Attitude control procedure in survival mode of a satellite carrying an instrument sensitive to solar radiation

Abstract

A method is described for controlling the attitude of a satellite in low Earth orbit in survival mode, said satellite comprising an instrument sensitive to solar radiation. The method comprises: implementing attitude control (100) using a control law according to which: - magnetocouplers are controlled to limit variations in the Earth's magnetic field, - an internal kinetic moment is controlled along a predetermined axis. The method is characterized in that it further comprises: measuring an inertial rotation velocity (200) of the satellite, by means of an element of equipment for measuring an inertial rotation velocity of the satellite, and, at least when the norm of the measured inertial rotation velocity is less than a predetermined activation threshold, controlling (300) suitable inertial actuators to generate internal kinetic moments in the satellite's frame of reference.in order to increase the standard inertial rotation speed of the satellite.

Description

Domaine technique

[0001] This disclosure falls within the domain of attitude control of satellites in geocentric orbit, and more specifically concerns the attitude control of satellites in survival mode in low Earth orbit, where the satellite carries an instrument sensitive to solar radiation. Technique antérieure

[0002] In this application, "survival mode" means any attitude control mode of a satellite aimed, from an initial disturbed state, at ensuring sufficient sunlight for the solar generators to guarantee the electrical autonomy of a platform of said satellite until it is restored to a state close to nominal operating conditions.

[0003] Thus, the survival mode can be implemented immediately after separation from the launcher for the initial acquisition of the Sun and / or after the satellite mission has started in its mission orbit, in the event of any incident requiring interruption of the mission such as a failure of equipment such as a thruster.

[0004] For a satellite in survival mode in low Earth orbit, equipped with both magnetorquers and flywheels, it is known from patent application EP 0778201 A1 to control attitude using in particular a magnetorquer control law called "in B point", to indicate that it involves the derivative of the Earth's magnetic field B.

[0005] According to this B-point law, the Earth's magnetic field is measured along the three axes of a satellite frame. The measurements are differentiated with respect to time, then the derivatives are multiplied by a gain, and a current representing the result is passed through magnetorquers to create internal magnetic moments that tend to stop the variations of the Earth's magnetic field in the satellite frame, so that the satellite follows the lines of the Earth's magnetic field. Thus, for a polar orbit, the B-point law ultimately causes the satellite to rotate on its axis at a speed equal, in an inertial frame, to twice the orbital angular frequency (that is, the satellite completes two rotations per orbit) around an axis orthogonal to the plane of the orbit.

[0006] Furthermore, the flywheels are controlled to generate an internal angular momentum, known as the "survival angular momentum," along a predetermined axis in the satellite's reference frame. Due to this survival angular momentum generated by the flywheels, and because the B-law is used to control the magnetorquers, the satellite will naturally orient itself to rotate around the axis of survival angular momentum. In other words, the satellite orients itself so that the axis of survival angular momentum is orthogonal to the plane of its orbit. To maximize the average solar irradiance of the solar arrays, the axis of survival angular momentum can be predetermined based on the local time of the satellite's orbit.

[0007] We also know from patent EP 3 921 235 B1 a method for controlling the orbit of a satellite in survival mode which also implements a B-point law and further includes a step of searching for the Sun by means of a solar sensor, enabling the detection of whether the satellite is in the phase of visibility of the Sun and, when a phase of visibility of the Sun is detected, an attitude control step implementing a B-point magnetorquer control law, and during which the inertial actuators are also controlled to form torques aimed at placing and maintaining the satellite in an attitude in which the satellite's solar generator is directed towards the Sun.

[0008] In cases where the satellite includes at least one instrument sensitive to solar radiation, particularly an optical instrument, the implementation of these attitude control laws can present a risk of instrument damage due to glare at low speeds. Indeed, the implementation of a B-point law typically reduces the satellite's inertial rotation speed until it converges to a rotation speed equal to twice the orbital pulsation, as described above. During this period, the satellite's orientation changes, and the optical instrument's line of sight may, for example, be oriented towards the Sun, causing glare.

