FR2724364A1 - Triaxial stabilisation attitude control for nonequatorial satellite - Google Patents

Abstract

The satellite moving in a non-equatorial orbit incorporates an inertia wheel (52) introducing a kinetic momentum about its pitch axis (y). The components of magnetic field about the roll, pitch and yaw axes are measured and the components about the same axes are calculated from a predetermined model of the geomagnetic field assuming that the roll, pitch and yaw angles take predetermined desired values. A pitch stabilisation couple is determined w.r.t the pitch angle estimation obtained from the measured and calculated values of the roll and yaw axis electromagnetic field components. Roll and yaw stabilisation couples are obtained using the difference between the calculated and the measured values of the magnetic field component relating to the pitch axis. The pitch stabilisation couple is applied by rotating the inertia wheel. The roll and yaw stabilisation couple are applied using two magnetic-coupler (56,58) which are energised to generate momentum interacting with the pitch magnetic field component.

Description

THREE-AXIS STABILIZATION METHOD AND SYSTEM
OF A NON-EQUATORIAL ORBIT SATELLITE
The present invention relates to a method and a system for controlling the attitude of a non-equatorial orbit satellite.

 The known attitude control systems capable of providing stabilization of a satellite along its three axes most often include terrestrial or stellar sensors used to determine estimates of the roll, pitch and yaw angles of the satellite. If they make it possible to obtain relatively precise estimates of the angles, these sensors have the disadvantage of being relatively heavy, energy-consuming, and expensive. It would therefore be desirable to be able to dispense with it in the case of satellites for which a low cost price is sought, typically telecommunications satellites.

It is also known to estimate the attitude of the satellite on the basis of magnetometric measurements by using Kalman filtering. But the estimators of
Kalman are of a very complex implementation, which it is not currently possible to envisage on board the satellite, except to confer on it a very great complexity, a priori incompatible with the abovementioned objective of low cost price.

 In addition, the known methods for stabilizing a satellite along three axes have generally been developed for geostationary satellites, at least whose orbit is relatively close to the equatorial plane of the Earth.

When the inclination of the orbital plane increases, these methods are not always usable.

 In view of the above, an object of the present invention is to propose a method and a system for controlling the attitude of a satellite of non-equatorial orbit responding in a simple and economical manner to the problem of stabilization along three axes. The invention thus provides a method for controlling the attitude of a satellite of nonequatorial orbit having a roll axis, a pitch axis and a yaw axis and comprising an inertial wheel providing a kinetic moment along the pitch axis , in which we measure the components of the magnetic field along the roll, pitch and yaw axes of the satellite, and we compute, on board the satellite, magnetic field components along the same axes by applying a predetermined model of the magnetic field terrestrial and assuming that the roll, pitch and yaw angles take predetermined set values. A pitch stabilization torque determined on the basis of estimates of the pitch angle obtained on board the satellite is applied to the satellite. from the computed and measured components of the magnetic field along the roll and yaw axes, and we apply roll and yaw stabilization torques to the satellite d determined on the basis of the difference between the calculated and measured components of the magnetic field along the pitch axis.

 The roll and yaw stabilization torques can in particular be applied by means of magnetocouplers perpendicular to the pitch axis. To apply the stabilization torque along the pitch axis, use is preferably made of a control of the rotation of the inertial wheel associated with a desaturation control of this wheel. Desaturation can in particular be carried out continuously, by controlling the magnetocouplers perpendicular to the pitch axis so as to generate a desaturation torque of the inertial wheel by interaction with the components of the magnetic field along the roll and yaw axes.

 According to a second aspect, the invention proposes a system for controlling the attitude of a satellite of nonequatorial orbit, comprising magnetometric means for measuring the components of the magnetic field along a roll axis, a pitch axis and an axis of satellite yaw, an inertial wheel providing a kinetic moment along the pitch axis, means for generating stabilizing torques in roll, pitch and yaw, and means for controlling means generating stabilizing torques including means for calculate magnetic field components according to the roll, pitch and yaw axes by applying a predetermined model of the earth's magnetic field and assuming that the roll, pitch and yaw angles take predetermined set values. control are arranged to control the means generating stabilization torques so as to apply a stabilizing torque to the satellite pitching determination determined on the basis of estimates of the pitching angle obtained from the calculated and measured components of the magnetic field along the roll and yaw axes, and to apply roll and yaw stabilization torques to the satellite determined on the basis of the difference between the calculated and measured components of the magnetic field along the pitch axis.

