RU2197412C2 - Method of control of spacecraft by means of powered gyroscopes and jet engines located at angle relative to axes of body base - Google Patents

Abstract

FIELD: combined control of attitude and motion of center of mass of spacecraft. SUBSTANCE: present total angular momentum of spacecraft

is determined according to proposed method by vector of angular momentum in powered gyroscope system and by vector of angular velocity of spacecraft. Electric rocket jet engines are selected at projections of thrusts on preset direction of orbit correction and are grouped in all probable combinations. Change of vector

is predicted for each group at definite interval of correction. Besides that, effect of external magnetic, gravitational and solar light fluxes on spacecraft is taken into account in addition to effect of engines. Moment and interval of time of arrival of this vector

at boundary of permissible magnitudes are determined. During this interval magnitudes of correction pulses of each group of engines are determined and group with maximum pulse is included into action. In the course of correction of orbit, difference of predicted and present magnitudes of vector

Description

 The invention relates to astronautics, namely to control the orientation and movement of the center of mass of spacecraft (SC).

 A known method of controlling a spacecraft [1], equipped with jet engines (RD) with directed at the angle of the axes of the associated basis and offset from the center of mass of the vehicle by the lines of action of the rods. In this method, the required control moment is applied to the spacecraft’s hull simultaneously along the three axes of the connected basis by installing the RD in parallel planes and turning on those of them whose projections of the control moment vectors on the axis of the required control moment are summed and mutually compensated relative to the remaining axes of the connected basis. In addition, the spacecraft’s orbit is corrected for each of two given directions, coinciding with the directions of the axes of the connected basis, by applying the thrusts of jet engines to work out the pulses specified in accordance with the direction and magnitude of the linear correction speed vectors along the indicated axes. Moreover, to compensate for disturbing moments relative to the third axis of the connected basis, control moments are applied from the taxiways located on the same planes, the projections of the moment vectors of which on the indicated first and second axes of the connected basis and the projections of their traction forces on these axes are mutually compensated.

 This control method allows to reduce the number of taxiways and fuel costs for the correction of the spacecraft orbit, but they do not solve the important issue of obtaining the maximum correction speed. In addition, in the proposed method, controlling the orientation of the spacecraft in the process of correcting the orbit with the help of RD is not very accurate, and this is essential, for example, for communication satellites, the orientation accuracy of which should be no worse than 12 '.

в текущие моменты времени t, в том числе и в момент времени t₀, проверяют выполнение условия принадлежности значений

области S располагаемых значений вектора кинетического момента в системе силовых гироскопов и в случае насыщения системы СГ в момент времени t_S определяют суммарное значение векторов управляющих моментов от двигателей ориентации при условии поочередного отключения каждого i-го двигателя, где i= l, 2, ...,n - номера РД, участвующих в коррекции орбиты, создают разгрузочный момент для системы силовых гироскопов двигателями ориентации, суммарный момент которых имеет наибольшую проекцию на направление, противоположное вектору

при соответствующем отключенном двигателе ориентации, а в случае, когда этот управляющий момент не является разгрузочным, для разгрузки силовых гироскопов включают ту пару двигателей ориентации, не участвующих в коррекции орбиты, момент которой имеет наибольшую проекцию на направление, противоположное вектору

при этом никакой из указанных i-х двигателей не отключают, в процессе проведения коррекции орбиты и разгрузки силовых гироскопов прогнозируют изменения указанного суммарного вектора кинетического момента для случая коррекции орбиты, с учетом всех работающих указанных i-х двигателей на интервале от текущего момента времени разгрузки до расчетного момента времени окончания коррекции, суммируют указанные спрогнозированные изменения вектора с текущим значением суммарного вектора

определенным на момент начала прогноза

проверяют условие принадлежности полученных векторных сумм указанной области S и одновременно условие непринадлежности

области S и, если в момент времени не выполняются оба эти условия, продолжают проводить коррекцию орбиты с одновременной разгрузкой силовых гироскопов, а если выполняется хотя бы одно из указанных условий, прекращают разгрузку силовых гироскопов за счет подключения указанного отключенного i-го двигателя к процессу коррекции орбиты или отключения указанной разгрузочной пары РД, после чего продолжают проверять выполнение условия принадлежности указанного вектора суммарного кинетического момента