[0009] Instrument glare is defined as the period during which direct or reflected solar radiation is incident on a sensitive area of ​​the instrument (typically, in the case of an optical instrument, the sensitive area may include optical components such as lenses and mirrors, as well as electronic components, including optoelectronic sensors). However, in the case of glare at low speeds, the duration for which the instrument is glare increases and can lead to a temperature rise that is detrimental to the instrument. Résumé

[0010] The purpose of this disclosure is to address all or part of the limitations of prior art solutions, including those described above, by proposing attitude control of a satellite in survival mode carrying a solar radiation sensitive instrument, which greatly reduces the risks of damage to the onboard instrument due to slow, i.e., too long, glare from the onboard instrument.

[0011] In this regard, a method is proposed according to claim 1.

[0012] Thus, the proposed attitude control method includes measuring the inertial rotation speed of the satellite using a gyroscope, and, if a low inertial rotation speed is detected, controlling the inertial actuators to increase this inertial rotation speed.

[0013] This process is implemented regardless of the instrument's orientation and therefore does not require knowledge of the sun's position relative to the instrument. However, it eliminates the risk of damage to the instrument due to glare by ensuring a minimum inertial rotation speed for the satellite. Thus, when glare occurs, controlling the inertial rotation speed reduces the exposure time of the instrument's sensitive components to a duration short enough to prevent overheating or damage.

[0014] Since the inertial actuators are only activated when the inertial rotation speed is below a predetermined trigger threshold, and since this activation is based on the satellite's inertial rotation speed, the actuator control has minimal impact on the satellite's final attitude. In particular, the attitude control according to the invention has no effect on the expected long-term behavior of a B-shaped pattern.

[0015] In embodiments, when the measured inertial rotational speed is below the predetermined trigger threshold, the inertial actuators are controlled to generate an incremental angular momentum of determined magnitude and direction.

[0016] In some embodiments, the norm of the incremental angular momentum is a decreasing function of the measured velocity, between a maximum increment value and a zero value when the measured inertial rotational velocity is equal to the triggering threshold.

[0017] In some embodiments, the decreasing function of the measured velocity is continuous at the inertial rotational velocity value corresponding to the trigger threshold on at least two orders of differentiation. For example, the decreasing function of the measured velocity is a power function of at least order 2 or an exponential function.

[0018] In some embodiments, the norm of the incremental angular momentum is constant and equal to the maximum value when the measured inertial rotational speed is less than or equal to a second threshold, lower than the triggering threshold.

[0019] According to the invention, the value of the inertial rotation speed corresponding to the triggering threshold is determined as a function of a maximum permissible exposure time of the optical instrument to the sun.

[0020] In some embodiments, the measurement and control steps of the inertial actuators are iterative, and the direction of the incremental angular momentum is equal to the satellite inertia multiplied by the direction of the natural rotational velocity of the satellite, corresponding to the direction of the measured inertial rotational velocity of the satellite from which is deduced the incremental angular momentum applied to the previous iteration of the control step of the inertial actuators.

[0021] In embodiments, the measurement and control steps of the inertial actuators are iterative and, when the measured inertial rotational speed is less than a safety threshold lower than the trigger threshold, the direction of the incremental angular momentum is the last direction of incremental angular momentum determined during a previous iteration of the inertial actuator control step.

[0022] In some embodiments, when the measured inertial rotational speed becomes greater than the safety threshold, the direction of the incremental angular momentum is determined by time interpolation between the last direction of incremental angular momentum commanded to the inertial actuators and the direction of natural rotational speed of the satellite.

[0023] In some embodiments, the control law is a biased point B law.

[0024] According to another object, a satellite is proposed for placement in a low inclined orbit, comprising at least one instrument sensitive to solar radiation, magnetorquers adapted to form internal magnetic moments in a satellite frame, inertial actuators adapted to form internal angular moments in said satellite frame and magnetometers adapted to measure the Earth's magnetic field, said satellite being characterized in that it further comprises equipment for measuring an inertial rotation speed of the satellite and a control module for the magnetorquers and inertial actuators, said control module being configured to implement an attitude control method in survival mode according to the preceding description.