Other features and advantages of the present invention will appear in the description below of a preferred but nonlimiting embodiment, with reference to the accompanying drawings, in which
- Figure 1 is a diagram showing a satellite in a non-equatorial earth orbit
- Figure 2 is a schematic representation of components of an attitude control system according to the invention on board a satellite
- Figure 3 is a block diagram of the attitude control system; and
- Figures 4A to 4C are graphs showing an example of changes in the roll, pitch and yaw angles stabilized by the system according to the invention.

Figure 1 shows the orbit O described by a satellite S around the Earth T. The orbit is inclined in the sense that the orbital plane forms with the equatorial plane of the
Earth an angle i of at least 20 typically. The orbit is low, that is to say that the satellite evolves at a distance from the Earth typically between 200 and 2000 kilometers, in an area where the Earth's magnetic field is neither too weak nor too disturbed. The invention will be described below in the case of a circular orbit.

We define a roll axis x, a pitch axis y and a yaw axis z forming an orthonormal trihedron linked to the satellite. The roll angle, noted, is defined as the orientation error around the direction of the instantaneous speed vector of the satellite. The pitch angle, denoted O, is defined as the orientation error around the direction normal to the orbital plane. The yaw angle, noted, is defined as the orientation error around the direction of the satellite pointing to the center of the Earth. When stabilization along the three axes of the satellite is exactly achieved in the case of an orbit circular, we have ç = O = W = 0, and the axes x, y and z coincide respectively with the axis of the velocity vector, with the axis normal to the orbital plane and with the axis pointing towards the center of the
Earth.

 The attitude control system according to the invention comprises magnetometric means for measuring the components of the magnetic field along the roll, pitch and yaw axes of the satellite, constituted for example by two two-axis magnetometers or, as in the case illustrated schematically in FIG. 2, by a magnetometer 50 with three axes respectively aligned along the x, y and z axes.

 The attitude control system comprises an inertial wheel 52, driven by a motor 54, the axis of rotation of which is aligned along the axis of pitch y of the satellite.

The inertial wheel 52 provides a coupling between the roll dynamics and the yaw dynamics of the satellite. The dynamics of the satellite is that of a rigid body having an on-board kinetic moment H generated by the wheel 52 along the pitch axis, and to which are applied disturbing torques C'x, C'y and C'z as well as stabilization torques Cx, Cy and Cz generated by the attitude control system. The equations of movement are written, at small angles 1x <P + H # 0 # = Cx '+ Cx' (1)
IyO + H = Cy + Cy (2) Iv # - H (p + ## 0 # = Cz + C z (3) with Ix, Iy and 1z representing the moments of inertia of the satellite respectively along the roll axes, of pitch and yaw, and 0 representing the orbital pulsation of the satellite. These general equations highlight a decoupled pitch dynamic, which can be written
IyO = Cy + Cy -H
It will be noted that, when the pitch stabilization is carried out by controlling the rotation of the inertial wheel 52, the term Cy representing the pitch stabilization torque is confused with the term -H.

On the other hand, relations (1) and (3) highlight the dynamics coupled in roll and yaw, where two natural frequencies of free dynamics appear: the long-term movement taking place approximately at the orbital pulsation, and short-term nutation. According to the frequency bands considered, we can therefore write + + HO) (p = cx + CX (LT) (5) -H (p + H # 0 # = Cz + Cz (LT) (6) for long movement) term, and IXÇ + Xf = Cl + cl (7)
- = Cz + Cz (8) for the short-term nutation movement. In relations (5) and (7), the notations Cx (LT) and Cx (CT) designate the long-term and short-term parts of the roll stabilization torque, respectively. In equations (6) and (8) , the notations Cz (LT) and Cz (CT) respectively designate the long-term and short-term parts of the yaw stabilization torque.

