RU2769770C1 - Method for controlling a ground-based antenna complex to ensure reception and transmission of information in the communication path with a space vehicle in a quasi-geostationary orbit and control system for implementation thereof - Google Patents

Abstract

FIELD: controlling.

SUBSTANCE: group of inventions relates to control of a ground-based antenna complex (GAC) with a limited directional pattern relative to the angular oscillation amplitudes of the subsatellite point of a space vehicle (SV) in a quasi-geostationary orbit (QGSO). According to the method, a daily trajectory of the subsatellite point of the SV is approximated by a Lissajous figure, based whereon, the geometric centre of the SV is calculated. The stability of the SV information reception and transmission path is ensured by the condition of finding the actual angle between the vector of the current position of the SV relative to the GAC and the vector of the geometric centre of the SV within the directional pattern of the GAC. The proposed control system determines, in particular, the accuracy of the applied analytical method within the interval of prediction of the SV movement.

EFFECT: possibility of controlling the GAC receiving information from the SV in the QGSO based on the analytical method for predicting the orbit of said SV based on the calculated coordinates of the subsatellite point thereof.

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Description

The present invention relates to the field of astronautics and is intended to control an antenna complex with an insufficiently wide radiation pattern relative to the angular amplitudes of the trajectory of the sub-satellite point of the spacecraft while providing an information path with the spacecraft (communication, remote sensing, etc.) in a quasi-geostationary orbit.

The publication “An antenna mount for tracking geostationary satellites” (J Dijk, E.J. Maandersand, J.M.J. Oostvogels, May 1977, Netherlands) was chosen as the closest analogue on the development of a special propulsion system for a ground-based antenna complex for working with spacecraft in geostationary orbit. The disadvantage of this propulsion system of the antenna complex can be attributed to its exclusive purpose for ensuring the reception and transmission of information in the communication path with a spacecraft in geostationary orbit in the vicinity of its standing point, which makes it impossible to use it for an information path with a spacecraft in other orbits - the lack of the principle of interchangeability in terms of a full-rotation propulsion system. The second limiting factor is the complexity of the technical implementation and the limitations of the mathematical apparatus.

The mathematical apparatus for describing the trajectories of spacecraft orbits based on Lissajous figures (Lissajous orbits) is used in modeling the movement of a spacecraft in the vicinity of the Lagrange points (L1 and L2 in the Earth-Moon system), proposed in US patent 7744036 B2, 06/29/2010 and other publications . In these publications, there is no information about the analytical method for controlling the antenna complex for receiving information from a spacecraft in a quasi-geostationary orbit based on the well-known Lissajous figure, taking into account the most significant perturbing factors for this orbit.

In the development of known solutions, an analytical method is proposed for controlling the antenna complex for receiving information from a spacecraft in a quasi-geostationary orbit relative to the geocentric coordinates of a sub-satellite point at the initial time.

A method is proposed for controlling a ground-based antenna complex to ensure the reception and transmission of information in the communication path with a spacecraft in a quasi-geostationary orbit, in which the control of the antenna complex for receiving information from a spacecraft in a quasi-geostationary orbit is carried out relative to the coordinates of the sub-satellite point at the initial time in the geocentric coordinate system. In the proposed method, the daily trajectory of the sub-satellite point is approximated by the Lissajous figure and the antenna complex is pointed to the geometric center of the spacecraft at the time points t _i (i=1.2,…m) specified with a constant step on the time interval for predicting the movement of the spacecraft T _pr , according to the condition of stability of the communication path between the antenna complex and the spacecraft in a quasi-geostationary orbit F _add –F _i ≥F _zap , where F _i is the actual angle between the vector of the current position of the spacecraft relative to the ground receiving-transmitting complex and the vector of the geometric center; F _add - the maximum allowable angle between the vector of the current position of the spacecraft relative to the ground receiving-transmitting complex and the vector of the geometric center, determined by the antenna pattern and gain; F _zap - margin for angle F between the position vector of the spacecraft relative to the ground transceiver complex and the vector of the geometric center, which determines the control law for angle F. The method will be implemented in the control system of the ground antenna complex, which includes a prediction subsystem using analytical mathematical relations to calculate the GMT angular coordinates of the sub-satellite point, taking into account their changes at the current time relative to the coordinates of the sub-satellite point at the initial time and providing confirmation of the validity of the applicability of the analytical method on the time interval of predicting the motion of the spacecraft T _CR .

