RU2708468C1 - Holding method of geostationary spacecraft - Google Patents

Abstract

FIELD: astronautics.

SUBSTANCE: invention relates to the space equipment. In the method of holding a spacecraft (SC) in a given range of longitudes and latitudes of a working position on an orbit, calculating inclination corrections on two nominally opposite active sections (AS), calculating current vectors of eccentricity for one and the same moment – end moment of second AS so that in first version engine thrust is considered only at first AS, in second version engine thrust is considered only at second AS, according to minimum deviation of one and the other eccentric vectors from target vector, working AS and corresponding engine are selected. Stable centripetal effects of spacecraft evolution on longitude and evolution of SC eccentricity vector on orbital position are generated and maintained by the whole set of regular corrections.

EFFECT: increased accuracy of longitude retention, narrowing of spacecraft retention limits.

1 cl

Description

The present invention relates to the field of space technology and can be used to hold the spacecraft in a given range of geographical longitudes and latitudes of the working position in geostationary orbit.

The well-known "Method for the simultaneous correction of retention of the inclination vector of the orbit and the period of revolution of a three-axis stabilized spacecraft", patent RU No. 2381965. According to this method, the required angle of deviation of the thrust vector of the engine from the normal to the orbit in the yaw plane is determined, based on ensuring the specified accuracy of the correction of the period of revolution of the spacecraft and the required changes for the correction of the transversal and orthogonal components of the velocity vector of the spacecraft, the deviations of the directions of the thrust vectors of the engines are set , calculate the duration of the engines according to the formulas:

where τ ₁ , τ ₂ - the duration of the engines, s;

J _n , J _τ are the thrust impulses required for corrections, respectively, of the inclination vector of the orbit and the spacecraft orbital period, Н⋅с;

F ₁ , F ₂ - engine thrust, N;

θ ₁ , θ ₂ are the angles of deviation of the thrust vectors of the engines from the normal to the plane of the orbit in the yaw plane along the smallest arc,

and carry out the correction by a pair of engines installed on opposite sides from the normal to the orbit, for which they are turned on sequentially for the estimated duration of work. The following sequence of operations is performed (all angular values are expressed in radians):

1. Determine the required angle (θ) of the deviation of the engine thrust vector from normal to orbit, based on ensuring the specified accuracy of the correction of the spacecraft rotation period and the required changes for the correction of the transversal and orthogonal components of the spacecraft velocity vector.

The angle θ is calculated by the formula

where θ is the acute angle of deviation of the engines on different sides from the normal to the orbit in the yaw plane;

due to the fact that

should

δθ is the error with which the position of the spacecraft in the yaw plane is maintained relative to the center of mass;

δV _τ is the specified maximum relative error in the implementation of the correcting pulse to change the spacecraft revolution period;

ΔV _τ is the required maximum change for the correction of the transversal component of the spacecraft velocity vector during the period of its active existence, m / s;

(составляющие вектора наклонения i_x=sin(i)⋅cos(Ω); i_y=sin(i)⋅sin(Ω), Ω - долгота восходящего узла орбиты), м/с.ΔV _n is the required change for the correction of the orthogonal component of the spacecraft velocity vector, corresponding to the calculated maximum change in the inclination vector

(components of the inclination vector i _x = sin (i) ⋅cos (Ω); i _y = sin (i) ⋅sin (Ω), Ω is the longitude of the ascending node of the orbit), m / s.

It should be noted that the method does not require angular turns of the spacecraft. Engines are installed structurally at pre-calculated angles θ ₁ and θ ₂ .

2. Define the directions of the thrust vectors of the engines.

Two engines are installed relative to both axis of the normal to the orbit. The directions of the engine thrust vectors are now set by deviations from the normal to the orbit in the yaw plane at the angles “+ θ” and “-θ”. In the general case, the moduli of these angles may not be equal.