[0025] In some embodiments, the inertial actuators are reaction wheels.

[0026] In some embodiments, the equipment for measuring the inertial rotation speed of the satellite is a gyroscope.

[0027] According to another object, a computer program product is described, characterized in that it comprises a set of program code instructions which, when executed by a processor of a satellite control module, configure said control module to implement the attitude control method in survival mode according to the preceding description. Brève description des dessins

[0028] Other features, details, and advantages will become apparent upon reading the detailed description below and analyzing the attached drawings, on which: Fig. 1 [ Fig. 1 ] is a schematic representation of one embodiment of a satellite. Fig. 2 [ Fig. 2 [ ] schematically represents the main steps of an attitude control process in survival mode according to an embodiment Fig. 3 [ Fig. 3 ] represents an example of the evolution of the norm of the velocity increment given to the satellite as a function of the measured inertial velocity. Fig. 4a [ Fig. 4a ] represents an example of the Sun's trajectory relative to an instrument's glare cone, without the implementation of the attitude control method. Fig. 4b [ Fig. 4b ] represents the trajectory of the Sun relative to a cone of glare from an instrument, from similar initial kinematic conditions, with the implementation of the attitude control method. Description des modes de réalisation

[0029] The present invention relates to the attitude control of a satellite 10 in survival mode in low geocentric orbit.

[0030] As previously stated in this application, the survival mode is an attitude control mode implemented immediately after separation from the launcher and / or after the mission of satellite 10 has begun, in the event of any incident requiring the interruption of the mission (collision with a meteorite, failure of a thruster, etc.)

[0031] By "low Earth orbit," we mean that the maximum altitude of the satellite is such that the local Earth magnetic field is significant enough to allow the use of magnetorchers to control the satellite's attitude. In practice, this condition is met particularly when the satellite's maximum altitude is less than 2000 kilometers.

[0032] In what follows, we will use the concept of an inertial frame of reference, that is, a reference frame in which the principle of inertia, according to which every free point mass continues in uniform rectilinear motion, is verified. In practice, for a satellite orbiting the Earth, we can consider, by approximation, that a geocentric frame of reference—that is, a frame of reference centered on the center of the Earth and comprising three orthogonal axes pointing towards three stars sufficiently far from the Earth to appear fixed (for the time period considered during the implementation of the process)—is an inertial frame of reference. We can also consider as an inertial frame of reference a heliocentric frame of reference—that is, a frame of reference centered on the center of the Sun and comprising three orthogonal axes pointing towards three stars sufficiently far from the Sun to appear fixed (for the time period considered during the implementation of the process).

[0033] There figure 1 schematically represents an example of the realization of a satellite 10 according to the invention.

[0034] A satellite frame of reference is associated with the satellite 10, for example centered on a center of mass O of the satellite 10, comprising three axes X, Y, and Z orthogonal to each other. The satellite frame of reference is fixed to the satellite 10, that is to say, it is entirely defined by the geometry of the satellite 10, and any rotation of the satellite in an inertial frame of reference translates into an equivalent rotation of the satellite frame in an inertial frame of reference.

[0035] The satellite comprises a body 11. In the non-limiting example shown on the figure 1 The body 11 is substantially rectangular in shape. The satellite also includes at least one solar array 12, and typically two solar arrays arranged on either side of said body. However, the number of solar arrays carried by the satellite is not limited.

[0036] The satellite also includes at least one solar-sensitive instrument 14. For example, instrument 14 may be an optical instrument. When the satellite is in orbit, the aiming axis of the optical instrument may be oriented towards Earth for an Earth observation mission. However, as mentioned above, during survival mode, the satellite's rotations in its inertial frame may cause the solar-sensitive components of instrument 14—in particular, for an optical instrument, the aiming axis—to be oriented towards the Sun, thus causing glare and heating of these sensitive components.

[0037] The satellite also includes several actuators implemented for attitude control. In particular, the satellite includes a set of magnetorquers 15 adapted to generate an internal magnetic moment of arbitrary axis in the satellite frame.

