RU2657809C1 - Method of determining of space craft own rotation about center of mass angular velocity - Google Patents

Abstract

FIELD: astronautics.

SUBSTANCE: invention relates to spacecrafts (SC) orientation control by a solar sensor. Method consists in the Sun angular position measuring (two angles) in the SC own axes in successive time intervals. Angular velocity estimates are calculated on the basis of the measured angles from simplified (integer) formulas followed by their filtration (to reduce the effect of the solar sensor short-term false readings). Enabled estimation of all three components of the SC angular velocity without use (in case of failure) of angular velocity sensors.

EFFECT: increasing the SC reliability with a decrease in the load on the onboard computer.

1 cl, 2 dwg

Description

The invention relates to the field of space technology and can be used in control systems for the orientation of spacecraft (SC).

Known methods for determining the relative angular velocity of the SPACECRAFT during the oscillatory process of controlling the orientation of an object to a moving landmark, which allows to determine the relative angular velocity of the SPACECRAFT around its center of mass (CM) with respect to the moving landmark (copyright certificate of the USSR No. 1819831 of 1990, No. 1819832 of 1990, patent RU No. 2396188 from 2009).

The method described in the copyright certificate No. 1819831 consists in determining that the relative angular velocity of the spacecraft is determined by the information on the rotation speed of the flywheels of electromotive engines (EDM) at the moment when the angular deviation of the oriented axis from the direction to the landmark reaches extreme values (USSR copyright certificate No. 1819831, 1990, IPC B64G 1/24).

The disadvantage of this method is the impossibility of its application in the modes of preserving the survivability of the spacecraft due to the unsuitability of using the EDM in this mode (the modes of ensuring the survivability of the spacecraft are traditionally carried out using jet engines due to the limited energy resources in these modes).

The method described in the copyright certificate No. 1819832, is that the relative angular velocity is defined as the difference between the measured current absolute angular velocity and the angular velocity, memorized at the time the angular deviation of the oriented axis from the direction to the landmark of extreme values (USSR copyright certificate No. 1819832, 1990, IPC B64G 1/24).

The disadvantage of this method is the inability to determine its own angular velocity of rotation of the spacecraft around its center of mass without the use of speed measuring devices.

As a prototype, the method described in patent RU No. 2396188 was selected, which consists in the fact that during the time interval Δ, projections onto the connected axes of the spacecraft (OX _KA , OY _KA , OZ _KA ) of a unit vector directed from the center are determined masses per star, according to the formulas:

Where:

β _POS - projection onto the axis OX _{KA of the} unit direction vector to the star;

α _POS - the projection onto the axis OZ _{KA of the} unit direction vector to the star;

γ _KA - projection onto the OY _KA axis of a unit direction vector to the star;

α, and β are the results of measuring the current direction to the star, for example, the Sun;

X _POS - the maximum value of β, measured by the device of orientation to the Sun along the axis OX _KA ;

Z _POS - the maximum value of α measured by the indicated device along the OZ _KA axis, the angles ϕ _{KA (t)} , ψ _{KA (t)} , θ _{KA (t)} between the projections of the unit vector on the plane of the axes connected with the KA and these axes are calculated by the formulas:

calculate the difference in the values of these angles in the time interval Δ and, as a result of dividing them by the value Δ, determine the values and signs of the projections ω _x , ω _y , ω _{z of the} vector of the average mean angular velocity ( ω _KA ) of the spacecraft on its connected axis OX _KA , OY _KA , OZ _KA .

The technical result of the known method is the ability to determine the angular velocity vector of the spacecraft’s own rotation according to the results of measuring the direction to the Sun or other stars in a linked coordinate system (patent RU No. 2396188, 2009, IPC B64G 1/24).

The disadvantages of this method include the impossibility of determining the intrinsic angular velocity of the spacecraft rotation around the direction to the Sun or other stars, the use of high-resource mathematical functions (for example, trigonometric functions in calculating the angles ϕ of the _{spacecraft (t)} , ψ of the _{spacecraft (t)} , θ _{KA (t)} ), which significantly impede the implementation in digital machines with support only for integer mathematics, as a result of which limited mathematical functionality, as well as obtaining false values of angular velocity with short-term inaccuracies testimony from the device.

The objective of the present invention is to provide a method for determining the angular velocities of the spacecraft’s own rotation around the center of mass, including around the direction to the Sun, using integer mathematical operations and providing protection against short-term false readings from the solar sensor (SD) for an algorithm that is not required high accuracy in determining the angular velocity of the spacecraft rotation around the CM.

The problem is solved as follows.