3. Adjust the direction of the thrust vectors of the engines.

When installing engines on a spacecraft at angles “+ θ” and “-θ”, the geometric axis of the engine is taken as the direction of the engine thrust vector. However, due to the error in the installation of the engine and the deviation of the actual direction of the thrust vector of the engine from its geometric axis, the actual angles of direction of the thrust vectors differ from the calculated ones. Therefore, an adjustment is made in which the actual angles of deviation of the engine thrust vectors from the normal are determined. To carry out the adjustment, the engines are switched on in turn, and after each switching on, trajectory measurements are carried out. By changing the parameters of the orbit, the actual angles θ ₁ and θ _{2 are} determined for the first and second engines of each of the semi-axes of the normal to the orbit. For example, for a geostationary orbit, the angles θ ₁ and θ ₂ can be determined by the formula

where μ is the gravitational parameter of the Earth, km ³ / s ² ;

ΔT - change in the spacecraft rotation period due to engine operation (determined by the results of trajectory measurements), s;

R is the radius of the nominal stationary orbit of the spacecraft, km;

а - acceleration created by the engine, km / s ² ;

τ is the duration of the engine, s.

4. Calculate the duration of the engines.

The sum of the projections of the thrust impulses of the first and second engines on the normal to the orbit should be equal to the required impulse for the correction of the inclination vector of the orbit, i.e.

On the other hand, the difference between the projections of the thrust pulses of the first and second engines on the transversal should be equal to the required pulse for the correction of the spacecraft rotation period, i.e.

Solving equations (8) and (9) together with respect to τ ₁ and τ ₂ , we obtain (1) and (2).

5. Carry out a correction with a pair of engines.

Corrections are made by sequentially turning on the first engine for τ ₁ seconds and the second engine for τ ₂ seconds.

The pulses J _n , J _{τ are} determined by the strategy of real spacecraft retention according to well-known formulas, for example, P.E. Elyasberg “Introduction to AES Flight Theory”, M., Nauka, 1965

where J _τ is the required impulse for correcting the spacecraft orbital period, kg⋅km / s;

m is the mass of the spacecraft, kg;

μ - gravitational parameter of the Earth, km ³ / s ² ;

ΔT is the required change in the period for applying for correction, s;

R is the radius of the nominal stationary orbit, km,

as well as G.M. Chernyavsky, V.A. Bartenev, V.A. Malyshev, “Control of the orbit of a stationary satellite,” Moscow, Mashinostroenie, 1984, pp. 129, 138. The moments of engine start-up are determined from the condition that the middle of the interval of operation of the engines corresponds to the point of optimal application of pulses. With continuous correction by two engines in a stationary orbit, you can use the following working formulas (all angular values are expressed in radians):

where t ₀ - some initial time, seconds from the reference era;

[Δi _y ⋅sign ( a _z ) / Δi _x ⋅sign ( a _z )] - right ascension of the middle of the active section;

в координатах:Δi _y , Δi _x - the required components of the change in the inclination vector

in coordinates:

Ω is the longitude of the ascending node of the spacecraft orbit;

and _z is the orthogonal acceleration, km / s ² ;

- отклонение от точки центра в момент t_0;

- deviation from the center point at time t _0;

S ₀ - average Greenwich stellar time at time t _0;

λ_c - longitude of the center - the center of the orbital position;

n is the average spacecraft motion, s ^-1 ;

V _cp is the average orbital velocity, km / s.

The described method, “A method for simultaneously correcting the retention of the inclination vector of the orbit and the period of revolution of a three-axis stabilized spacecraft” in the claimed form as a method of two-parameter correction is impeccable. To maintain a geostationary spacecraft in an orbital position, a strategy and tactics of holding it in a narrow region in longitude, as well as inclination and eccentricity vectors, are required. The fact that only two parameters are corrected (even if by the same engines at the same time) can be considered a disadvantage of the prototype - it could be a way of simultaneous three-parameter, and not two-parameter, correction of geostationary spacecraft retention.