 In the detailed embodiment below, the pitch stabilization torque is applied by controlling the motor 54 for driving the wheel 52, and the roll and yaw stabilization torques are applied by two magnetocouplers 56, 58 each placed parallel to the roll-yaw plane xz. In the example shown in FIG. 2, the magnetocoupler 56 is arranged to produce a component of magnetic moment Mx parallel to the roll axis suitable for generating the torque stabilization in yaw by interaction with the component of the earth's magnetic field along the pitch axis, and the magnetocoupler 58 is arranged so as to produce a component of magnetic moment Mz parallel to the yaw axis suitable for generating the stabilization torque in roll by interaction with the component of the Earth's magnetic field along the pitch axis.

 The application of the stabilization torques is supervised by a control unit 60 illustrated in block diagram form in FIG. 3. The control unit 60 is entirely located on board the satellite S, and can for example be produced on the basis of processors of digital processing, or specialized circuits.

In the diagram of FIG. 3, the control unit 60 comprises a block 62 for calculating components Box, By * and B z of the earth's magnetic field along the roll, pitch and yaw axes. These Box *, Byt and Bz components are calculated by applying a pre-established model of the Earth's magnetic field, and assuming that the roll, pitch and yaw angles are in accordance with the setpoint: # = 0 = 'v = 0. De such models of the Earth's magnetic field are well known; they are most often in the form of series developments whose order is chosen all the higher as one wishes a precise modeling. If one supposes that the angles #, O and v are small, then one can write to first order #Bx = Bz # - Byv (9) bBy = Bxv - Bz # (10) SBz = By # - Bx # (11) where 8Bx = Bx * - Bx, 8By = By - By and #Bz = Bzt - Bz each denote the difference between the calculated and measured components of the magnetic field, respectively along the roll, pitch and yaw axes. Relations (9) and (11) make it possible to obtain a 0 estimate of the pitch angle given by Ot = (Bz8Bx - Bx8Bz) / (Bx2 + Bx) (12)
We can show that the difference # 0 = 0 * - O between this estimate and the true value of the pitch angle is equal to cotg (i) x (2 sinX + ç cos #) where i designates the orbital inclination and X denotes the true magnetic anomaly. We therefore have in all circumstances AO <cotg (i) x max (#max, 2Vmax) (13), that is to say that good stabilization in roll and yaw ensures a relatively accurate estimate of the pitch angle. As the orbit is not equatorial, the factor cotg (i) further reduces the estimation error in pitch.

With reference to FIG. 3, the estimate (12) of the pitch angle is obtained by the estimation block 64, and supplied to block 66 which calculates the pitch stabilization torque Cy. Stabilization in pitch can be carried out by a simple proportional-derivative control preceded by a low-pass filtering of the estimates Ot, intended to eliminate the short-term variations. The couple
Cy is then written cy = -K0O * - Kvet (14) the first term being proportional to the estimate 0 *, and the second proportional to the time derivative of the estimate 0 *. The Kg and optimal control gains can be determined by means of preliminary simulations of the satellite dynamics.

 The determined value of the pitch stabilization torque Cy is supplied to the motor 54 so that the latter communicates to the inertial wheel 52 a corresponding acceleration.

 The control of the roll and yaw angles must be coupled to take account of the free dynamics. This is done with the only information available concerning only the roll and yaw angles: the measurement of the component of the magnetic field along the pitch axis.

The short-term part of the roll and yaw stabilization torques Cx and C z is taken proportional to the time derivative ABy of the difference between the calculated and measured components of the magnetic field along the pitch axis: CX (CT) = kl8By and Cz (CT) = k26By From relations (7), (8) and (10), the dynamics of the short-term roll and yaw movement is then written, in the absence of disturbing torque, and neglecting the variations of the earth's magnetic field in the nutation frequency band:
IXÇ + k1Bz # + (H-k1Bx) # = 0 (15) Iz # - k2BXt - (H-k2BZ) = o (16)
We then choose the gains kl and k2 according to kl = kBz and k2 = -kBx (17) where k is a positive coefficient. Solving the differential equations (15) and (16) then leads to the Laplace variable equation s
+ k IxIx + IzBz + IzBz) H2 = 0 (18)
IxIz IxIz
To obtain in the worst case a damping # (we typically take # = 0.7), we then choose the coefficient k according to k = 2tH / (BOsin i) 2 (19)
B0 being of the order of the norm of the geomagnetic field at the level of the equatorial plane (B0 - 2x10-5 T for an orbit of 200 to 2000 km). Expression (19) is in the case where the 1x 1z approximation is verified.

