An orbit transfer and positioning method for electric propulsion GEO satellite

Abstract

The present invention discloses an electric propulsion GEO satellite orbit transfer and fixed-point method, which belongs to the field of satellite orbit dynamics technology, and includes the following steps: S1, establishing a small-thrust satellite orbit dynamics model based on multi-perturbation and earth shadow constraints; S2, constructing a Lypunov function according to the small-thrust satellite orbit dynamics model, and using the Lypunov function to construct an RQ-Law feedback control model; S3, optimizing the weight parameters of the RQ-Law feedback control model; S4, using the optimized RQ-Law feedback control model to complete orbit transfer and fixed-point. In view of the problem that the current satellite orbit transfer time is long, the present invention proposes an innovative method, which integrates the traditional orbit transfer and fixed-point optimization into one stage, thereby realizing the integration of orbit transfer and fixed-point.

Description

Technical Field

[0001] The invention belongs to the technical field of satellite orbit dynamics, and in particular relates to an orbit transfer and positioning method for an electric propulsion GEO satellite. Background Art

[0002] The orbit transfer and fixed-point capture of electric propulsion GEO satellites is the process of transferring the satellite from a low orbit to GEO (geostationary orbit) and reaching a designated orbital position under the thrust of the electric propulsion system. The main characteristics of this process are long flight time and strong dynamic nonlinearity. The constraints and goals of orbit transfer and fixed-point capture are inconsistent. It is necessary to formulate appropriate orbit transfer and fixed-point capture strategies to achieve the shortest time or the lowest fuel consumption under the given constraints and orbit accuracy conditions.

[0003] The traditional electric propulsion GEO satellite orbit transfer and positioning is to pursue the lowest fuel consumption or the shortest time in the orbit transfer process, and the highest possible positioning accuracy in the positioning process, so the orbit transfer and positioning capture are mainly carried out in segments. However, the segmented orbit transfer and positioning control strategy requires orbit determination and orbit control for each segment during implementation, which increases the operational process of satellite orbit transfer and positioning, and further increases the number of ground station measurement and control interventions, the flight time of the entire process, and the actual fuel consumption of the satellite.

[0004] In order to enable electric propulsion satellites to quickly and accurately complete the flight process when only the initial orbit and the fixed-point target orbit position are known, and to reduce the flight time and the burden of ground station measurement and control, it is necessary to improve the traditional segmented control to an integrated orbit transfer and fixed-point control problem, effectively shortening the flight time of the entire process of satellite orbit transfer and fixed-point while ensuring the terminal fixed-point accuracy requirements, so as to improve the efficiency of satellite orbit transfer, thereby supporting new mission requirements such as high-orbit rapid deployment, space attack and defense, and orbital game. However, how to integrate the orbit control of these two stages is a difficult problem, so it is urgent to propose an integrated method for orbit transfer and fixed-point of electric propulsion GEO satellites. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes an electric propulsion GEO satellite orbit transfer and positioning method.

[0006] The technical solution of the present invention is to provide an electric propulsion GEO satellite orbit transfer and positioning method comprising the following steps:

[0007] S1. Establish a low-thrust satellite orbital dynamics model based on multiple perturbations and earth shadow constraints;

[0008] S2. According to the orbital dynamics model of the small thrust satellite, the Lypunov function is constructed, and the RQ-Law feedback control model is constructed using the Lypunov function;

[0009] S3, optimizing the weight parameters of the RQ-Law feedback control model;

[0010] S4. Use the optimized RQ-Law feedback control model to complete orbit transfer and positioning.

[0011] Furthermore, S1 includes the following sub-steps:

[0012] S11, obtaining satellite orbit parameters, and determining state quantities according to the satellite orbit parameters;

[0013] S12. Based on the state quantities, a low-thrust satellite orbital dynamics model is established under multi-perturbation and earth shadow constraints.

[0014] Further, in S11, the satellite orbit parameters include the orbit semi-major axis, the vector of the orbit eccentricity, the component of the orbit eccentricity, the vector of the orbit inclination, the component of the orbit inclination and the true longitude;

[0015] In S11, the expression of the state quantity X is:

[0016] X = [afghkl] T ;

[0017] Where a is the semi-major axis of the orbit, f is the vector of the orbital eccentricity, g is the component of the orbital eccentricity, h is the vector of the orbital inclination, k is the component of the orbital inclination, and l is the true longitude.

