RU2587764C2 - Method for determining inertia tensor of spacecraft in flight - Google Patents

Abstract

FIELD: space.

SUBSTANCE: invention relates to determination of mass-inertia characteristics of spacecraft. Method includes orientation of spacecraft and stabilisation in an inertial coordinate system (CSI) of its axis, nearest to axis of maximum moment of inertia. Further, method includes spinning spacecraft around said axis with angular speed of not less than 2°/s. Method also includes measuring in system of spacecraft construction lines direction of recorded stars and angular velocity of spacecraft to a certain moment in time. Latter depends on time of spinning spacecraft and interval of movement of spacecraft, weakly disturbed by action of gravity gradient and calculated with a certain coefficient of reliability. Said stars are identified and determined in CSI direction thereon. Inertia tensor of spacecraft is defined by said directions on stars and values of angular velocity of spacecraft.

EFFECT: technical result consists in improvement of reliability of determination of inertia tensor of spacecraft, including in the absence of on-board inertial actuators.

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Description

The invention relates to space technology and can be used to clarify the mass-inertial characteristics of spacecraft (SC).

The inertia tensor of any solid is an important characteristic for controlling its motion. Therefore, a number of methods have been developed for determining the inertia tensor of the body, described, for example, in [1] (Method for determining the inertia tensor and coordinates of the center of mass of the body and device for its implementation, patent RU 2348020 C1). In the analogue method [1], a predetermined movement is communicated to the body, and the inertia tensor of the body is determined from measurements of the motion parameters. The main disadvantage of the method [1] and other similar methods is the lack of the possibility of their application to determine the inertia tensor of the spacecraft in flight.

At the same time, it should be noted that the inertia tensor changes during the spacecraft flight. This change occurs due to the spacecraft fuel consumption in flight, the docking and undocking of new blocks and elements from the spacecraft, the movement of goods inside the spacecraft piloted by the astronauts, etc. Therefore, the inertia tensor should be determined during the spacecraft flight, since It is an important characteristic for controlling the motion of a spacecraft. Accurate knowledge of the mismatch of the main central axes of inertia of the spacecraft and the construction axes of the spacecraft is especially important, since nominally, engines for controlling the motion of spacecraft are usually installed relative to the building axes of the apparatus. In the event of an abnormal mismatch due to the indicated reasons, serious problems will arise between the SC construction axes and its main inertia axes for controlling the SC motion.

To determine the spacecraft inertia tensor in flight, a method was proposed [2] (Sevastyanov NN, Branets VN, Banit Yu.R., Belyaev M.Yu., Sazonov VV “Determination of the inertia tensor of geostationary satellites“ Yamal "according to telemetry information. KIAM Preprint No. 17 named after MV Keldysh, 2006). The proposed method [2], taken by the authors as a prototype, includes inertial orientation and spacecraft turns and measurement of the total kinetic moment of the flywheels. When the orientation of the spacecraft is changed by its turns, measurements of the total kinetic moment of the flywheels (inertial actuators) determine the inertia tensor of the spacecraft in flight.

The disadvantage of the prototype method is associated with low accuracy in determining the inertia tensor of the spacecraft and the need to use measurements from inertial actuators (IIO) [2]. At the same time, many spacecraft do not have an IIO. For example, the Progress Transport Cargo Ship (TGC), which is the main transport cargo ship in the ISS program, does not include an IIO. At the same time, due to the movement of cargo by astronauts inside the Progress TGK and the consumption of a large amount of fuel at the TGK, its inertia tensor changes during the flight. Especially important is the knowledge of the angular mismatch of the main axes of inertia of the THC and its construction axes, since TGC orientation and correction engines are installed relative to the ship’s building axes.

The problem to which the present invention is directed is to determine the inertia tensor of the spacecraft in flight.

The technical result of the invention is to reliably determine the inertia tensor of the spacecraft even if there is no IIO on board.