The well-known "Method of holding a geostationary spacecraft at a given orbital position", patent RU No. 2481249, which is taken as a prototype. According to this method, which includes the entire distinguishing part of the analogue of RU No. 2381965, given above: 1 - apply a test action to the spacecraft body by turning on the engine; 2 - measure the values of the anode current and voltage on the electrodes of the plasma engine during the application of the verification and corrective actions; 3 - average the obtained values over the entire measurement interval; 4 - calculate traction when applying a corrective action according to:

where F _i - engine thrust with the i-th conventional number, N;

- коэффициент трансформации,

- transformation ratio,

относится к проверочным определениям тяги двигателей коррекции;index

relates to test definitions of thrust correction engines;

I _i - the average value of the anode current, and ;

U _i - the average value of the voltage at the electrodes, in,

5 - determine the nominal dependence of the sidereal circulation period after the correction of the retention from the current spacecraft position in longitude relative to the center of the orbital position; 6 - reinstall in the inertial space the reference plane, perpendicular to the equatorial plane, passing through the middle of the upcoming current active spacecraft orbit, 7 - at each retention step, they transmit to the autonomous navigation system the time of the middle of the active section and 8 - give it the function of determining according to the path data measurements of the actual sidereal circulation period, as the difference of consecutive moments of the spacecraft crossing this plane, 9 - if the actual sidereal circulation periods diverge from the forecasted periods by more than the maximum error of determining and predicting the period, - go into non-offline hold mode and 10 - plan test inclusions motors to clarify the coefficients of transformation of current and voltage into engine thrust, and 11 - through the whole set of corrections cause alive steady centripetal effect on the evolution of spacecraft orbital position.

In operation 11, the centripetal effect of the evolution of the spacecraft at the orbital position means the centripetal effect of the evolution of the spacecraft in longitude.

определяют по известным методикам, исходя из фактического значения изменения корректируемого параметра орбитального движения КА, например, периода обращения.I-th engine thrust

determined by known methods, based on the actual value of the change in the corrected parameter of the orbital motion of the spacecraft, for example, the period of revolution.

The prototype is overloaded with details that are ineffective over a long time interval of the active existence of the spacecraft. For example, the determination of traction by the readings of sensors of current strength and voltage of a running engine. In the autonomous mode of holding the spacecraft at a given orbital position, test inclusions are not needed. They are needed outside this mode, when an error in determining the thrust becomes the main cause of spacecraft exits from the confinement regions. Of course, traction refinement is useful. And it must be carried out in accordance with some pre-established regulations. In the autonomous hold mode, when the necessary hold correction corrections are regularly and often carried out, it is possible to successfully use a certain nominal table of thrusts of efficient engines and to refine the thrust only because of the clearly rude results of ballistic support for the spacecraft flight. But, if you do not specify the engine thrust, then there is no need to reinstall the control plane in the inertial space. The scope of work on ballistic support is complex, and there is no need to cover it with a single technical solution. Of the distinctive part of the prototype, we take in the restrictive part of the present invention only the determination of the nominal dependence of the sidereal circulation period after the correction of the retention from the current spacecraft position in longitude relative to the center of the orbital position and the challenge and maintenance of a stable centripetal effect of the spacecraft evolution at the orbital position. The line of retention (dependence) can have a rather complicated appearance, however, the essence boils down to a line passing on the plane [T - sidereal period; λ - Greenwich longitude] through the center of the orbital position [T _sv - stellar period; λ _C - center] from bottom to top and from left to right under the selected experimental path angle to one of the coordinate axes. The analogue is selected as a prototype precisely by determining the nominal dependence and maintaining the centripetal effect.

The task is to create a method that is as efficient as possible in terms of energy consumption to maintain the center of mass of the spacecraft, whether it’s just keeping it in a narrow area in latitude and longitude, whether it be collocation in this area.