[0018] Furthermore, in S1, the expression of the orbital dynamics model of the low-thrust satellite is:

[0019]

[0020] In the formula, X is the state quantity, A is the acceleration coefficient matrix, Q′ is the acceleration generated by the electric thrust, and u p is the earth shadow constraint coefficient, is the transformation matrix from the orbital coordinate system to the J2000ECI coordinate system, is the perturbation acceleration of J2, a sum is the solar gravitational acceleration, a moon is the gravitational perturbation acceleration of the ball, a drag is the atmospheric drag acceleration, a srp is the solar pressure perturbation acceleration, b is the Kepler drift term, T 0 is the electric thrust, I sp is the specific impulse of the electric propulsion thruster, g 0 is the standard gravitational acceleration, and m is the mass of the satellite.

[0021] Furthermore, in S2, the expression of the Lypunov function Q is:

[0022]

[0023] Where P is the penalty function, W p is the relevant weight, is the scaling function, is the orbital element number of the GEO satellite, is a scalar weight, is the augmented set of target orbital elements, is the maximum rate of change of each orbital element of the GEO satellite relative to the thrust direction and true longitude, a is the orbit semi-major axis, f is the vector of orbital eccentricity, g is the component of orbital eccentricity, h is the vector of orbital inclination, k is the component of orbital inclination, is the set of orbital elements.

[0024] Furthermore, in S2, the expression of the RQ-Law feedback control model Z is:

[0025]

[0026] In the formula, is the orbital element number of the GEO satellite, is the number of unaugmented target position orbital elements; L c is the true longitude of the GEO satellite, L T is the true longitude of the target location, ψ is the weight set of each parameter, and Q is the Lypunov function.

[0027] Furthermore, S3 includes the following sub-steps:

[0028] S31, constructing initial state constraints and optimal time indicators;

[0029] S32. Optimize the weight parameters of the RQ-Law feedback control model using the initial state constraints and the optimal time index.

[0030] Furthermore, in S31, the expression of the initial state constraint is:

[0031]

[0032] Where, t 0 is the initial moment, a(t 0 ) is the semi-major axis of the orbit at the initial moment, f(t 0 ) is the vector of orbital eccentricity at the initial moment, g(t 0 ) is the component of orbital eccentricity at the initial moment, h(t 0 ) is the vector of the orbital inclination at the initial moment, k(t 0 ) is the component of the orbital inclination at the initial moment, l(t0 ) is the true longitude at the initial moment, a D 、f D , g D 、h D , k D , l D are the orbital elements of the initial orbit respectively.

[0033] Furthermore, in S31, the expression of the optimal time index J is:

[0034]

[0035] Where, t 0 is the initial time, t f The terminal moment.

[0036] The beneficial effects of the present invention are:

[0037] (1) The present invention aims to solve the problem of long satellite orbit transfer time and proposes an innovative method, which optimizes and integrates the traditional orbit transfer and fixed-point in stages into one stage, thus realizing the integration of orbit transfer and fixed-point.

[0038] (2) The present invention improves the traditional phased orbit transfer and fixed-point optimization method of electric propulsion GEO satellites and establishes an orbit transfer and fixed-point integrated control model; it not only significantly reduces the time of satellite orbit transfer and reduces the cost of ground station measurement and control, but also improves the efficiency of satellite orbit transfer; this method can support new application needs such as rapid high-orbit deployment, space offense and defense during wartime, and orbital game, and provides strong support for the further development of satellite technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Flow chart of orbit transfer and positioning method for electric propulsion GEO satellite;

[0040] Figure 2 It is a three-dimensional diagram of the satellite motion trajectory in segmented stage 1;

[0041] Figure 3 It is a three-dimensional diagram of the satellite motion trajectory in the segmented stage 2;

[0042] Figure 4 It is a three-dimensional map of the integrated satellite motion trajectory;

[0043] Figure 5 It is the curve diagram of segmented satellite semi-major axis variation;

[0044] Figure 6 It is the curve diagram of the change of the semi-major axis of the integrated satellite;

[0045] Figure 7 It is the curve diagram of segmented satellite eccentricity variation;

[0046] Figure 8 It is the curve diagram of integrated satellite eccentricity change;

[0047] Fig. 9 It is a curve diagram of segmented satellite orbit inclination variation;

