having +.>Then there is a guaranteed value control rate u = -R -1 B T PZ, u is the control input such that the cost function satisfies the following condition +.>Wherein->To ensure the value of the value control law.
To demonstrate the above conclusion, the lyapunov function is defined as follows: v=1/2Z T PZ, the following equation can be obtainedLet Z' = (a+Δa) z+bu, Z (t) 0 )＝Z 0 Substitution therein may result in the following equation +.>Substituting the guaranteed value control law into this equation can result in the following equation +.>By->The definition of (2) can give the following inequality +.>
Will beSubstitution therein may result in the following inequality +.>Integrating the two sides of the inequality can obtain the inequality +.>Because P is a positive definite matrix, so that V (infinity) is not less than 0, inequality->This is true.
And step four, controlling release recovery by applying the guaranteed value control law in a tethered satellite system.
Stability of the control law is analyzed as follows.
Since Q is a semi-positive definite matrix and R is a positive definite matrix, the following relationship Z is satisfied T QZ+u T Ru is more than or equal to 0, and because P is positive definite matrix, the guaranteed value of the control law satisfies the relationship ofWherein the method comprises the steps ofλ(P) represents a Pmin characteristic value, +.>Representing the maximum eigenvalue of P. Since the initial conditions are uncertain, i.e. Z 0 Is uncertain, but Z 0 The control law is bounded, so the control law is bounded in guaranteed value, so the cost function is bounded, so when the time t goes to infinity, the state Z approaches to 0, and the stability of the linear uncertainty system under the uncertainty of initial conditions is ensured.
Finally determiningIf the uncertainty ΔA element is bounded, i.e. |ΔA|d, according to +.>Definition of->Wherein->For the maximum eigenvalue of matrix D, it is then demonstrated that either non-zero vector y has +.>Using the evidence-based method, it is assumed that the presence of a non-zero vector h satisfies the following condition +.>Then there is a positive definite matrix qfullFoot->So that
Since the matrices Q and P are positive definite matricesIs Lyapunov equation, so matrix +.>The characteristic values are negative and are not consistent with the assumption that the value of the absolute value delta A is less than or equal to D, so the assumption is not true, and the evidence is obtained.
Numerical simulation verification
The writing platform of the numerical simulation software of the embodiment is a matrix laboratory platform (i.e. Matlab platform), and the Matlab series products are widely applied in the field of aerospace engineering, and are very reliable numerical simulation software in the development process of dynamics and control related problems. And combining the invention, writing a dynamic model method and a control system method, carrying out numerical simulation on given parameters, and verifying the correctness of a designed control method.
The release process balance point parameter q=1, the tethered satellite initial conditions and system parameters are shown in table 1, and the guaranteed value controller control parameters are shown in table 2.
TABLE 1 initial conditions and System parameters for tethered satellites
TABLE 2 guaranteed value controller parameters
| Parameters (parameters) | Numerical value |
| Positive weighting matrix Q | diag{[1,1,1,1]} |
| Positive weighting matrix R | 1 |
Design consideration of the eccentricity maximum e max The guaranteed value control law, 0.1, controls the release process of the tethered satellites and is compared to an LQR controller with the same controller parameters as the control law, resulting in simulation results as shown in fig. 2-9. As can be seen from comparison of the two simulation results, the two control laws control the release process of the tethered satellite, so that the tethered satellite can be released stably, but the tension required by the two control laws has a period less than 0, and the period less than 0 requires the main star thrust to compensate the tension deficiency; the control law of ensuring that the system parameters are not designed to be determined is considered, so that after the tethered satellite is released, the steady-state precision of the length of the tethered satellite is higher, the variation amplitude is smaller, the steady-state precision of the interior angle of the surface is higher, the in-plane swing is smaller, and the method has certain engineering significance.
Recovery process balance point parameter q=0.125, tethered satellite initial conditions and system parameters are shown in table 3, and guaranteed value controller control parameters are shown in table 4.