The solution to this problem lies in the fact that in the method of holding the geostationary spacecraft, including determining the nominal dependence of the sidereal circulation period after correcting the hold on the current position of the spacecraft in longitude relative to the center of the orbital position, calling and maintaining a stable centripetal effect of the spacecraft evolution at the orbital position, new operations are introduced, consisting in the fact that, against the background of autonomous navigation, in the intervals between regular corrections, at the next retention step: determine the nominal and diametrically opposed active sites for correcting the inclination vector; determining deviations of the current value of the sidereal circulation period from the nominal sidereal circulation period after correction; by the sign of these deviations, two correction engines with the required projection of the thrust vectors in the transverse direction are selected from the available pairs; calculate the correction of the inclination vector of the orbit with one engine; predict the motion of the center of mass of the spacecraft from the initial moment on the current day to the moment (t _to ) the end of the second-time execution of the active section of the two possible, for the purpose of completely working out the required correction parameters of the inclination vector taking into account the thrust only in the first active section corresponding to the engine number selected first; determine the current eccentricity vector e _1k ; predicting the motion of the center of mass of the spacecraft from the initial moment on the current day to the moment t _to , taking into account the thrust only in the second active section, corresponding to the engine number selected by the second; determine the current eccentricity vector e _2k ; determine the translation vectors for both correction options from the relations:

where e _c is the aiming vector;

choose the engine according to the active working area, where the smallest translation vector is implemented; carry out correction with one engine; Through the totality of regular corrections, a stable centripetal effect of the evolution of the eccentricity vector of the orbit of the spacecraft is caused and maintained for an arbitrarily long time.

The implementation of the proposed method involves the following sequence of operations:

1. The nominal dependence of the sidereal rotation period after simultaneous correction of the retention of the inclination vector of the orbit and the rotation period of the three-axis stabilized spacecraft from the current spacecraft position in longitude relative to the center of the orbital position is determined.

The retention strategy in this case is that the aiming point always remains the point [λ _c ; T _sound ], the orientation in the phase space [T; The λ] (or [T; Δλ = λ-λ _C ]) lines of the retention strategy are basically the same; spacecraft departures in longitude due to spacecraft libration (off-center geopotential), this is the main thing they always have, albeit not in one, but for 3 simultaneous corrections of the period and inclination (depending on the angle of deviation of the thrust vector of the engine from the normal to the orbit in the yaw plane), the desired direction to the center of the orbital position, and, with the steady-state retention process, deviations in the average longitude winding from the center longitude are no more than ± 1 arcmin .; over the period from stellar days make up no more than ± 2 s. In this area, the spacecraft is guaranteed for the entire period of operation, provided that the autonomous navigation system operates smoothly or when the spacecraft motion parameters are continuously determined using the ground-based control system.

This paragraph corresponds to paragraph 5 of the characterizing part of the prototype formula.

2. Determine the nominal diametrically opposite active sections for the correction of the inclination vector.

Right ascents and transit times of the spacecraft in the middle of the AC are determined by formulas (13) and (11), respectively.

3. Select an inclination vector correction engine.

The inclination vector correction engine is selected by the sign of the deviation of the current sidereal circulation period from the nominal sidereal circulation period after correction (T _nom ). The inclination vector correction engines are selected from the available pairs located relative to both semiaxes of the normal to the orbit, which are free from restrictions on the inclusion in the calculation period of time and the sign of the projection of the thrust on the transversal is opposite to the sign of the change in the orbital velocity, as well as the sign ΔТ _nom. .

4. Calculate the correction of the inclination vector of the orbit by one engine.

We are only interested in the exact execution of the correction of the inclination vector. The duration of the selected engine is calculated by the well-known formula (12) by dividing the left and right parts by the mass of the spacecraft.

5. The motion of the center of mass of the spacecraft is predicted from the initial moment on the current day to the moment (t _to ) the end of the second-time execution of the active section of the two possible, for the reason of complete development of the required correction parameters of the inclination vector taking into account the thrust only in the first active section corresponding to the engine number selected first.

It is fundamentally important that the location scheme of the correction engines allows, in conjunction with the longitude retention strategy selected in the proposed method, at each retention step to constantly engage only one correction engine that implements the strategy of holding the inclination vector of the spacecraft orbit. As a result, it is not the exit to T _nom that is monitored, but the tendency towards that, but, as field tests show, this is enough to successfully keep the spacecraft in longitude. The retention range of ± 0.05 ° is within the scope of this method, if e is not more than (0,0002-0,00029).