области S вплоть до завершения коррекции и в случае невыполнения этого условия повторяют разгрузку системы СГ при помощи двигателей ориентации, создающих указанный момент, или при помощи разгрузочной пары двигателей ориентации, не участвующих в процессе коррекции орбиты.The closest analogue to the spacecraft control method using reactive executive bodies (see [2]), used as a prototype, includes determining the required value of the spacecraft’s orbit correction speed, determining the correction time interval (t ₀ , t _k ), maintaining a given the orientation of the spacecraft using power gyroscopes (SG) during the correction of the orbit by the orientation engines, the measurement of the values of the kinetic moment vector in the system of power gyroscopes and the angular velocity vector spacecraft span, determining from the measured values of the kinetic moment vector in the system of power gyroscopes, the spacecraft angular velocity vector and the known values of the spacecraft inertia moments of the total kinetic moment vector of the spacecraft

at current moments of time t, including at time t ₀ , check that the condition for the values to belong

the domain S of the available values of the vector of kinetic moment in the system of power gyroscopes and in the case of saturation of the SG system at time t _S determine the total value of the vectors of control moments from the orientation engines, provided that each i-th engine is turned off, where i = l, 2, .. ., n - numbers of taxiways participating in orbit correction, create an unloading moment for the system of power gyroscopes with orientation engines, the total moment of which has the greatest projection in the direction opposite to the vector

with the corresponding orientation motor switched off, and in the case when this control moment is not unloading, to unload the power gyroscopes, include that pair of orientation engines that are not involved in the orbit correction, the moment of which has the greatest projection in the direction opposite to the vector

in this case, none of the indicated i-th engines is turned off, during the correction of the orbit and unloading of power gyroscopes, changes in the indicated total vector of the kinetic moment are predicted for the case of orbit correction, taking into account all the working specified i-th engines in the interval from the current moment of unloading to the estimated time of the end of the correction, summarize the specified predicted changes in the vector with the current value of the total vector

defined at the time the forecast began

check the membership condition of the obtained vector sums of the indicated domain S and simultaneously the non-membership condition

areas S and, if at the moment both of these conditions are not met, continue to correct the orbit while unloading the power gyroscopes, and if at least one of these conditions is fulfilled, stop unloading the power gyroscopes by connecting the indicated disabled i-th engine to the correction process the orbits or shutdowns of the indicated unloading pair of taxiways, after which they continue to verify that the conditions of membership of the specified vector of the total kinetic moment

region S until the completion of the correction and if this condition is not fulfilled, the unloading of the SG system is repeated using the orientation engines that create the specified moment, or using the unloading pair of orientation engines that are not involved in the orbit correction process.

 The disadvantage of the control method described in the prototype is the use of a large number of taxiways (24 taxiways) to control the spacecraft, as well as the fact that they do not select those taxiways for orbit correction, which will allow it to be carried out without saturation of the SG system, which, as a result , will lead to the need for unloading the SG system using the taxiway, which is not desirable, because this is due to the additional consumption of the working fluid and the deterioration of the orbit caused by the work of the taxiway.

 The problem solved by the proposed method is to increase the control accuracy when using jet engines with the action lines of the rods and power gyroscopes directed at an angle to the axes of the connected basis and displaced relative to the center of mass of the apparatus, minimizing the flow of the working fluid and the effect on the spacecraft orbit, due to the need to turn on the taxiway for unloading the accumulated SG kinetic moment.

в отличие от известного способа, определяют по измеренным в момент времени t₀ значениям вектора кинетического момента в системе силовых гироскопов, вектора угловой скорости космического аппарата и известным значениям моментов инерции космического аппарата начальное значение суммарного вектора кинетического момента космического аппарата

из установленных на борту космического аппарата реактивных двигателей выбирают i-e двигатели, векторы тяг которых обеспечивают заданное направление коррекции орбиты, определяют n-e группы, где n=1, 2,..., k, где k - максимальное число групп, включающих все возможные комбинации из i-х реактивных двигателей, прогнозируют изменения суммарного вектора кинетического момента