et une fréquence de coupure haute de l'ordre de cinq fois la fréquence de nutation th. Le signal ainsi filtré est dérivé et multiplié respectivement par les coefficients kl et k2 (avec k donné par la relation (19)) pour obtenir Cx(CT) et Cz(CT). To obtain the short-term part Cx (cT) Cz (CT) of the roll and yaw stabilization torques, the difference 8By is subjected to bandpass filtering typically having a low cut-off frequency of the order of a fifth of the frequency of nutation

and a high cut-off frequency of the order of five times the nutation frequency th. The signal thus filtered is derived and multiplied respectively by the coefficients kl and k2 (with k given by equation (19)) to obtain Cx (CT) and Cz (CT).

 The long-term stabilization torques in roll and yaw are taken proportional to the difference aBy between the calculated and measured components of the magnetic field along the pitch axis: Cx (LT) = K18By and Cz (LT) = K2 # By .

Equations (5) and (6) then become v + # 0 # = Cx '/ H + (K1 / H) (B, W - Bz9) (20) # - # 0 # = Cz' / H - (K2 / H) (Bxv - Bz #) (21)
An approach in terms of Laplace transform is no longer rigorous with the terms of magnetic field.

We can, however, write the decoupled equations where the depreciation term appears (in Laplace variable) - (W / H) / (KlBx + K2Bz) s
To keep this term always positive and ensure long-term control, we then take
K1 = -KBX and K2 = -KBz (22) where K is a positive coefficient. Therefore, the damping term for long-term dynamics is given by
2 2 (K / H) (Bz2 + Box2) and the coefficient K is determined as a function of the damping # which one wishes to obtain in the worst case (typically # 0.7) according to
K = 2 # H # 0 / (B0 sin i) 2 (23)
To obtain the long-term damping torques Cx Cx (LT) and Cz (LT), the difference signal #By is subjected to low-pass filtering with a cut-off frequency significantly lower than the nutation frequency, and we multiply the signal thus filtered by the coefficients K1 and K2 (with K given by equation (23)) to obtain Cx (LT) and Cz (LT).

Total stabilization torques in roll and yaw
Cx = Cx (CT) + Cx (LT) and Cz = Cz <CT) + (LT) are obtained by a calculation block 68 (Figure 3), and addressed to another calculation block 70 which determines the magnetic moments Mx and Mz to be applied by the magnetocouplers 56 and 58.

The magnetocouplers 56 and 58 are supplied so as to produce on the one hand a magnetic moment (MX (s), Mz <S)) generating the stabilization torques in roll and yaw by interaction with the component of the magnetic field according to the pitch axis, and another magnetic moment
(MX (d), Mz (d)) generating a desaturation torque of the inertial wheel along the pitch axis by interaction with the components of the magnetic field along the roll and yaw axes.

The desaturation commands are defined so as to always keep a desaturation torque of the same sign as the pitch stabilization torque Cy. The desaturation torque of the inertial wheel has a component MX (d) along the roll axis of the form MX (d) = - CyBz / (Bx2 + Bz2) (24) and a component Mz (d) along the axis yaw of the form M z (d) = CyBX / (Bx2 + Bz2) (25)
Interaction with the Earth's magnetic field then generates a desaturation torque equal to c along the pitch axis. Two parasitic torques are also generated along the roll and yaw axes, which are treated as disturbing torques, that is to say included in the
terms Cx 'and C z' in relations (1) and (3).

The roll and yaw control is performed using the component of the magnetic field along the pitch axis MX (s) = Cz / By and Mz (s) = Cx / By (26)
The orbit being non-polar, the magnetic field By along the pitch axis is never zero, and two magnetocouplers are therefore sufficient to carry out the control.