6. Determine the current eccentricity vector e _1k .

7. Predict the motion of the center of mass of the spacecraft from the initial moment on the current day to the moment t _to , taking into account the thrust only in the second active section, corresponding to the engine number selected by the second.

8. Determine the current eccentricity vector e _2k .

9. Determine the translation vectors for both correction options from the relationships:

Δe ₁ = e _1k -e _c ;

Δе ₂ = е _2к- е _ц .

10. Select the engine according to the active working area, where the smallest translation vector is implemented.

11. Carry out a correction with one engine.

This operation should be considered a hallmark in relation to both analogues.

12. Create a centripetal effect of the evolution of the spacecraft in longitude.

Through corrections of the inclination vector, a stable centripetal effect of the evolution of the spacecraft in longitude at the orbital position is caused and maintained for an arbitrarily long time.

This paragraph corresponds to paragraph 11 of the characterizing part of the prototype formula.

13. Create a centripetal effect of the evolution of the eccentricity vector of the spacecraft orbit.

By selecting eccentricity vectors before correcting the motion parameters of the spacecraft, the centripetal effect of the evolution of the real eccentricity vector is evoked and maintained for an arbitrarily long time.

Retention corrections are the primary physical operations, the call of the centripetal effect of the evolution of the eccentricity vector of the SC orbit is secondary physical operations on the object, and the centripetal effect itself is a distinctive physical property of the method object.

Next p.p. 1-13 are repeated during the active life of the spacecraft.

For any transfers of the spacecraft in the geostationary orbit and in the process of routine work to clarify the engine thrusts, test inclusion of the engines is carried out in accordance with paragraphs. 1-4 of the characterizing part of the prototype formula.

The present method of geostationary spacecraft retention offers a three-parameter simultaneous and combined correction: a set of variable parameters is necessary and sufficient. The executive body is one of the currently selected engines.

It should be noted that in the event of engine failures and possible insurmountable restrictions, the method automatically loses its advantages over other methods that fall into similar circumstances, that is, it most likely will fall into two methods: the method of holding in longitude and inclination and the method of holding in eccentricity.

The proposed method of retaining a geostationary spacecraft allows:

1) almost completely eliminate the need for correction of the circulation period and eccentricity by longitude correction engines;

2) create a centripetal effect of the evolution of the eccentricity vector of the SC orbit, that is, reliably hold the SC in small areas of the target points.

3) increase the accuracy of longitude retention from ± 0.1 ° to ± 0.05 °.

Claims (5)

A method of retaining a geostationary spacecraft (SC), including determining the nominal dependence of the sidereal circulation period after correcting the retention from the current position of the SC in longitude relative to the center of the orbital position, calling and maintaining a stable centripetal effect of the evolution of the SC at the orbital position, characterized in that, against the background of an autonomous navigation, in between regular corrections, at the next retention step: determine the nominal diametrically opposite active sections Ki for the correction of the inclination vector; determining deviations of the current value of the sidereal circulation period from the nominal sidereal circulation period after correction; by the sign of these deviations, two correction engines with the required projection of the thrust vectors in the transverse direction are selected from the available pairs; calculate the correction of the inclination vector of the orbit with one engine; predict the motion of the center of mass of the spacecraft from the initial moment on the current day to the moment (t _to ) the end of the second-time execution of the active section of the two possible for the consideration of the complete development of the required correction parameters of the inclination vector taking into account the thrust only in the first active section corresponding to the engine number selected first; determine the current eccentricity vector e _1k ; predicting the motion of the center of mass of the spacecraft from the initial moment on the current day to the moment t _to , taking into account the thrust only in the second active section, corresponding to the engine number selected by the second; determine the current eccentricity vector e _2k , determine the translation vectors for both correction options from the relations: Δе ₁ = е _1к- е _ц; Δе ₂ = е _2к- е _ц , where e _c is the aiming vector; choose the engine according to the active working area, where the smallest translation vector is implemented; carry out correction with one engine; Through the totality of regular corrections, a stable centripetal effect of the evolution of the eccentricity vector of the orbit of the spacecraft is caused and maintained for an arbitrarily long time.