The determination of the angular velocity of rotation of the spacecraft from the SD around the center of mass consists in measuring the angular position of the Sun relative to the axes associated with the spacecraft’s body at successive time intervals and calculating an estimate of the angular velocity based on the data obtained. The calculation of the estimation of the angular velocity of the spacecraft differs from the method used in the prototype in that the calculation of the estimates of the angular velocity of the spacecraft is based on the need to determine the three components of the angular velocity (including around the direction to the sun) and use only integer mathematics from the readings of the SD. The assessment of the angular velocity of the own rotation of the spacecraft is determined by the formula

In addition, the proposed method provides for filtering the calculated estimates, which reduces the influence of false readings of the solar sensor on the calculated estimates of the angular velocity of the spacecraft. Filtration is carried out according to the formula:

where α _i , α _{i -1} is the angle alpha from the solar sensor at the current time and the previous one;

β _i , β _{i - 1} - beta angle from the solar sensor at the current time and the previous one;

k is a piecewise continuous function replacing the cosine of the angle;

Δ t is the time period between two information acquisitions;

- оценки угловых скоростей КА;

- estimates of the angular velocity of the spacecraft;

- коэффициенты фильтра;

- filter coefficients;

- используемая угловая скорость в текущий момент времени и предыдущий.

- used angular velocity at the current time and previous.

The technical nature of the claimed method is illustrated by drawings.

In FIG. 1 shows the SD, its axis and the relationship with the axes of the spacecraft; angles determined by LED.

In FIG. Figure 2 shows an example of the influence of two angular velocities on the motion of the Sun in the field of view of LEDs.

In FIG. 1 and FIG. 2, the following notation is introduced:

OX _KA , OY _KA , OZ _KA - axis of the coordinate system associated with the spacecraft body and passing through its CM;

OX _SD , OY _SD , OZ _SD - the axis of the coordinate system of the SD (for ease of understanding of the invention, their direction coincides with the direction of the axes of OX _KA , OY _KA , OZ _KA );

+ α, -α, + β, -β - directions of reference angles alpha and beta;

- вектор направления на Солнце;

- direction vector to the sun;

α _S , β _S - angles of deviation of the Sun in the coordinate system of SD;

, ω _x , ω _у , ω _z - угловая скорость вращения КА и ее проекции на оси связанной с КА системы координат.

, ω _x , ω _y , ω _z is the angular velocity of the spacecraft and its projection on the axis of the coordinate system associated with the spacecraft.

The essence of the invention lies in the fact that the movement of the Sun in the field of view of diabetes occurs due to the rotation of the spacecraft. Having information about the two angles of the position of the Sun in the field of view of the sensor, one can evaluate the change in three projections of the angular velocity of the spacecraft, and then filter the resulting estimate to reduce the effect of false readings of LEDs on the calculated angular velocity.

(ω _x , ω _у , ω _z ) и по изменениям координат Солнца в разные моменты времени можно восстановить значение компонент ω _x , ω _у , ω _z угловой скорости КА. Координаты Солнца в поле зрения СД и границы поля зрения прибора представлены на фиг. 1.The rate of change of direction on the Sun per revolution for the spacecraft in near-Earth orbit (assuming there is no proper rotation of the spacecraft around its center of mass) does not exceed 2.33⋅10 ^-7 rad / s. Therefore, the movement of the Sun in the field of view of the sensor is more (mainly) due to the rotation of the spacecraft with its own angular velocity

( ω _x , ω _у , ω _z ) and by changing the coordinates of the Sun at different points in time, it is possible to restore the value of the components ω _x , ω _у , ω _{z of the} angular velocity of the spacecraft. The coordinates of the Sun in the field of view of the LED and the boundaries of the field of view of the device are presented in FIG. one.

Consider the movement of the Sun in the field of view of LEDs at two consecutive instants of time i and i-1 . The coordinates of the Sun in the field of view of the sensor will be α _i , β _i and α _{i -1} , β _{i -1,} respectively. The movement of the Sun in the field of view along the angle α is affected by the velocities along the OZ _KA and OX _KA axes, and along the angle β , the velocities along the OY _KA and OX _KA axes are affected by the following formulas:

where α _i , α _{i -1} is the angle alpha with LED at the current and previous time points;

β _i , β _{i -1} - angle of beta with diabetes at the current and previous time points;

- истинная угловая скорость КА;

- true angular velocity of the spacecraft;

Δ t is the period of time between two pieces of information.

FIG. 2 illustrates the formation of the coordinates of the Sun in formulas (9), under the assumption that the angular velocity in OY _KA is zero, for clarity of disclosure of the invention. For other variants of the distribution of the spacecraft rotation speed along the channels, illustrations are constructed in a similar way.

For the claimed method, which does not require high accuracy in determining the angular velocity of rotation of the spacecraft, with the field of view of the device not exceeding 90 °, formula (9) is written as follows:

- вычисленные оценки углов α и β в момент времени;Where

- calculated estimates of the angles α and β at time;

k _{α , β} is a piecewise continuous function that replaces the cosine of the angle (for α _i , β _i no more than 0.262 rad k _{α , β were} taken equal to 0.99, for α _i , β _i more than 0.262 rad k _{α , β were} taken equal to 0.90), the sines of the corners are replaced by the corners themselves;

- оценки угловых скоростей КА, которые необходимо найти.