[0048] Fig.10 It is the curve diagram of the integrated satellite orbit inclination change;

[0049] Fig.11 It is the curve diagram of the change of segmented satellite thrust angle α;

[0050] Fig.12 It is the curve diagram of the thrust angle α change of the integrated satellite;

[0051] Fig.13 It is the curve diagram of segmented satellite thrust angle β change;

[0052] Fig.14 This is the curve of the integrated satellite thrust angle β change. DETAILED DESCRIPTION

[0053] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0054] like Figure 1 As shown, the present invention provides an electric propulsion GEO satellite orbit transfer and positioning method, comprising the following steps:

[0055] S1. Establish a low-thrust satellite orbital dynamics model based on multiple perturbations and earth shadow constraints;

[0056] S2. According to the orbital dynamics model of the small thrust satellite, the Lypunov function is constructed, and the RQ-Law feedback control model is constructed using the Lypunov function;

[0057] S3, optimizing the weight parameters of the RQ-Law feedback control model;

[0058] S4. Use the optimized RQ-Law feedback control model to complete orbit transfer and positioning.

[0059] In an embodiment of the present invention, in order to improve the efficiency of orbit transfer and fixed-point transfer of electric propulsion GEO satellites, shorten the time of orbit transfer, reduce the fuel consumption of the satellite throughout the process and the measurement and control burden of the ground station, a feedback control model for integrated orbit transfer and fixed-point of GEO satellites is designed, and the time optimal strategy task of satellite orbit transfer and fixed-point is modeled as a Q-method weight parameter optimization problem based on Lyapunov function, and the optimal time strategy under time performance indicators, initial constraints, and terminal constraints is obtained, so as to realize the integrated control of orbit transfer and fixed-point of electric propulsion GEO satellites, and support tasks such as rapid deployment of high orbits, orbital games, and space attack and defense.

[0060] In this embodiment of the present invention, S1 includes the following sub-steps:

[0061] S11, obtaining satellite orbit parameters, and determining state quantities according to the satellite orbit parameters;

[0062] S12. Based on the state quantities, a low-thrust satellite orbital dynamics model is established under multi-perturbation and earth shadow constraints.

[0063] In the embodiment of the present invention, in S11, the satellite orbit parameters include the orbit semi-major axis, the vector of the orbit eccentricity, the component of the orbit eccentricity, the vector of the orbit inclination, the component of the orbit inclination and the true longitude;

[0064] In S11, the expression of the state quantity X is:

[0065] X = [afghkl] T ;

[0066] Where a is the semi-major axis of the orbit, f is the vector of the orbital eccentricity, g is the component of the orbital eccentricity, h is the vector of the orbital inclination, k is the component of the orbital inclination, and l is the true longitude.

[0067] In S11, the improved equinox root number [pfghkl] is used to describe the orbital motion of the electric propulsion GEO satellite. The expressions of each root number are as follows:

[0068] p=a(1-e 2 )

[0069] f=ecos(ω+Ω)

[0070] g=esin(ω+Ω)

[0071] h=tan(i / 2)cosΩ

[0072] k=tan(i / 2)sinΩ

[0073] L = Ω + ω + θ;

[0074] Among them, p is the orbit semi-diameter, e is the orbit eccentricity, i is the orbit inclination, Ω is the ascending node equator, ω is the perigee argument, and θ is the true anomaly angle. Studies have found that using the semi-major axis a instead of the orbit semi-diameter p has better control performance.

[0075] In the embodiment of the present invention, in S1, the expression of the low-thrust satellite orbital dynamics model is:

[0076]

[0077] In the formula, X is the state quantity, A is the acceleration coefficient matrix, Q′ is the acceleration generated by the electric thrust, and u p is the earth shadow constraint coefficient, is the transformation matrix from the orbital coordinate system to the J2000ECI coordinate system, is the perturbation acceleration of J2, a sum is the solar gravitational acceleration, a moon is the gravitational perturbation acceleration of the ball, a drag is the atmospheric drag acceleration, a srp is the solar pressure perturbation acceleration, b is the Kepler drift term, T 0 is the electric thrust, I sp is the specific impulse of the electric propulsion thruster, g 0 is the standard gravitational acceleration, and m is the mass of the satellite.