на определенном интервале времени коррекции орбиты для каждой из n-х групп, при этом учитывают влияние на космический аппарат внешних возмущающих моментов и моментов сил от каждого i-го реактивного двигателя, входящего в n-ю группу, рассчитывают суммарный вектор кинетического момента космического аппарата при работе n-й группы реактивных двигателей

определяют по выполнению условия

где S - область допустимых значений вектора кинетического момента для проведения коррекции орбиты, момент времени t_sn выхода суммарного вектора кинетического момента для каждой из n-х групп на границу области S, определяют для каждой из n-х групп интервал времени выхода суммарного вектора кинетического момента на границу области S Δt_n = t_sn-t₀, определяют величины импульсов коррекции для каждой из n-х групп двигателей

где

- суммарное значение проекций i-х реактивных двигателей n-й группы на направление коррекции орбиты, выбирают из условия

для коррекции орбиты n'-ю группу реактивных двигателей, включают для коррекции орбиты в момент времени t₀ n'-ю группу реактивных двигателей, в процессе коррекции орбиты сравнивают суммарные значения, полученные для n'-й группы реактивных двигателей

с текущими значениями

и в случае выполнения условия

где ΔG - суммарное значение вектора кинетического момента, определяющее допустимое расхождение прогнозируемого значения с измеренным, продолжают коррекцию орбиты, в противном случае прекращают коррекцию орбиты, присваивают текущему значению времени t значение t₀ и производят повторный выбор n'-й группы реактивных двигателей для коррекции орбиты указанным выше образом.The problem is solved in that in the proposed method of controlling a spacecraft using power gyroscopes and jet engines, located at an angle to the axes of the associated basis, including determining the required value of the speed of correction of the orbit of the spacecraft, determining the time interval for the correction (t ₀ , t _k ) , maintaining a given orientation of the spacecraft with the help of power gyroscopes in the process of orbit correction by jet engines, while measuring the values of the kinetic vector about the moment in the system of power gyroscopes and the angular velocity vector of the spacecraft, determining from the measured values of the vector of kinetic moment in the system of power gyroscopes, the angular velocity vector of the spacecraft and the known values of the moments of inertia of the spacecraft the values of the total vector of the kinetic moment of the spacecraft

unlike the known method, it is determined from the values of the vector of kinetic moment in the system of power gyroscopes, the angular velocity vector of the spacecraft and the known values of the moments of inertia of the spacecraft, measured at the time t _{0, the} initial value of the total vector of the kinetic moment of the spacecraft

of the jet engines installed on board the spacecraft, i.e. engines whose thrust vectors provide a given direction of orbit correction, determine ne groups, where n = 1, 2, ..., k, where k is the maximum number of groups including all possible combinations of i-th jet engines, predict changes in the total vector of kinetic moment

for a certain interval of orbit correction time for each of the n-th groups, the effect of external disturbing moments and moments of forces from each i-th jet engine entering the n-th group is taken into account, the total vector of the kinetic moment of the spacecraft is calculated at work of the n-th group of jet engines

determined by the fulfillment of the conditions

where S is the region of admissible values of the vector of kinetic moment for orbit correction, the time moment t _{sn of the} output of the total vector of kinetic moment for each of the n-th groups to the boundary of the region S, for each of the n-groups the time interval of the output of the total vector of kinetic moment is determined to the boundary of the region S Δt _n = t _sn -t ₀ , determine the values of the correction pulses for each of the n-th groups of engines

Where

- the total value of the projections of the i-th jet engines of the n-th group on the direction of the correction of the orbit, choose from the conditions

to correct the orbit, the n'th group of jet engines, include for correcting the orbit at time t _{0 the} n'th group of jet engines, in the process of correcting the orbit, the total values obtained for the n'th group of jet engines are compared

with current values

and if the condition is met

where ΔG is the total value of the vector of kinetic moment, which determines the permissible discrepancy between the predicted value and the measured one, the orbit correction is continued, otherwise the orbit correction is stopped, the value t _{0 is} assigned to the current time value t, and the nth group of jet engines is re-selected for orbit correction as indicated above.

