Aeronautics and astronautics – Spacecraft – Attitude control
Reexamination Certificate
1999-11-19
2001-10-23
Jordan, Charles T. (Department: 3644)
Aeronautics and astronautics
Spacecraft
Attitude control
C244S079000
Reexamination Certificate
active
06305647
ABSTRACT:
The present invention relates to methods and apparatuses for steering the attitude of a satellite by controlling the orientation the axis of rotation of the wheels of a cluster or array of control moment gyros (CMGs) on board the satellite.
Control moment gyros differ from reaction wheels of the kind commonly used for controlling the attitude of a satellite by exchange of angular momentum, in that they are mounted on respective gimbals that can each be steered by at least one motor about at least one axis orthogonal to the axis of rotation of the gyro wheel. In most cases the wheels are driven at a speed that is constant or that varies little once they are in action.
A cluster of CHGs must have at least three CMGs to make it possible to reorient the three-dimensional frame of reference associated with the satellite into any attitude, and it must have at least two CMGs for steering about two axes. In practice, at least four CMGs are used in a cluster so as to provide redundancy.
A cluster of CMGs constitutes an intertial actuator which can be controlled to apply torque imparting a specified angular speed profile to the satellite, where the specification is generally download from a ground station. The torque is generated by causing the gimbal axis to rotate in such a manner as to cause the CMG wheel to precess. For the wheel of order i, the torque C
i
due to the gyroscopic effect is given by:
C
i
=H
i
&sgr;
i dot
where H
i
is the moment of inertia of the wheel; and &sgr;
i dot
is the speed of rotation.
C
i
=H
i
&sgr;
i dot
where H
i
is the moment of inertia of the wheel; and &sgr;
i dot
is the speed of rotation.
A satellite generally has an attitude control system that receives input signals from sensors enabling its angular position to be determined in an inertial frame of reference. This system which generally has a relatively long time constant enables the satellite to be maintained in a reference attitude by controlling the motors of the reaction wheels, or the motors of the gimbals, when the satellite is fitted with CMGs.
In the case under consideration herein, where attitude is controlled by means of a cluster of CMGs, the control system begins by determining the torque that needs to be applied and must deduce therefrom the speed that should be applied to the gimbals of the CMGS. The angular positions of the gimbals vary over time. The ability to provide a total torque C is consequently not steady and not linear. It can be written in matrix form as follows:
C=A(&sgr;).&sgr;
dot
(1)
where A is the Jacobian matrix, a
ij
=∂H
i
/∂&sgr;
j
, where i=1 to 3 and j=1 to 4 (or more generally from one to the number of CMGs).
Given the torque C to be delivered, a conventional guidance method consists in inverting equation (1) so as to obtain the reference speeds &sgr;
c dot
to be given to the gimbals.
Certain missions provide for the attitude of the satellite to be changed to a large extent over a short period of time. CMGs are particularly suitable to such “agile” missions. At present, essentially two methods are used for determining the speed profile to be imposed on the gimbals of the CMGs.
In a first method, guidance can be said to be “local”, and on each request for torque, the angular speed required for each gimbal is calculated using equation (2), which amounts to pseudo-inversion of the Jacobian. The constraint imposed to accommodate the redundancy is to seek movement requiring minimum energy.
&sgr;
c dot
=[A′(A.A′)
−1
]C. (2)
Experience shows that that approach often leads to abandoning a CMG whose reorientation towards the required direction requires too much speed of all of the gimbals, with the result that in the end the cluster has one wheel that is “sleeping” while all the others are grouped together in an opposite direction. The cluster is thus in a singular configuration: angular momentum is at a maximum in said opposite direction and it is impossible to obtain torque in said direction.
There are algorithms for local avoidance of singularities due to the gimbals being set into motion, for example requiring the total resulting torque to be zero. However, those algorithms are not very effective since the approach of a singularity is detected late due to a lack of predictions concerning the torque profile to be followed. This means that the capacity of the cluster needs to be over dimensioned so as to be able to avoid most singularities.
Another approach which can be referred to as continuous overall guidance requires calculation to be performed prior to beginning a maneuver to change the attitude of the satellite in order to determine the best trajectory for reconfiguring the cluster &sgr;(t) throughout the maneuver, so as to avoid going close to any singular configuration. That calculation is very time consuming. It must be performed on the ground and then transferred.
The present invention seeks to provide a method making it possible when steering attitude by means of CMGs, to avoid the problem of singularities while putting a limit on the associated calculation load. The invention thus makes it possible to take full advantage of the capacity of the cluster whenever it is required to tilt the attitude of the satellite.
For this purpose, the invention makes use specifically of the fact that the torque capacity of a CMG is limited only by the maximum speed of rotation of the gimbal drive motor. The invention also makes use of the observation that it is possible to pass transiently through a singular configuration, providing this takes place while the cluster of CMGs is being reconfigured into a predetermined reference configuration and providing the gimbals at that time are moving with high angular speed.
Consequently, the invention provides a method of steering the attitude of a satellite by controlling one of the CMGs in a cluster (generally of at least four CMGs), having respective wheels mounted on gimbals that are mounted to rotate on a platform of the satellite about different orientation axes, which method comprises the steps of:
on the basis of starting conditions and end conditions relating to attitude and angular speed and time, determining a cluster configuration that is remote from any singular configuration such that exchanging angular momentum between the cluster of CMGs and the satellite during a given length of time will give rise to the desired attitude maneuver; and
bringing the orientation of each gimbal in simultaneous and independent manner into its reference orientation by using an angular position reference applied in an open loop in the local servo-control of the angular positions of the gimbals.
It is advantageous to cause the gimbal drive motors to accelerate in the minimum length of time compatible with the mechanical strength of the CMGS, and then to continue operating at a steady speed, and then to return to zero speed.
The invention thus makes it possible to reduce the time required for tilting purposes by shortening the stages of angular acceleration and deceleration at the beginning and at the end of a maneuver. In practice, acceleration can be quasi-instantaneous compared with the response time of the attitude servo-control system. The internal angular momentum is reoriented into the appropriate direction to obtain the desired speed and attitude profile for the satellite before said system can act.
The existence of redundancy makes it possible to have a degree of freedom in selecting the configuration of the tilting cluster. Amongst possible criteria for making a selection, it is often advantageous to select one of the following:
maximizing the square root of the determinant of (AA′), which amounts to maximizing margin relative to singularities;
minimizing the infinite norm of the vector s, where the vector s is the vector of the norms of the rows of A′ (A.A)
−1
, which corresponds to maximum steerability in three axis torque for the end configuration;
infinite norm of minimum &sgr;, which corresponds to
Defendini Ange
Lagadec Kristen
Best Christian M.
Jordan Charles T.
Larson & Taylor.PLC
Matra Marconi Space France
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