[0078] In the embodiment of the present invention, in S2, the expression of the Lypunov function Q is:

[0079]

[0080] Where P is the penalty function, W p is the relevant weight, is the scaling function, is the orbital element number of the GEO satellite, is a scalar weight, is the augmented set of target orbital elements, is the maximum rate of change of each orbital element of the GEO satellite relative to the thrust direction and true longitude, a is the orbit semi-major axis, f is the vector of orbital eccentricity, g is the component of orbital eccentricity, h is the vector of orbital inclination, k is the component of orbital inclination, is the set of orbital elements. The unit of Q is the square of time, which reflects the time to complete orbit transfer and fixed point. The smaller Q is, the shorter the time to complete orbit transfer and fixed point is.

[0081] In the embodiment of the present invention, in S2, the expression of the RQ-Law feedback control model Z is:

[0082]

[0083] In the formula, is the orbital element number of the GEO satellite, is the number of unaugmented target position orbital elements; L c is the true longitude of the GEO satellite, L T is the true longitude of the target location, Ψ is the weight set of each parameter, and Q is the Lypunov function.

[0084] In this embodiment of the present invention, S3 includes the following sub-steps:

[0085] S31, constructing initial state constraints and optimal time indicators;

[0086] S32. Optimize the weight parameters of the RQ-Law feedback control model using the initial state constraints and the optimal time index.

[0087] In the embodiment of the present invention, in S31, the expression of the initial state constraint is:

[0088]

[0089] Where, t 0 is the initial moment, a(t 0 ) is the semi-major axis of the orbit at the initial moment, f(t 0 ) is the vector of orbital eccentricity at the initial moment, g(t 0 ) is the component of orbital eccentricity at the initial moment, h(t 0 ) is the vector of the orbital inclination at the initial moment, k(t 0 ) is the component of the orbital inclination at the initial moment, l(t 0 ) is the true longitude at the initial moment, a D 、f D , g D 、h D , k D , l D are the orbital elements of the initial orbit respectively.

[0090] In the optimization process, it is necessary to consider whether the all-electric propulsion satellite will enter the target orbit at the corresponding transfer time, so the terminal constraints need to be considered. The transfer orbit optimization problem is converted into an unconstrained parameter optimization problem, so the terminal constraints need to be weighted into the performance indicators. Since the target orbit of the orbit transfer process is the geostationary orbit (GEO), it is only necessary to make the four orbital elements of semi-major axis, eccentricity, orbit inclination and true longitude reach the target value.

[0091] In the embodiment of the present invention, in S31, the expression of the optimal time index J is:

[0092]

[0093] Where, t 0 is the initial time, t f The terminal moment.

[0094] In the embodiments of the present invention, in order to better illustrate the purpose and advantages of the present invention, the specific implementation mode of the present invention is further described in detail below with reference to the accompanying drawings.

[0095] In order to verify the effectiveness of the electric propulsion satellite orbit placement solution proposed in this invention, simulation was performed in Python 3.8 environment. The simulation step of the whole orbit transfer was set to 0.01 day. The physical parameters of the electric propulsion satellite are shown in Table 1, and the initial orbital elements and target orbital elements are shown in Table 2. The maximum allowable error of the electric propulsion satellite terminal is shown in Table 3.

[0096] Table 1

[0097] parameter value unit Electric thrust 0.8 ox Specific impulse 3500 m / s <![CDATA[Drag coefficient C d > 2.2 - <![CDATA[Reflection coefficient C r > 1.68 - Effective area S 40 Square meter

[0098] Table 2

[0099]

[0100] Table 3

[0101] Orbital parameters Entering orbit Fixed point unit Semi-major axis 1500 1500 rice Eccentricity 0.00085 0.00085 - Orbital inclination 0.01 0.01 Spend True longitude - 0.01 Spend

[0102] The weight optimization algorithm used this time is the particle swarm algorithm, and the time for optimizing the weight parameters in two stages, orbit transfer and fixed point, is compared. The results show that the method of integrating orbit transfer and fixed point is faster than the optimization time of transfer and fixed point segmentation, and achieves near-optimal integration of orbit transfer and fixed point for electric propulsion GEO satellites under multi-perturbation and earth shadow constraints.

[0103] Through the optimized weight parameters, the changes of various parameters in the process of the electric propulsion satellite transferring from the GTO orbit to the GEO orbit and completing the fixed-point mission are analyzed as follows: Figures 2 to 14 . Figure 2 and Figure 3 The three-dimensional motion trajectory diagram considering orbit transfer and fixed-point segmentation, Figure 4 It is a three-dimensional motion trajectory diagram integrating orbit transfer and fixed point.