[0038] The satellite also includes a set of 16 inertial actuators, such as reaction wheels or gyroscopic actuators, adapted to form internal angular momenta in the satellite frame.

[0039] In addition, the satellite includes equipment 17 for measuring the satellite's inertial velocity, for example, a gyroscope. Alternatively, equipment 17 may also be a star tracker, adapted to measure the coordinates of one or more stars in the satellite's frame of reference, allowing the measurement of the satellite's inertial velocity from the displacement of the target stars measured by the sensor.

[0040] Satellite 10 also includes a control module (not shown in the figures) adapted to control the magneto-couplers and inertial actuators.

[0041] The control module includes, for example, at least one processor and at least one memory in which a computer program product is stored, in the form of a set of program code instructions to be executed to implement the various steps of a method for controlling the satellite's attitude in survival mode, as described below. In a variant, the control module includes one or more programmable logic circuits of the FPGA, PLD, etc. type, and / or specialized integrated circuits (ASICs) adapted to implement all or part of the steps of the method 50 for controlling the attitude of said satellite 10 in survival mode.

[0042] In other words, the control module includes a set of means configured by software (specific computer program product) and / or hardware (FPGA, PLD, ASIC, etc.) to implement the attitude control process of satellite 10 in survival mode.

[0043] With reference to the figure 2 We will now describe the main steps of a survival mode attitude control process for satellite 10 according to embodiments.

[0044] Attitude control in survival mode includes the following steps: Implementation 100 of an attitude control using a control law, Measurement 200 of an inertial rotation speed of the satellite during the implementation of said control law, and Increase 300 of the norm of the inertial rotation speed of the satellite when the latter, obtained in the measurement step, becomes less than a predetermined trigger threshold.

[0045] In step 100, the control law implemented includes the control of the magnetorquers 15, based on local values ​​of the Earth's magnetic field, to generate internal magnetic moments in the satellite frame, aiming to limit variations in the Earth's magnetic field within the satellite frame. The local values ​​of the Earth's magnetic field can be provided by measurements taken by one or more magnetometers (not shown in the figures), or by estimates provided by an Earth magnetic field model that receives as input the position of the satellite 10. This position can be estimated using a GNSS (Global Navigation Satellite System) receiver such as a GPS (Global Positioning System) receiver, not shown in the figures.

[0046] The control law also includes commands for generating an internal angular momentum within the satellite along a predetermined axis, and a minimum magnitude that is a function of at least the satellite's inertia. This internal angular momentum can, for example, be generated by the satellite's inertial actuators. Due to this angular momentum along a predetermined axis, and the internal magnetic moments generated by the magnetorches 15, the satellite naturally orients itself to rotate about its own axis of angular momentum.

[0047] In some embodiments, the control law is a so-called biased B-point law, or one using a biased B-point law.

[0048] According to the biased point B law, the internal magnetic moment generated by the magnetorquers 15 includes a term proportional to the derivative of the local values ​​of the Earth's magnetic field, and a bias, which is a term proportional to a cross product between the local Earth's magnetic field and a determined vector, the gain of which is determined as a function of the desired rotational speed of the satellite.

[0049] The biased B-point distribution can, for example, be expressed as follows: M MTQ → = − K B ⋅ d b → dt + ω CTRL → × b → Expression in which: M MTQ corresponds to the internal magnetic moment formed by the magnetorquers, K B corresponds to a strictly predetermined positive gain. d b → dt is the derivative of the Earth's unitary magnetic field b measured or estimated in the satellite frame, which is equal to B / ∥ B ∥ where Bis the Earth's magnetic field as measured or estimated in the satellite reference frame. ω CTRL is a predetermined vector, and × denotes the cross product.