 The proposed spacecraft control method will allow for orbit correction without saturation of the SG system. The spacecraft is equipped with jet engines with thrust action lines directed at an angle to the axes of the associated basis and displaced relative to the center of mass of the apparatus. With this placement of the taxiway, the number of taxiways decreases (from 24 in the prototype to 8 in the proposed method), and therefore, the cost of the spacecraft decreases, its mass decreases, which will allow to derive a large payload of the launch vehicle with the same characteristics as for the apparatus described in the prototype , spending less working fluid, thereby increasing the life of the spacecraft.

To clarify the essence of the proposed method are shown in figures 1 to 3. In FIG. 1 shows the layout of the blocks of the taxiway KA (in the block there can be both one engine and several engines that create traction in a given direction). Figure 2 illustrates the maneuver of translating the midpoint of the expected offset to the origin. Figure 3 shows a graph of changes in the components of the vector of the kinetic moment of the spacecraft (G _x , G _y , G _z ) in time t.

(ССК). Управление ориентацией КА осуществляется силовыми гироскопами. При удержании космического аппарата на геостационарной орбите (ГСО) возникает задача удержания его в рабочей точке с заданной точностью по долготе и широте. Решается эта задача с использованием восьми электрореактивных двигателей. С их помощью осуществляется коррекция орбиты КА и одновременно управление кинетическим моментом КА.As an example illustrating the proposed spacecraft control method, we consider the control of a geostationary spacecraft equipped with eight blocks of electro-reactive taxiways (see Fig. 1) when correcting its orbit. Figure 1 shows the spacecraft body, blocks of orientation engines 1-8 and the coordinate system rigidly connected with the spacecraft

(SSK). The orientation of the spacecraft is controlled by power gyroscopes. When the spacecraft is held in geostationary orbit (GSO), the task arises of holding it at a working point with a given accuracy in longitude and latitude. This problem is solved using eight electric propulsion engines. With their help, the orbit of the spacecraft is corrected and the kinetic moment of the spacecraft is simultaneously controlled.

 The inclination correction is ensured by working at one or two maneuvering intervals on a turn. The midpoints of these intervals should be located on the line of nodes of the target and initial orbit planes [3], [4].

- маневр, который переводит среднюю точку ожидаемого смещения в начало координат,

- пассивное изменение вектора наклонения

от момента между i-й и i+1-й коррекциями. Принято, что при коррекции наклонения ликвидируется только составляющая, параллельная направлению векового ухода. В этом случае вектор наклонения циклически изменяется с полугодовым периодом и амплитудой ≈0.025^o. С целью минимизации наибольшего изменения вектора наклонения выбирается такой маневр

который переводит среднюю точку ожидаемого смещения в начало координат [см. фиг.1]

где

- пассивное изменение вектора

от момента между i-й и i+1-й коррекциями. Величина потребного импульса определяется по формуле

где v_kp - скорость спутника на ГСО.FIG. 2 illustrates the maneuver of translating the midpoint of the expected offset to the origin. The following notation is introduced on it:

- a maneuver that translates the midpoint of the expected offset to the origin,

- passive change of the inclination vector

from the moment between the i-th and i + 1-th corrections. It is accepted that during the correction of inclination, only the component parallel to the direction of secular care is eliminated. In this case, the inclination vector changes cyclically with a six-month period and an amplitude of ≈0.025 ^o . In order to minimize the largest change in the inclination vector, such a maneuver is chosen

which translates the midpoint of the expected offset to the origin [see figure 1]

Where

- passive vector change

from the moment between the i-th and i + 1-th corrections. The magnitude of the required impulse is determined by the formula

where v _kp is the satellite velocity at GSO.

 When correcting the true inclination vector, the optimal interval between corrections is 3-5 days; when correcting the secular displacement, 1-3 days. An increase in the correction interval is undesirable since this will lead to a significant increase in ballistic losses due to the long duration of the active sites.

 Correction of the eccentricity and period of circulation is provided by transverse impulses.