[0104] Figure 5 and Figure 6 The satellite semi-major axis change curves of the segmented and integrated methods are shown in Figure 2. By comparison, the time required for the integrated method to complete the process from orbit transfer to fixed point is significantly shorter than that of the segmented method. Figures 7 to 14The curves of the change of satellite eccentricity, orbit inclination and thrust angle direction by integrated method and segmented consideration are shown. By comparison, the time of integrated method is shorter than that of segmented consideration, achieving near-optimal electric propulsion GEO satellite orbit transfer and fixed-point integrated orbit change under multi-perturbation earth shadow constraints.

[0105] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. An electric propulsion GEO satellite orbit transfer and positioning method, characterized in that: The following steps are involved: S1. Establish a low-thrust satellite orbital dynamics model based on multiple perturbations and earth shadow constraints; S2. According to the orbital dynamics model of the small-thrust satellite, the Lyapunov function is constructed, and the RQ-Law feedback control model is constructed using the Lyapunov function; S3, optimizing the weight parameters of the RQ-Law feedback control model; S4, using the optimized RQ-Law feedback control model to complete orbit transfer and positioning; The S1 comprises the following sub-steps: S11, obtaining satellite orbit parameters, and determining state quantities according to the satellite orbit parameters; S12. According to the state quantity, a low-thrust satellite orbit dynamics model based on multi-perturbation and earth shadow constraints is established; In S11, the satellite orbit parameters include the orbit semi-major axis, the vector of the orbit eccentricity, the component of the orbit eccentricity, the vector of the orbit inclination, the component of the orbit inclination and the true longitude; In S11, the expression of the state quantity X is: ； Where a is the semi-major axis of the orbit, f is the vector of the orbital eccentricity, g is the component of the orbital eccentricity, h is the vector of the orbital inclination, k is the component of the orbital inclination, and l is the true longitude; In S1, the expression of the orbital dynamics model of the low-thrust satellite is: ； In the formula, X is the state quantity, A is the acceleration coefficient matrix, is the acceleration generated by the electric thrust, u p is the earth shadow constraint coefficient, is the transformation matrix from the orbital coordinate system to the J2000 ECI coordinate system, is the perturbation acceleration of J2, a sum is the solar gravitational acceleration, a moon is the gravitational perturbation acceleration of the ball, a drag is the atmospheric drag acceleration, a srp is the solar pressure perturbation acceleration, b is the Kepler drift term, T0 is the electric thrust, I sp is the specific impulse of the electric propulsion thruster, g0 is the standard gravitational acceleration, and m is the satellite mass; In S2, the expression of the Lyapunov function Q is: ； Where P is the penalty function, W p is the relevant weight, is the scaling function, is the orbital element number of the GEO satellite, is a scalar weight, is the augmented set of target orbital elements, is the maximum rate of change of each orbital element of the GEO satellite relative to the thrust direction and true longitude, a is the orbit semi-major axis, f is the vector of orbital eccentricity, g is the component of orbital eccentricity, h is the vector of orbital inclination, k is the component of orbital inclination, represents the set of orbital elements; In S2, the expression of the RQ-Law feedback control model Z is: ； In the formula, is the orbital element number of the GEO satellite, is the number of unaugmented target position orbital elements; L c is the true longitude of the GEO satellite, L T is the true longitude of the target location, is the weight set of each parameter, Q is the Lyapunov function; The S3 comprises the following sub-steps: S31, constructing initial state constraints and optimal time indicators; S32, optimizing the weight parameters of the RQ-Law feedback control model using the initial state constraint and the optimal time index; In S31, the expression of the initial state constraint is: ； Where t0 is the initial time, a(t0) is the semi-major axis of the orbit at the initial time, f(t0) is the vector of the orbital eccentricity at the initial time, g(t0) is the component of the orbital eccentricity at the initial time, h(t0) is the vector of the orbital inclination at the initial time, k(t0) is the component of the orbital inclination at the initial time, l(t0) is the true longitude at the initial time, and a D 、f D , g D 、h D , k D , l D are the orbital elements of the initial orbit respectively; In S31, the expression of the optimal time index J is: ； In the formula, t0 is the initial time, t f The terminal moment.

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