[0050] In the absence of bias, applying the law at point B causes the satellite to rotate about its axis at a speed equal, in an inertial frame of reference, to twice the orbital angular frequency around the angular momentum axis. Bias increases this rotational speed. The gain ω CTRL (which is the magnitude of the vector) can be determined to result in a rotational speed of the satellite in an inertial frame of reference with a magnitude strictly greater than 2. ω 0 | and equal to or less than 4.| ω 0 |, ω 0 being the orbital pulsation of the satellite 10 in an inertial frame of reference. Of course, this speed is reached at the end of a convergence period, during which the inertial rotation speed of the satellite is variable, being able to take values ​​respectively lower than, or even zero, or values ​​higher than this speed reached at the end of the convergence period.

[0051] During step 200, the satellite's inertial rotational velocity is measured along the three axes of the inertial frame. Measuring the inertial velocity provides information on the relative speed of movement between the Sun and the satellite. This measurement is advantageously performed by a gyroscope 17, which offers a high level of precision and a short response time, i.e., on the order of less than 100 milliseconds, thus allowing for a short reaction time for the implementation of step 300.

[0052] The measurement of the satellite's inertial rotational speed is implemented repeatedly at a predetermined frequency during the execution of the control law 100 described above. For example, the acquisition frequency of this speed is advantageously at least once per second; it could, for example, be between 1 Hz and 20 Hz.

[0053] The norm of the inertial rotation speed thus measured is, at each iteration of step 200, compared to a so-called trigger threshold T 1, for the implementation of step 300, which includes the control of the inertial actuators 16 so as to increase the norm of the inertial rotation speed of the satellite 10, when the norm of the speed is or becomes less than this trigger threshold.

[0054] The trigger threshold T1 is defined by a value for the inertial rotation speed of the satellite. In some embodiments, this value corresponds to a minimum inertial rotation speed below which exposure of the instrument to the Sun would be too prolonged and therefore likely to damage the instrument. Advantageously, the value of the trigger threshold T1 is thus determined based on a maximum permissible exposure time of the instrument to the Sun, possibly with an added safety margin. As a non-limiting example, the speed value corresponding to the trigger threshold T1 could be, for example, between 5 and 15 mrad / s.

[0055] During step 300, the inertial actuators are activated to generate incremental angular momentum (i.e., momentum added to any angular momentum already generated by these actuators), with a predetermined magnitude and direction, to increase the magnitude of the inertial rotational velocity. Increasing the magnitude of the velocity therefore corresponds to adding a velocity increment of a predetermined magnitude, with a direction corresponding to that of the satellite's instantaneous inertial rotational velocity, to the measured velocity. Thus, the satellite's axis of rotation remains unchanged, and the rotation is not disturbed but only accelerated if it reaches the trigger threshold.

[0056] In the following, Δω inc denotes the vector corresponding to the satellite's velocity increment. Considering a target rotational velocity increment Δω inc for the satellite, this increment is related to the increment vector ΔH mom of the angular momentum controlled by the inertial actuators as follows: Δ H Mom = I sat ∗ Δ ω inc

[0057] Where Δ H Mom is the incremental angular momentum, and I sat is the inertia matrix of the satellite.

[0058] In embodiments, and with reference to the figure 3 , the norm of the angular momentum increment, denoted ∥Δ H Mom ∥ (and therefore the magnitude of the velocity increment) is a decreasing function of the measured velocity, between a maximum increment value, reached for example at zero velocity, and a zero value, which is reached when the measured inertial rotational velocity is equal to the trigger threshold T1. In other words, considering a satellite 10 whose inertial rotational velocity gradually decreases until it reaches the trigger threshold T1, the magnitude of the incremental angular momentum ∥Δ H Mom ∥ controlled to the inertial actuators 16 increases progressively as the rotation speed of the satellite decreases, so as to achieve a stronger speed correction if it becomes too low.

[0059] In some embodiments, this function is a continuous function, with at least two differentiation orders, at the point where the value of the inertial rotational speed equals the trigger threshold T1. For example, the function can be a power function of order 2 or higher, or an exponential function. This allows for gradual acceleration and avoids excessively abrupt speed changes that could damage certain equipment onboard the satellite.