TABLE 3 initial conditions and System parameters for tethered satellites
TABLE 4 guaranteed value controller parameters
Design consideration of the eccentricity maximum e max The guaranteed value control law, 0.01, controls the recovery process of the tethered satellites and is compared to an LQR controller with the same controller parameters as the control law, resulting in simulation results as shown in fig. 10-17. From comparison of the two simulation results, the guarantee value control law of the uncertain design is considered to be higher than the LQR control law of the uncertain design is not considered, the recovery speed in the recovery process is higher, the change amplitude of the internal angle and the external angle of the face is larger, but the steady-state precision of the rope length and the internal angle of the face is higher after the recovery is completed.
Through the steps, the method for controlling the release and recovery of the tethered satellite is obtained by combining the tethered satellite shimmy kinematic equation deduced in the step one and the control rate obtained in the step three; the obtained orbital motion equation of the mass center of the tethered satellite describes the orbital motion of the mass center of the tethered satellite in an uncontrolled state; step five, carrying out numerical simulation, and verifying the feasibility and accuracy of a control system; the control law of the guaranteed value designed by the method can effectively control the release and recovery process of the tethered satellites, so that the release and recovery process of the tethered satellites is stable and has higher steady-state precision.
The invention also provides an embodiment of the tethered satellite release recovery control system, which comprises a processor and a memory, wherein the processor and the memory are in communication connection, and 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 recovery control method.
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.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
Claims (2)
1. The method for controlling the release and recovery of the tethered satellite is characterized by comprising the following steps of:
establishing a dynamic equation of the shimmy of the tethered satellite and an orbital motion equation of the mass center of the tethered satellite based on an orbit coordinate system and a body coordinate system of the tethered satellite system;
the dynamic equation of the tethered satellite shimmy is:
wherein omega o Is the orbital angular velocity of the tethered satellite system, mu is the gravitational constant, R c Centroid orbit radius, F te For tether tension, l is the tether length, the mass of the active star is m m The mass of the target star is m s TetheredMass is m t The mass of the whole system is m=m m +m s +m t ，Q l ，Q α ，Q β The generalized force corresponding to the generalized coordinates l, alpha and beta;
the mass center orbit motion equation of the tethered satellite is as follows:
wherein a is the semi-long axis of the mass center orbit of the tethered satellite, e is the orbit eccentricity, Ω is the right ascent intersection point, i is the orbit inclination angle, ω is the near-point amplitude angle, θ is the true near-point angle, R c Is the radius of the centroid orbit, p is the orbit semi-diameter, f u ，f h ，f r The mass center acceleration of the tethered satellites is respectively in an orbit coordinate system S o Components in the x-axis, y-axis, z-axis,wherein J 2 Is constant, R E The average equatorial radius of the earth, mu is the constant of gravitational force, psi is the latitude amplitude angle,/>Three-body gravitation of solar pair tethered satellite in orbit coordinate system S o The components on the x-axis, y-axis, z-axis of the middle,/->Three-body gravitation of lunar pair tethered satellites in orbit coordinate system S o Components in the middle x-axis, y-axis, z-axis;
linearizing a dynamic equation of the shimmy of the tethered satellite, and then converting the dynamic equation to obtain a state equation Z after linearization of the dynamic equation;
the dynamic equation linearization step of the tethered satellite shimmy is as follows:
the dynamic equation of the tethered satellite shimmy is simplified to the following equation:
wherein->
According to the simplified dynamic equation of the shimmy of the tethered satellite, a nonlinear state equation of the tethered satellite is obtained, and then the state equation is linearized at a zero point, and the state equation is obtained as follows:
wherein the method comprises the steps of
Control input quantity->
According to the system parameter uncertainty caused by the linear state equation Z of the dynamic equation and the orbit eccentricity of the mass center of the tethered satellite, designing a value control law;
specifically, the state equation Z after linearizing the dynamics equation is brought into the guaranteed value control law u= -R -1 B T In PZ, u is the control input quantity, and the control law of the guarantee value of the release and recovery of the tethered satellite is obtained,
wherein Q is a semi-positive definite matrix, R is a positive definite matrix, and P is a matrix satisfying the Li-Ka equationPositive definite matrix, < >>To satisfy +.>Is a matrix of the (c) in the matrix,
determining itemsUncertain item->The release recovery is controlled in a tethered satellite system using the guaranteed value control law.
2. The tethered satellite release recovery control system comprises a processor and a memory, wherein the processor and the memory are in communication connection with each other, and 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 recovery control method according to claim 1.
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