If the orbit approaches a polar orbit (i 90), it is possible to use a third magnetocoupler to generate the stabilization torques in roll and yaw.

As the magnetic field also has roll and yaw components, the commands M, (s) and Mz (S) create torques along the pitch axis. These disturbing torques are periodic and absorbed by the inertial wheel.

 Note that in equations (9) to (12), (15) to (18), (20) to (22) and (24) to (26) given above, we can take as values of Bx , By and Bz either the components of the Earth's magnetic field measured by the magnetometer (50), or those calculated by block 62, the differences that this implies being negligible when the attitude angles, O and v are small.

FIGS. 4A to 4C illustrate results of simulations carried out on an attitude control system as described above. The magnetic field model
(block 62) was taken as a harmonic development at order 4, with an error of less than 5% compared to the real eating field represented by a harmonic development at order 8. On an orbit at 1000 km inclined by i = 60-, the simulations showed stabilization with an accuracy of around 3- in roll and yaw and around 6 in pitch, with an inertial wheel 52 with a kinetic capacity of 10 Nms. FIGS. 4A to 4C represent the variations in the roll, pitch and yaw angles over a period of the order of a day. The magnetic control moments remain at moderate values (less than 30 Am2), compatible with implementation on board a mini-satellite. Performance can be further improved by increasing the angular momentum of the wheel.

 The attitude control method which has just been described is of a particularly simple implementation, so that it can be entirely implemented on board the satellite. The means used to generate the stabilization or desaturation couples may be different from those which have been described by way of example; it is possible in particular to use, as a replacement or in addition to magnetocouplers, other inertial wheels or nozzles ...

 It is also possible to envisage supplying the magnetometer and the magnetocouplers with time-sharing, in order to minimize the disturbances of the measurements by the magnetocouplers.

Claims (15)