The working interval of longitudes Δλ is determined from the condition
Δλ = Δλ _ass -2δe ^max -Δλ $\genfrac{}{}{0ex}{}{\text{max}}{\text{c}}$ -Δλ _np -2e _max (3),
where Δλ _ass = 0.1 ^° - the specified interval of the spacecraft retention in longitude; δe ^max is the maximum amplitude of eccentricity oscillations relative to the average value (≈10 ^-4 ); Δλ $\genfrac{}{}{0ex}{}{\text{max}}{\text{c}}$ = 0.019 ^° - the amplitude of the semi-annual fluctuations of average longitude, caused by the attraction of the Sun; Δλ _etc. - the forecast error in the sighting point; е _max - the maximum permissible value of eccentricity (≈2 • 10 ^-4 ).

The parameters of the single-pulse correction of the sidereal circulation period are determined from the condition for correcting λ and decreasing the eccentricity at the turn, where Δλ goes beyond the specified boundaries. The angular duration of the active site is determined by the formula
ζ = -1,4λ (t _Tp ) W _n aω _e (4),
where ω _e = 0.7292 * 10 ^-4 rad / s is the angular velocity of the Earth; W _n - average transverse acceleration; t _Tr - the moment the correction begins.

Курс тяги определяется из условия:
ψ=0, при ζ>0
ψ=Pi, при ζ<0 (6)
Для удержания эксцентриситета в принятых границах проводится двухимпульсная коррекция, параметры которой следующие:

При планировании коррекцию наклонения орбиты необходимо разносить по времени с коррекцией эксцентриситета. Для уменьшения баллистических потерь коррекции в рабочей точке нужно проводить с минимальной периодичностью (1-2 дня).The magnitude of the required pulse of speed is determined by the formula

The thrust rate is determined from the condition:
ψ = 0, for ζ> 0
ψ = Pi, for ζ <0 (6)
To maintain the eccentricity at the accepted boundaries, a two-pulse correction is carried out, the parameters of which are as follows:

When planning, the correction of the inclination of the orbit must be posted in time with the correction of the eccentricity. To reduce ballistic losses, corrections at the operating point should be carried out with a minimum frequency (1-2 days).

Denote by i = 1, 2, 3 the numbers of the axes of the associated basis. Let the projection of the vectors of control forces (P _i ) and moments (M _i ) on these axes from each engine block have the form:
- for block 1 - (0, P ₂ , P ₃ ), (-M ₁ , -M ₂ , M ₃ );
- for block 2 - (0, P ₂ , P ₃ ), (-M ₁ , M ₂ , -M ₃ );
- for block 3 - (0, -P ₂ , P ₃ ), (M ₁ , -M ₂ , -M ₃ );
- for block 4 - (0, -P ₂ , P ₃ ), (M ₁ , M ₂ , M ₃ );
- for block 5 - (0, -P ₂ , -P ₃ ), (-M ₁ , M ₂ , -M ₃ );
- for block 6 - (0, -P ₂ , -P ₃ ), (-M ₁ , -M ₂ , M ₃ );
- for block 7 - (0, P ₂ , -P ₃ ), (M ₁ , M ₂ , M ₃ );
- for block 8 - (0, P ₂ , -P ₃ ), (M ₁ , -M ₂ , -M ₃ ).

Suppose that the correction of the orbit should be carried out in the direction of the -Y axis of the associated basis (SSC). For this purpose, you can use engine blocks 3, 4, 5, 6 (see figure 1), creating traction in a given direction. The best option is to use all the engine blocks listed above that create traction in a given direction. In this case, maximum thrust is created along the -Y axis, and disturbances from the operation of these engines caused by the displacement of the thrust vectors relative to the center of mass of the spacecraft are mutually compensated. In the case when it is impossible to use all of the listed engines, for example, RD 3, 4, 5, or 4, 5, 6, or 3, 5, 6 blocks can be used. But in this case, uncompensated disturbing moments along all axes arise. It is more preferable to use in this case a pair of taxiway blocks. Analyzing the projections of the draft vectors and moments on the axis of the connected basis, we can conclude that, for the correction of the orbit in the corresponding directions of the 2nd and 3rd axes of the SSK, it is sufficient to use, for example, a pair of taxiway blocks, which creates traction in the desired direction and mutually compensates the traction in the other direction. In the case of the above placement of taxiway blocks, these are the following pairs of taxiway blocks:
1) for correction in the direction of the Y axis: 1st and 8th; 2nd and 7th;
2) for correction in the direction of the -Y axis: 3rd and 6th; 4th and 5th;
3) for correction in the direction of the Z axis: 1st and 4th; 2nd and 3rd;
4) for correction in the direction of the -Z axis: 5th and 8th; 6th and 7th.