The technical result is achieved by the fact that in the method for determining the inertia tensor of a spacecraft in flight, including the inertial orientation and turns of the spacecraft, the spacecraft is oriented, stabilizing its construction axis in the inertial coordinate system, which is closest to the axis corresponding to the maximum moment of inertia, spin the spacecraft around of this construction axis with an angular velocity of Ω _{2 of} at least 2 ° / s, is measured in the construction coordinate system of the spacecraft abradable stars and the angular velocity of the spacecraft up to the point in time

,T = T ₀ + Δt, where $$\Delta t=\frac{\mathrm{four}{\Omega }_2\cdot R^3}{3\cdot {\mu }_{gR}\cdot K}$$

,

where T ₀ is the time instant of the spin of the spacecraft;

Δt is the time interval of the weakly perturbed motion of the spacecraft;

Ω ₂ - the angular velocity of the spin around the construction axis, the nearest axis of the maximum moment of inertia;

R is the radius of the orbit;

µ _gr - gravitational parameter of the Earth;

K is the reliability coefficient,

Recognize the registered stars, determine in the inertial coordinate system the directions to the identified stars, and determine the inertia tensor of the spacecraft from the directions measured by the stars and the angular velocity of the spacecraft measured and determined on the time interval Δt.

Due to the implementation of the proposed actions, the determination of the inertia tensor of the spacecraft is carried out reliably and even if there is no IIO on board the spacecraft. The actions of the method provide a weakly perturbed motion of the spacecraft on the time interval Δt. This allows one to reliably determine the spacecraft inertia tensor even in the absence of an IIR on board. The angular motion of a spacecraft is influenced mainly by gravitational and aerodynamic disturbing moments, and the main influence on most spacecraft is exerted by the gravitational moment.

The relation for Δt is obtained for a spacecraft having an elongated shape, taking into account the action of a gravitational perturbing moment on it. When deriving the relation for Δt, the maximum value of the gravitational moment acting around the transverse axis of the spacecraft is taken into account. To increase the reliability of providing slightly disturbed traffic over a time interval Δt, a special reliability coefficient K is introduced. The reliability coefficient can be taken, for example, 10. For Progress TGK, for example, Δt turns out to be several tens of minutes. At this time interval, the angular motion of the spacecraft is considered unperturbed. The inertia tensor of the spacecraft in this case is determined by the measured and determined parameters by minimizing the functional

, $$F_{\Omega }={\displaystyle \sum _{n=\mathrm{one}}^N{\displaystyle \sum _{i=\mathrm{one}}^3{\left[{\Omega }_i^{\left(n\right)}-{\Omega }_i\left(t_n\right)\right]}^2}}$$

,

on solutions of a system of equations (Euler equations written in a dimensionless form)

, $${\dot{\omega }}_2=\frac{{\mu }^{\text{'}}-\mu }{1-\mu {\mu }^{\text{'}}}\cdot {\omega }_3{\omega }_1$$

, $${\dot{\omega }}_3=-{\mu }^{\text{'}}{\omega }_1{\omega }_2$$

, $${\dot{\omega }}_{\mathrm{one}}=\mu {\omega }_2{\omega }_3$$

, $${\dot{\omega }}_2=\frac{{\mu }^{\text{'}\text{'}}-\mu }{\mathrm{one}-\mu {\mu }^{\text{'}\text{'}}}\cdot {\omega }_3{\omega }_{\mathrm{one}}$$

, $${\dot{\omega }}_3=-{\mu }^{\text{'}\text{'}}{\omega }_{\mathrm{one}}{\omega }_2$$

,

, $${\mu }^{\text{'}}=\frac{I_2-I_1}{I_3}$$

, $${\Omega }_i={\displaystyle \sum _{k=1}^3{в}_{iк}{\omega }_k\left(i=\mathrm{1,}\mathrm{2,}3\right)}$$

,Where: $$\mu =\frac{I_2-I_3}{I_{\mathrm{one}}}$$

, $${\mu }^{\text{'}\text{'}}=\frac{I_2-I_{\mathrm{one}}}{I_3}$$

, $${\Omega }_i={\displaystyle \sum _{k=\mathrm{one}}^3{\mathrm{at}}_{i\mathrm{to}}{\omega }_k\left(i=\mathrm{one,}23\right)}$$

,

ω ₁ , ω ₂ , ω ₃ - components of the angular velocity on the main central axis of inertia;

I ₁ , I ₂ , I ₃ - moments of inertia of the spacecraft;

in _ik - elements of the transition matrix between coordinate systems formed by the building axes and the main central axes of inertia of the spacecraft;

- приближенные измеренные значения компонент угловой скорости в строительной системе координат. $${\Omega }_i^{\left(n\right)}$$

- approximate measured values of the components of the angular velocity in the construction coordinate system.

Minimizing Φ _Ω is the first step in determining the desired quantities and is carried out by the Gauss-Newton method.