 1. Method for controlling the attitude of a satellite (S) of non-equatorial orbit having a roll axis, a pitch axis and a yaw axis and comprising an inertial wheel (52) providing a angular momentum (H ) along the pitch axis, in which the components of the magnetic field are measured along the roll, pitch and yaw axes of the satellite, and on the satellite the magnetic field components are calculated along the same axes in applying a predetermined model of the earth's magnetic field and assuming that the roll, pitch and yaw angles ((p, O, 'v) take predetermined set values, characterized in that a torque of pitch stabilization (Cy) determined on the basis of estimates (o *) of the pitch angle obtained on board the satellite from the calculated and measured components of the magnetic field along the roll and yaw axes, and in this that we apply to the couple satellite s roll and yaw stabilization  (Cx, Cz) C z> determined on the basis of the difference (6By) between the calculated and measured components of the magnetic field along the pitch axis.  2. Method according to claim 1, characterized in that the estimates (0 *) of the pitch angle are obtained according to the formula: 0 * = (Bz 8Bx Bx 8Bz) / (Bx2 + Bz2) where 8Bx and 8B denote the differences between the calculated and measured components of the magnetic field respectively along the roll and yaw axes, and Bx and B denote the calculated or measured components of the magnetic field respectively along the roll and yaw axes.  3. Method according to claim 1 or 2, characterized in that the pitch stabilization torque (Cy) is determined so as to have a part proportional to the estimate (0 *) of the pitch angle and a proportional part to the time derivative of the estimate (8 *) of the pitch angle.  4. Method according to any one of claims 1 to 3, characterized in that the roll and yaw stabilization torques (Cx, Cz) are determined so as to each have a part (Cx (L7), Cz (LT) )) proportional to the difference <8By) between the calculated and measured components of the magnetic field along the pitch axis and a part  <Cx (CT), Cz (CT)) proportional to the time derivative of said difference.  5. Method according to claim 4, characterized in that the respective parts Cx (cT) and Cz (CT) of the roll and yaw stabilization torques which are proportional to the derivative of the difference between the calculated and measured components are obtained. of the magnetic field along the pitch axis according to the formulas: Cx (CT) = k Bz 8 and Cz (CT) = -k Bx where - ABy denotes the derivative of said difference; - Bx and B z denote the calculated or measured components of the magnetic field respectively along the roll and yaw axes; and - k denotes a positive coefficient.  6. Method according to claim 4 or 5, characterized in that the respective parts are obtained Cx (LT) and Cz (LT) of the roll and yaw stabilization torques which are proportional to the difference between the calculated and measured components of the magnetic field along the pitch axis according to the formulas: Cx (LT) = -K Bx aBy and Cz (LT) = -K Bz8Bv where - 8By denotes said difference; - Bx and B z denote the calculated or measured components of the magnetic field respectively along the roll and yaw axes; and - K denotes a positive coefficient.  7. Method according to any one of claims 1 to 6, characterized in that the pitch stabilization torque (Cy) is applied by a control of rotation of the inertial wheel (52).  8. Method according to any one of claims 1 to 7, characterized in that the roll and yaw stabilization torques (Cx, Cz) are applied by at least two magneto-couplers (56,58) perpendicular to the pitch axis that is fed so as to produce a magnetic moment generating the roll and yaw stabilization torques by interaction with the component of the magnetic field along the pitch axis.  9. Method according to claims 7 and 8, characterized in that it supplies the magneto-couplers  (56,58) so as to also produce a magnetic moment generating a desaturation torque of the inertial wheel along the pitch axis by interaction with the components of the magnetic field along the roll and yaw axes.  10. Method according to claim 9, characterized in that the magnetic moment generating a desaturation torque of the inertial wheel has a component MX (d) along the roll axis of the form MX (d) = - CyBz / (Bx2 + Bz2) and a component Mz (d) along the yaw axis of the form Mz (d) = CyBX / (Bx2 + Bz2), where Cy designates the pitch stabilization torque, and Bx and B z designate the components calculated or measured magnetic field respectively according to the roll and yaw axes.  11. Satellite attitude control system  (S) of non-equatorial orbit, comprising magnetometric means (50) for measuring the components of the magnetic field along a roll axis, a pitch axis and a yaw axis of the satellite, an inertial wheel (52) providing a angular momentum <H) along the pitch axis, means (54, 56, 58) generating stabilizing torques in roll, pitch and yaw, and means (60) for controlling means generating stabilizing torques including means (62) for calculating magnetic field components along the roll, pitch and yaw axes by applying a predetermined model of the earth's magnetic field and assuming the roll, pitch and yaw angles (, 8 , W) take predetermined set values, characterized in that the control means (60) control the means for generating stabilization torques so as to apply to the satellite a determined stabilization torque in pitch (Cy) on the basis of estimates (0 *) of the pitch angle obtained from the calculated and measured components of the magnetic field along the roll and yaw axes, and to apply stabilization torques in roll and yaw to the satellite (Cx, Cz) determined on the basis of the difference (6By) between the calculated and measured components of the magnetic field along the pitch axis.  12. System according to claim 11, characterized in that the control means (60) obtain the estimate (8t) of the pitch angle according to the formula: and (Bz6Bx-Bx8Bz) / (Bx2 + Bz2) where 8Bx and 8B z denote the differences between the calculated and measured components of the magnetic field respectively along the roll and yaw axes, and Bx and B z denote the calculated or measured components of the magnetic field respectively along the roll and yaw axes.  13. System according to claim 11 or 12, characterized in that the means for generating pitch stabilization torques are constituted by a motor (54) for driving the inertial wheel in rotation (52), associated with desaturation means .  14. System according to any one of claims 11 to 13, characterized in that the means for generating control torques along the roll and yaw axes are constituted by at least two magneto-couplers (56, 58) perpendicular to the pitch axis.  15. System according to claims 13 and 14, characterized in that the control means (60) control the supply of the magneto-couplers (56, 58) so as to produce on the one hand a magnetic moment of stabilization in roll and in yaw, generating the stabilization torques in roll and in yaw by interaction with the component of the magnetic field along the pitch axis, and on the other hand a magnetic desaturation moment generating a desaturation torque of the inertial wheel (52) along the pitch axis by interaction with the components of the magnetic field along the roll and yaw axes.