It should be noted that with such a choice of RD blocks in each of the cases listed above, an uncompensated moment arises, the presence of which leads to the accumulation of the kinetic moment by the SG system that supports the required orientation of the spacecraft. So, for example, when correcting the orbit in the direction of the -Y axis using the 3rd and 6th taxiway blocks, the force from their work will be equal to
P _Y = -2P ₂ (8),
the moments from the operation of these taxiway blocks along the X and Z axes are mutually compensated, and the moment along the Y axis is
M _Y = -2M ₂ (9)
The problem arises of compensating for this moment, since its presence can lead to saturation of the SG and, as a result, the need to turn on other taxiway blocks for its unloading. You can do this as follows. When planning the correction, it is possible to simulate at a given time interval the total moment acting on the spacecraft, and taking into account the dynamics of its change, choose the pair of taxiway blocks that will create the moment along the corresponding axis of the CCK, which has the opposite direction compared to the moment from the pair of taxiway blocks , and accordingly partially compensate for it. Partly because the moment from operating RD blocks will be much larger than the moment from external forces acting on the spacecraft (gravitational, aerodynamic, light pressure, magnetic, etc.). Nevertheless, the rate of accumulation of the kinetic moment of the SG will be lower, and this will make it possible to change the direction of accumulation of the kinetic moment of the SG in the opposite direction with two-pulse correction through a half-turn, for example, by choosing the RD blocks that create a disturbing moment in the opposite direction. In this example, these are blocks of taxiways 4 and 5, creating the same traction along the Y axis as the previous pair of blocks
P _Y = -2P ₂ (10),
but the moment from the operation of these taxiway blocks along the Y axis will be equal to
M _Y = 2M ₂ (11).

 Figure 3 presents a graph of the accumulation of kinetic moment during the flight of a geostationary communications satellite, obtained by integrating the following equations of motion of a geostationary communications satellite.

Здесь

- полный кинетический момент КА;

- кинетический момент системы СГ;

- угловая скорость КА;

- соответственно гравитационные моменты, вызванные влиянием на ССС гравитационных полей Земли, Луны и Солнца;

- магнитный момент, обусловленный взаимодействием магнитного поля Земли и собственного магнитного момента КА;

- орты векторов Земля - КА, Солнце - КА, Луна-спутник;

- тензор инерции КА;
μ_E = 3,986032•10⁵ км³/сек²;
μ_S = 1,32715445•10¹¹ км³/сек²;
μ_M = 4,90264•10⁵ км³/сек²
- гравитационные параметры Земли, Луны и Солнца;
R_E, R_S, R_M - радиус-векторы Земли, Луны и Солнца;

- момент от силы светового давления

которая возникает при попадании потока солнечного света на спутник и при его отражении;
S - площадь поперечного сечения КА;
Е₀ - мощность потока солнечного излучения;
с - скорость света;
r_* - средний радиус орбиты Земли;
Δ - расстояние от КА до Солнца;
k - коэффициент отражения света поверхностью КА;

- собственный магнитный момент КА;

- магнитное поле Земли.

Here

- the full kinetic moment of the spacecraft;

- kinetic moment of the SG system;

- angular velocity of the spacecraft;

- respectively, the gravitational moments caused by the influence on the SSS of the gravitational fields of the Earth, the Moon and the Sun;

- the magnetic moment due to the interaction of the Earth’s magnetic field and the spacecraft’s own magnetic moment;

- unit vectors of the Earth - spacecraft, the Sun - spacecraft, moon-satellite;

- spacecraft inertia tensor;
μ _E = 3.986032 • 10 ⁵ km ³ / s ² ;
μ _S = 1,32715445 • 10 ¹¹ km ³ / s ² ;
μ _M = 4.90264 • 10 ⁵ km ³ / s ²
- gravitational parameters of the Earth, the Moon and the Sun;
R _E , R _S , R _M - radius vectors of the Earth, the Moon and the Sun;

- moment from the force of light pressure

which occurs when a stream of sunlight hits a satellite and when it is reflected;
S is the cross-sectional area of the spacecraft;
E ₀ - power flow of solar radiation;
c is the speed of light;
r _* is the average radius of the Earth’s orbit;
Δ is the distance from the spacecraft to the sun;
k is the light reflection coefficient by the surface of the spacecraft;

- own magnetic moment of the spacecraft;

- magnetic field of the Earth.