The proposed invention is illustrated by a block diagram of modeling the control of the antenna complex with respect to the geocentric coordinates of the sub-satellite point shown in figure 1.

The implementation of the proposed method for controlling the antenna complex is based on pointing the antenna complex to the geometric center of the spacecraft at times t _i (i=1.2,…m), given with a constant step over a certain time interval of predicting the movement of the spacecraft T _pr , and approximating the daily trajectory sub-satellite point by the well-known Lissajous figure and its description by a system of equations of a periodic nature:

(one)

 – частоты,

– сдвиг фаз.where A, B are oscillation amplitudes,

– frequencies,

– phase shift.

In total, the following factors are taken into account.

1) Precession of the line of nodes of the orbit:

(2)

 – угловая скорость прецессии [рад/с],where

is the angular velocity of precession [rad/s],

 – экваториальный радиус Земли,

is the equatorial radius of the Earth,

a is the semi-major axis of the spacecraft orbit,

e is the eccentricity of the spacecraft's orbit,

n is the angular velocity of the spacecraft (2π radians divided by the period expressed in seconds),

i - inclination [°],

J ₂ is the second dynamic shape factor (1.08262668⋅10 ^-3 for the Earth).

2) Change in the Greenwich longitude of the sub-satellite point during one revolution of the spacecraft around the Earth:

(3)

 – угловая скорость вращения Земли вокруг своей оси [рад/с],where

is the angular velocity of the Earth's rotation around its axis [rad/s],

ΔT =T _Ω – T _ES is the difference between the orbital period of the spacecraft and the sidereal day T _ES ,

T _Ω is the draconian circulation period.

3) The daily trajectory of the sub-satellite point has a closed character and is determined by the inclination i, the eccentricity e and the perigee argument ω of the orbit.

The change in the longitude of the sub-satellite point of the spacecraft due to the influence of the precession of the line of nodes Ω _pday [rad/day] and due to the difference in the period of revolution from the sidereal day Δλ [rad/day] for the period Δt [day] will be:

(4)

In total with (4) GMT angular coordinates of the sub-satellite point (longitude and latitude) (X, Y) [°] taking into account their changes over time Δt [days] relative to the coordinates of the sub-satellite point (X ₀ , Y ₀ ) [°] at the initial moment time), are determined by systems of equations (formulas 5, 6, 7) based on the system of equations (1):

Case I: i = 0 and e ≠ 0

(5)

Case II: i ≠ 0 and e = 0

(6)

Case III: i ≠ 0 and e ≠ 0

(7)

where i is inclination [rad],

ω is the perigee argument [rad],

Ω _pday is the rate of precession of the line of nodes [rad/day],

Δλ is the rate of change of the Greenwich longitude of the sub-satellite point of the spacecraft due to the difference between its orbital period and sidereal day T _SS [rad/day],

e is the eccentricity of the spacecraft's orbit.

Knowing the GMT angular coordinates of the sub-satellite point at times t _i (i=1,2,…m) at a certain time interval T _CR , it is possible to determine the angular coordinates of the geometric center. Now, knowing the height of the spacecraft and the angular coordinates of the ground receiving-transmitting complex (φ _N , λ _N ) in the geocentric coordinate system, it is possible to calculate the values of azimuth A and elevation angle γ for any location of the ground receiving-transmitting complex.

From the point of view of the normal operation of the antenna complex in the information path with the spacecraft, there is a known radiation pattern, through which, taking into account the given gain level, the maximum allowable angle (F _add ) is determined between the vector of the current position of the spacecraft relative to the ground-based transceiver complex and the vector of the geometric center.

The condition of a stable information path between the antenna complex and the spacecraft in orbit, the parameters of which are slightly different from the geostationary orbit, is determined by the relation:

(eight)

where i is the inclination of the orbit,

e - eccentricity,

ω is the perigee argument,

T is the circulation period,

F _add , F _zap - the maximum allowable value and margin for the angle F.