[0060] In embodiments, and as represented in the example of the figure 3 The magnitude of the angular momentum increment is constant, and equal to the maximum increment value, when the magnitude of the inertial rotational velocity is less than a second threshold T2, which is lower than the trigger threshold; that is, when this magnitude is between 0 and T2. In other words, between speeds between T1 and T2: the lower the speed of the satellite, the higher the magnitude of the angular momentum increment; between speeds between 0 and T2: the magnitude of the angular momentum increment is constant and maximum.

[0061] Thus, we ensure the application of a maximum increment for all speeds between 0 and T2, which allows for very rapid correction for a speed range where the risk of damage in case of glare is particularly high.

[0062] The norm of the angular momentum increment is thus determined.

[0063] The direction of the angular momentum increment, denoted u Mom , is given by u Mom = I sat * u Rate , with I sat the inertia matrix of the satellite and u Rate the direction of the desired speed increment. u Rate is chosen to be equal to the direction of the satellite's natural rotation speed, denoted ω nat , which corresponds to the last measured inertial rotation speed of the satellite, from which the incremental angular momentum Δ is deduced ω inc,prev applied to the previous iteration of step 300 of the inertial actuator control: ω nat = ω sat / I − Δ ω inc , prev

[0064] It can be observed from the preceding equation that in certain cases, where the satellite's inertial rotation speed is too low, the direction of the angular momentum increment may not be determinable due to calculation discrepancies. In this case, the method advantageously provides that when the measured inertial rotation speed is below a safety threshold TS, the direction of the incremental angular momentum is not recalculated, but rather the last incremental angular momentum direction determined during a previous iteration of step 300 of the inertial actuator control is used. This effectively locks the direction of the angular momentum increment until the satellite's inertial rotation speed is reached again, allowing for the calculation of this direction. The safety threshold Ts is lower than the threshold T1 for triggering the satellite's speed increase. For example, it is less than 1 mrad / s.

[0065] In some embodiments, when the inertial rotational velocity of the satellite rises above the safety threshold Ts, the direction calculated for at least the next implementation of step 300 can be determined by time interpolation between the last incremental angular momentum direction commanded to the inertial actuators (i.e., during the previous iteration of step 300, including in the case of a lock-up as described above) and the natural rotational velocity direction of the satellite described above. In some embodiments, this method of calculating the direction is used for more than one implementation of step 300 following the return of the inertial rotational velocity to a level above the threshold Ts. For example, it can be used for a specified period of time or for a specified number of iterations of this step.This allows exiting the 310 direction lock state by ensuring a gradual change in direction of the rotation speed increment, and helps to limit disturbances on the control law as well as the risks of damage to the equipment on board the satellite.

[0066] 320 interpolation can, for example, be linear interpolation (LERP) or spherical linear interpolation (SLERP), which are classic interpolation techniques.

[0067] With reference to figures 4a et 4b An example of the Sun's trajectory relative to an optical instrument mounted on a satellite implementing attitude control is shown, respectively with and without an increase in the magnitude of the satellite's inertial rotation velocity when it falls below the trigger threshold T1. In these figures, the Sun's trajectory is represented by a curve on a sphere that represents all the spherical coordinates around the instrument, shown at the center. The dashed circle centered on the line of sight corresponds to the glare cone of the optical instrument, which must not be pointed at the Sun beyond a certain time. The shades of gray in the satellite's trajectory correspond to values ​​of the satellite's inertial rotation velocity; therefore, the darker the trajectory, the slower the velocity, and thus the longer the time spent at the given position.

[0068] In the case of the figure 4a We can thus observe that part of the Sun's trajectory passes through the glare cone, and at low speeds, this is potentially detrimental to the instrument. In the case of the figure 4b We observe that the Sun's speed remains high, thanks to the acceleration described above. Thus, even if the Sun passes through the optical instrument's glare cone, it does so at a speed high enough not to damage the instrument.

[0069] The proposed method, by increasing the inertial rotation speed of the satellite 10 each time it falls below a predetermined threshold, avoids the risk of glare without needing to know the instrument's position relative to the sun. This increase in speed is implemented without any prior knowledge or conditions regarding the instrument's orientation.