 As practice has shown, the forecast of the accumulation of the kinetic moment of the spacecraft obtained by solving equations (12) for the Yamal geostationary communications satellite gives good results.

It is not difficult to conclude that, being on the descending branch of the graph of the kinetic moment of the spacecraft, in order to reduce the influence of the disturbing moment on this axis from the work during the correction of the orbit
it is necessary to use for correction in the direction of the -Y axis that pair of taxiway blocks that leads to the appearance of a moment along + Y, i.e. a pair of taxiway blocks 4 and 5, and being on the ascending branch of the graph, a pair of 3 and 6, respectively. But, taking into account that the disturbing moment from the taxiway blocks is much larger than the disturbing moment from external forces, one cannot ignore the initial value of the kinetic moment of the spacecraft, t .to. this can lead to a rapid accumulation of the kinetic moment and, as a consequence, to the need for its unloading.

и имеет приращение ΔG_Y отрицательного знака, то логично выбрать для коррекции блоки РД 4 и 5 (см. фиг.3), дающие положительный возмущающий момент относительно оси Y (11) и имеющие следующие параметры (без учета знаков): Р₂=0,0265 Н, М₂=0,00237 Нм. Это соответствует, например, использованию электрореактивных двигателей М70-СПД.For example, suppose that it is necessary to carry out a correction of the spacecraft’s orbit in the direction of the -Y axis starting at time t ₀ = 18 hours. To carry out the correction of the spacecraft’s orbit, it is necessary to inform it of one RD pulse with a duration of Δt = 1 hour at this moment in time, the vector of the total kinetic moment of the spacecraft is

and has an increment ΔG _{Y of a} negative sign, it is logical to choose for correction the RD 4 and 5 blocks (see Fig. 3) that give a positive disturbing moment relative to the Y axis (11) and have the following parameters (excluding signs): P ₂ = 0 , 0265 N, M ₂ = 0.00237 Nm. This corresponds, for example, to the use of M70-SPD electric propulsion engines.

The force with which these RD blocks act on the spacecraft is equal according to (10)
P _Y = -2P ₂ = 0.053 N (10 ^/ ),
and uncompensated moment along the Y axis according to (11)
M _Y = 2M ₂ = 0.00474 (11 ^/ ).

а приращение кинетического момента КА, вызванное работой РД ΔG_YD за этот промежуток времени будет равно

Т. о., к концу процесса коррекции орбиты кинетический момент КА составит величину, равную

Кроме того, из анализа графиков на фиг.3 и направления действия тяг блоков РД видно, что в процессе коррекции орбиты данными блоками РД выхода суммарного вектора кинетического момента за пределы допустимой области не произойдет.The increment of the kinetic moment of the spacecraft, caused by the influence of external disturbing factors (gravitational moment, magnetic, etc.) during this time according to figure 3 will be

and the increment of the kinetic moment of the spacecraft caused by the work of the taxiway ΔG _YD for this period of time will be equal to

Thus, by the end of the orbit correction process, the kinetic moment of the spacecraft will be equal to

In addition, from the analysis of the graphs in Fig. 3 and the direction of action of the rods of the taxiway blocks, it can be seen that in the process of correcting the orbit with these blocks of the taxiway, the output of the total vector of the kinetic moment outside the allowable region will not occur.

In the case when the total vector of the kinetic moment of the spacecraft does not go beyond the range of permissible values, the single-pulse correction of the orbit of the spacecraft is justified, because the condition of motion of the vector of the kinetic moment of the spacecraft is fulfilled during the correction in the region of admissible values. If the total vector of the kinetic moment of the spacecraft is outside the range of acceptable values, then the correction is carried out until the time t _sn and then stops and the selection of new taxiways. It is possible, for example, to inform the SC of the next impulse, for working on the next correction interval, a pair of engines creating a disturbing moment, the vector of which is opposite to the vector of the disturbing moment created by the work of the RD on the previous correction interval. In our case, these are engine blocks 3 and 6. The beginning of the second interval of orbit correction must be carried out half a turn after the first interval. Thus, with two-pulse orbit correction, the effect on the gyrosystem caused by the operation of the taxiway can be leveled.