и текущим углом F должна быть не меньше F_зап. При невыполнении условия (8) необходимо обновление начальных условий и перенацеливание антенного комплекса в геометрический центр с новыми координатами.The difference between the maximum allowable angle

and the current angle F should not be less than F _app . If condition (8) is not met, it is necessary to update the initial conditions and redirect the antenna complex to the geometric center with new coordinates.

A refinement of the allowable period of applicability of the analytical method without updating the initial conditions (correction of the time interval T _pr ) is provided using an exact model of numerical integration of the motion of the spacecraft, taking into account the influence of disturbances due to the non-centrality of the Earth's gravitational field, the attraction of the Moon and the Sun, as well as the pressure of solar radiation.

The practical implementation of the proposed control system for the antenna complex for receiving and transmitting information from remote sensing of the Earth can be described as follows (Fig. 1).

The input data subsystem 1 includes functional blocks (computer components) that provide the initial conditions for the motion parameters of the spacecraft of the orbital group, the coordinates of the ground-based transceiver complex, the time interval for predicting the motion of the spacecraft T _pr , the values of the angles F _add and F _zap to implement the required law angle F.

Subsystem 2 for correcting the forecasting time interval T _pr , associated with the input data subsystem 1, is designed to simulate the motion of the spacecraft, includes functional blocks (computer components) for integrating the differential equations of motion of the spacecraft and generating output functions, and provides confirmation of the applicability of the analytical method over the time interval predicting T _PR .

Prediction subsystem 3 includes functional blocks (computer components) that provide:

- prediction of the position of the spacecraft at discrete times t _i ( φ _i and λ _i ) in the geocentric coordinate system on the prediction time interval T _CR using equations (4-7);

- calculation of the geometric center (pointing points of the antenna complex in the forecasting time interval);

- calculation of antenna pointing angles (elevation angle γ and azimuth A ).

Subsystem 4 of forming the assessment of the stability of the communication path includes functional blocks (computer components) that provide:

- comparison in a cycle on the time interval of prediction T _CR current value of the measured parameter F _i with the reference value F _add ;

- controls the fulfillment of the condition F _add - F _i ≥ F _zap , that is, the difference between the allowable and actual angles must not be less than the stock F _zap .

- completes the cycle in time or in case of non-fulfillment of the controlled condition and performs a transition to subsystem 1 to continue calculations at the next time interval with new initial conditions.

The choice of retargeting time and the calculation of the pointing angles of the antenna complex is provided by the computer equipment of the control system, in which changes in the values of the angular parameters of the tracked object are automatically determined and tracked.

Claims (6)

1. A method for controlling a ground-based antenna complex to ensure the reception and transmission of information in the communication path with a spacecraft in a quasi-geostationary orbit, in which the control of the antenna complex for receiving information from a spacecraft in a quasi-geostationary orbit is carried out relative to the coordinates of the sub-satellite point at the initial time in the geocentric coordinate system, characterized in that the daily trajectory of the sub-satellite point is approximated by the Lissajous figure and the antenna complex is pointed to the geometric center of the spacecraft positions at time points t _i (i=1.2,…m) specified with a constant step on the time interval of predicting the movement of the spacecraft T _pr , according to the stability condition of the communication path between the antenna complex and the spacecraft in a quasi-geostationary orbit F _add –F _i ≥F _zap , where F _i is the actual angle between the vector of the current position of the spacecraft relative to the ground receiving-transmitting complex and the vector of the geometric center; F _add - the maximum allowable angle between the vector of the current position of the spacecraft relative to the ground receiving-transmitting complex and the vector of the geometric center, determined by the antenna pattern and gain; F _zap - the margin for the angle F between the position vector of the spacecraft relative to the ground receiving-transmitting complex and the geometric center vector, which determines the control law for the angle F. 2. The control system for implementing the method according to claim 1, characterized in that it includes a prediction subsystem that uses analytical mathematical relations to calculate the Greenwich angular coordinates of the sub-satellite point, taking into account their changes at the current time relative to the coordinates of the sub-satellite point at the initial time and providing confirmation of the validity of the applicability of the analytical method on the time interval of predicting the motion of the spacecraft T _PR .

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