Ф _{Ω is} considered as a function of a set of eight parameters ω _iо = ω _i (t _о ) (i = 1, 2, 3), µ, µ ′, γ, α, β. The angles γ, α, β determine the position of the construction coordinate system оу ₁ у ₂ у ₃ relative to the coordinate system ox ₁ x ₂ x ₃ formed by the main central axes of inertia of the spacecraft.

The system oy ₁ y ₂ y ₃ can be translated into the system oy ₁ x ₂ x _{3 in} three successive rotations: 1) by an angle α around the axis oy ₂ , 2) by an angle β around a new axis oy ₃ , 3) by an angle γ around a new axis oy ₁ , coinciding with the axis ox ₁ .

Although the above Euler equations have solutions expressed in terms of elliptic functions, while minimizing Φ _Ω , as practical experience shows, it is advisable to integrate them numerically.

As the experience of information processing in solving similar minimization problems shows, the desired parameters can almost always be determined by minimizing the functional Ф _Ω . This is due, inter alia, to the fact that, at the considered processing interval, the angular motion of the spacecraft can be considered unperturbed.

At the second stage, to increase the reliability of determining the parameters of the inertia tensor of the spacecraft, the functional is minimized, compiled similarly in certain and measured directions to the star.

The most valuable for controlling the motion of the spacecraft is an accurate knowledge of the matrix elements in _ik (i.e., the angles γ, α, β). This is ensured by the implementation of the totality of actions and methods of the method.

Having determined the true position of the main central axes of inertia of the spacecraft, it is possible to control taking into account their position relative to the building axes of the spacecraft. Spinning of the spacecraft in the Sun can, for example, be performed not around the construction axis perpendicular to the plane of the solar panels, but around the main central axis of inertia of the spacecraft closest to it. This will increase the stability of rotation and increase the flow of electrical energy.

Currently, everything is technically ready for the implementation of the proposed method, for example, at TGK Progress or other spacecraft. At Progress TGK there are no IIOs. However, the control system of TGK Progress allows for inertial orientation, turns and spin of the spacecraft. To measure directions to the stars, a star sensor of the BOKZ or OZD type can be used. Stars that fall into the field of view of the sensor are recorded depending on the brightness incorporated in the device (stars can be registered, for example, up to the 6th magnitude). The recognition of the stars falling into his field of vision is carried out automatically (by the brightness of the stars and the angular distance between the registered stars). At TGCs, angular velocities are measured in the ship’s building coordinate system, direction to the Sun (which, strictly speaking, is a star). To determine the necessary directions and calculations, the TGC is equipped with an on-board computer system of the BVS.

The proposed method allows, by performing distinctive actions and techniques, to reliably determine the inertia tensor of the spacecraft even if there is no IIO on board it.

LITERATURE

1. The method of determining the inertia tensor and the coordinates of the center of mass of the body and a device for its implementation, patent RU 2348020 C 1.

2. Sevastyanov NN, Branets VN, Banit Yu.R., Belyaev M.Yu., Sazonov VV “Determination of the inertia tensor of geostationary satellites“ Yamal ”from telemetric information. Preprint IPM them. M.V. Keldysh №17, 2006

Claims (1)

A method for determining the inertia tensor of a spacecraft in flight, including the inertial orientation and turns of the spacecraft, characterized in that the spacecraft is oriented, stabilizing its construction axis in the inertial coordinate system, which is closest to the axis corresponding to the maximum moment of inertia, spin the spacecraft around this building axis with an angular velocity of Ω ₂ not less than 2 deg / s, measured in the construction coordinate system of the spacecraft directions to the recorded stars and the angular velocity of the spacecraft up to the point in time
T = T ₀ + Δt, $$\Delta t=\frac{\mathrm{four}{\Omega }_2\cdot R^3}{3\cdot {\mu }_{gR}\cdot K}$$

,
where T ₀ - the time instant of the spin of the spacecraft,
Δt is the time interval of the weakly perturbed motion of the spacecraft,
Ω ₂ - the angular velocity of the spin around the construction axis, the nearest axis of the maximum moment of inertia,
R is the radius of the orbit,
µ _gr - the gravitational parameter of the Earth,
K is the reliability coefficient,
the registered stars are recognized, the directions to the identified stars are determined in the inertial coordinate system, and the inertia tensor of the spacecraft is determined by the directions to the recognized stars measured and determined on the time interval Δt and the measurements of the angular velocity of the spacecraft.