 The proposed method for correcting the orbit of the spacecraft, although it can increase the correction time in comparison with the prototype, can increase the life of the spacecraft by reducing the consumption of the working fluid for the correction, or, having the same life, increase the mass of the payload using the same launch vehicle for launch SPACECRAFT IN ORBIT (since an increase in the payload of the SC is compensated by a decrease in the amount of the working fluid needed to hold the SC in orbit).

 Sources of information.

 1. "A control method for a spacecraft equipped with jet engines with angular directional axes of the connected base and rod lines of action displaced relative to the center of mass of the apparatus, a system for implementing the method, a block of jet engines of the system." Patent RU 2124461 C1.

 2. "A method for controlling a spacecraft using reactive executive bodies and a system for its implementation." Patent RU 2112716 C1.

 3. A.V.Sokolov and Yu.P. Ulybyshev "Multi-turn low-thrust maneuvers in the vicinity of the geostationary orbit." News of the Academy of Sciences. Theory and control systems. 1999, 2, pp. 95-100.

 4. G. M. Chernyavsky, V. A. Bartenev, V. A. Malyshev "Control of the orbit of a stationary satellite." Engineering, 1984

Claims (1)

A method for controlling a spacecraft using power gyroscopes and jet engines located at an angle to the axes of the associated basis, including determining the required value of the orbit correction speed of the spacecraft, determining the time interval (t ₀ , t _k ) for correcting, maintaining a given orientation of the spacecraft using power gyroscopes in the process of orbit correction by jet engines, while measuring the values of the kinetic moment vector in the system of power gyroscopes and the angle vector of the spacecraft’s speed, determination of the kinetic moment vector in the system of power gyroscopes, the spacecraft’s angular velocity vector, and taking into account the known values of the spacecraft’s moment of inertia, the values of the total kinetic moment vector of the spacecraft

characterized in that the initial value

the total vector of the kinetic moment of the spacecraft is determined by the said values of the vector of kinetic moment in the system of power gyroscopes and the angular velocity vector of the spacecraft measured at time t ₀ , taking into account the known values of the moments of inertia of the spacecraft, choose from the number installed on board the spacecraft, i-th jet engines, the thrust vectors of which provide a given direction of orbit correction, determine the nth groups (n = 1, 2, ..., k, where k is the maximum number of groups), VK luchshie all possible combinations of i-th jet engines, predict changes in the total vector of kinetic moment

over a certain time interval of the orbit correction for each of the n-th groups, taking into account the influence on the spacecraft of the external perturbing moments and moments of forces from each i-th jet engine included in the n-th group, the total vector of the kinetic moment of the spacecraft is predicted for work of the n-th group of jet engines

determine the fulfillment of the conditions

the time moment t _{sn of the} output of the total vector of kinetic moment for each of the n-th groups to the boundary of the region S of its values acceptable for the correction of the orbit, the time interval Δt _n = t _sn -t _{0 of the} output of the total vector of kinetic is determined for each of the n-groups moment to the boundary of the specified region S, determine the values of the correction pulses

for each of the n-th groups of engines, where

- the total value of the projection of the rods of the i-th jet engines of the n-th group on the direction of the orbit correction, is chosen for the correction of the orbit from the condition for maximizing the momentum

The n'th group of jet engines, which is turned on for the correction of the orbit at the indicated time t ₀ , during the correction of the orbit, the values of the total vector are compared

for the indicated n'th group of jet engines with current values of the vector

and continue to correct the orbit if the condition is met

where ΔG is the total value of the vector of kinetic moment, which determines the permissible discrepancy between its predicted value and the measured one, in which case the orbit correction is stopped, the current value of time t is assigned the value t _0, and the n'th group of jet engines is re-selected for orbit correction as described above way.

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