Claims

1. An attitude control method for a low-orbit satellite in survival mode, the satellite comprising an instrument sensitive to solar radiation, the method comprising: implementing (100) an attitude control using a control law according to which: - magnetorquers, adapted to form internal magnetic moments in a satellite frame, are controlled as a function of a measurement of the Earth's magnetic field by magnetometers, to limit variations of the Earth's magnetic field, - an internal angular momentum is controlled along a determined axis, the internal angular momentum having a minimum norm as a function of at least the inertia of the satellite, the method further comprising: measuring (200) a norm and a direction of an instantaneous inertial rotation speed of the satellite, by a measurement equipment of an inertial rotation speed of the satellite and at least when the norm of the measured inertial rotation speed is lower than a value corresponding to a predetermined trigger threshold as a function of a maximum authorized exposure time of the instrument to the sun, commanding (300) inertial actuators adapted to form internal angular momenta in said satellite frame, to increase the norm of the inertial rotation speed of the satellite, by a speed increment of determined norm, and the direction of which corresponds to that of the instantaneous inertial rotation speed of the satellite.

2. The method according to claim 1, wherein, when the measured inertial rotation speed is lower than the predetermined trigger threshold, the inertial actuators are controlled (300) to generate an incremental angular momentum of determined norm and direction.

3. The method according to claim 1 or 2, wherein the norm of the incremental angular momentum is a decreasing function of the measured speed, comprised between a maximum increment value and a null value when the measured inertial rotation speed is equal to the trigger threshold.

4. The method according to claim 3, wherein the decreasing function of the measured speed is continuous at the value of inertial rotation speed corresponding to the trigger threshold over at least two orders of derivation.

5. The method according to claim 4, wherein the decreasing function of the measured speed is a power function of order at least 2 or an exponential function.

6. The method according to one of claims 3 to 5, wherein the norm of the incremental angular momentum is constant and equal to the maximum value when the measured inertial rotation speed is lower than or equal to a second threshold, lower than the trigger threshold.

7. The method according to one of claims 2 to 6, wherein the steps of measuring (200) and commanding (300) the inertial actuators are iterative, and the direction of the incremental angular momentum is equal to the satellite inertia multiplied by the direction of the natural rotation speed of the satellite, corresponding to the direction of the measured inertial rotation speed of the satellite from which the incremental angular momentum applied in the previous iteration of the step of commanding the inertial actuators is deduced.

8. The method according to one of the preceding claims, wherein the steps of measuring (200) and commanding (300) the inertial actuators are iterative and, when the measured inertial rotation speed is lower than a safety threshold (Ts) lower than the trigger threshold, the direction of the incremental angular momentum is the last direction of incremental angular momentum determined during a preceding iteration of the step of commanding the inertial actuators.

9. The method according to claim 8, wherein, when the measured inertial rotation speed becomes greater than the safety threshold (Ts), the direction of the incremental angular momentum is determined by time interpolation between the last direction of incremental angular momentum commanded to the inertial actuators and the direction of the natural rotation speed of the satellite.

10. The method according to one of the preceding claims, wherein the control law is a biased B-dot law.

11. A satellite (10) intended to be placed in an inclined low orbit, comprising at least one instrument (14) sensitive to solar radiation, magnetorquers (15) adapted to form internal magnetic moments in a satellite frame, inertial actuators (16) adapted to form internal angular momenta in said satellite frame and magnetometers adapted to measure the Earth's magnetic field, said satellite (10) further comprising a measurement equipment (17) for an inertial rotation speed of the satellite and a control module for the magnetorquers and inertial actuators, said control module being configured to implement an attitude control method in survival mode according to any one of the preceding claims.

12. The satellite according to the preceding claim, wherein the inertial actuators (16) are reaction wheels.

13. The satellite according to claim 11 or 12, wherein the measurement equipment (17) for an inertial rotation speed of the satellite is a gyroscope.

14. A computer program product, comprising a set of program code instructions which, when executed in a satellite according to any one of claims 11-13, configure, in the module, said satellite to implement the attitude control method in survival mode according to any one of claims 1 to 10.

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