- estimates of the angular velocity of the spacecraft to be found.

The difference between estimates and measurements of the coordinates of the Sun occurs for the following reasons: inaccurate knowledge of angular velocity, SD error, and calculation error. Obviously, the measurement error and the calculation error make a less significant contribution compared to the speed knowledge error.

From (10) we obviously obtain estimates of the velocities along the axes OZ _KA and OY _KA

будет вызвана неучтенной скоростью по оси OX_KA. Аналогичные рассуждения справедливы и для угла β. В таком предположении оценку угловой скорости по оси OX_KA определим по формулеTo obtain an estimate of the angular velocity along the OX _KA axis, suppose that the difference in the angle α ( α _i - α _{i -1} ) is the result of the influence of the angular velocity along the OZ _KA axis, then the difference between the angle estimate and the angle itself

will be caused by the unaccounted velocity along the axis OX _KA . Similar considerations hold for angle β. Under this assumption, the estimate of the angular velocity along the axis OX _{KA is} determined by the formula

or

To reduce the effect of short-term false LED readings, the calculated estimates of the angular velocity are additionally filtered

- коэффициенты фильтра

;Where

- filter coefficients

;

- используемая угловая скорость КА в текущий и предыдущий моменты времени.

- used angular velocity of the spacecraft at the current and previous points in time.

The values of the filter coefficients lie in the range (0 ... 1) and are selected on the basis of the required convergence rate of the filter, the SD parameters and the necessary accuracy of determining the spacecraft’s own angular velocity.

вместо их оценок

, тогда формулы вычисления оценок угловой скорости принимают окончательный видWe substitute the angular velocities used in the right-hand sides of system (11) and equation (14)

instead of their ratings

then the formulas for calculating the estimates of the angular velocity take the final form

Thus, the algorithm for determining and filtering the angular velocity of the spacecraft by the solar sensor is as follows.

a) at the first iteration, the angular position of the Sun in the coordinate system associated with the spacecraft is determined and stored. The initial values of the used speeds and their estimates come from other sources or, in their absence, are taken equal to zero;

b) from the second iteration, the following actions are repeated at each measurement step:

1) the solar sensor determines the angular position of the Sun relative to the axes associated with the spacecraft;

2) using formulas (15), an estimate of the angular velocity of the spacecraft’s own rotation at the current time is calculated from the data stored in the previous step and the current measurements about the angular position of the Sun (indices i-1 and i, respectively);

3) according to the obtained estimates of the angular velocity according to formulas (14), the values of the used speed at the current time are obtained;

4) current information about the position of the Sun, the values of control speeds and their estimates are remembered for the next iteration.

составила не более 0.1°/с, если Солнце находилось на краю поля зрения СД, и не более 0.05°/с при отклонении направления на Солнца от центра поля зрения СД до 45°.This method for determining angular velocities without the use of spacecraft speed sensors has been successfully confirmed by tests as part of a geostationary spacecraft, the error in determining the angular velocity of a spacecraft with selected filter coefficients

amounted to not more than 0.1 ° / s, if the Sun was at the edge of the field of view of the LED, and not more than 0.05 ° / s when the direction to the Sun deviated from the center of the field of view of the LED to 45 °.

Thus, the proposed method for determining the intrinsic angular velocity of a spacecraft using a solar sensor, without the use of instruments for measuring the angular velocity of a spacecraft and without the use of complex mathematical calculations, allows one to determine all three components of the angular velocity vector and reduces the influence of errors of the solar sensor on determining the angular velocity of a spacecraft. This invention can be effectively used for medium and heavy spacecraft as a backup algorithm for determining the angular velocity in case of failure of the angular velocity sensors in orientation modes for which the required error in determining the angular velocity of rotation of the spacecraft is not more than 0.1%.

Claims (11)

A method for determining the angular velocity of the spacecraft’s own rotation around the center of mass, which consists in measuring the angular position of the Sun relative to the axes associated with the spacecraft (SC) body at successive time intervals and calculating an estimate of the angular velocity, characterized in that the estimation of the angular velocity of the spacecraft’s own rotation determined by the formula

and then filter it according to the formula

where α _i , α _i-1 is the angle alpha from the solar sensor at the current time and the previous one, β _i , β _i-1 - beta angle from the solar sensor at the current time and the previous one, k _{α, β} is a piecewise continuous function replacing the cosine of the angle, Δt is the period of time between two pieces of information,

- estimates of the angular velocity of the spacecraft,

- filter coefficients,

- used angular velocity at the current time and previous.

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