Satellite Attitude Control Using CMG When tops are no longer toys...
Inverted gyroscopic pendulum.
A cradle freely rotating around a horizontal axis rests on a stop.
It supports a motor-reduction gear which is used to tilt
a gyroscopic spinner (with a kinetic momentum of 10 Nms)
around its diameter. The tilt angle control law brings the cradle
to an equilibrium position (centre of gravity of the moving assembly
above the rotation axis).
(High resolution image: 120 Ko )
A CMG (control moment gyro) is an actuator consisting of a spinner with a sustained kinetic moment modulus h and one or two motor-driven tilt axes. One-axis CMGs are used to generate very high dynamic moments. The produced gyroscopic torque is proportional to h and to the precession rate (i.e. tilting rate). It is orthogonal to the precession axis and is directly transmitted to the satellite by the tilt motor bearings. Two-axis CMGs are less used and have a limited dynamic moment since the produced gyroscopic torque has to be partially compensated by the tilt motor. Our work concerns only one-axis CMGs. They have better efficiency than flywheels and are a powerful solution for satellite attitude control, but they are much more complex to use.
Like flywheels, CMGs can be considered either as generators of torques applied to the satellite or as generators of kinetic moment exchanged with the satellite momentum. The axes of the kinetic and dynamic (gyroscopic) moments produced by a CMG are changing in the satellite reference system : they rotate in the plane perpendicular to the tilt axis. Moreover, the higher the dynamic moment, the faster they rotate. To generate a kinetic or dynamic moment in a given direction, it is necessary to combine at least three elementary kinetic moments or gyroscopic torques in variable, non-coplanar directions. A configuration in which all the directions of the gyroscopic torques are coplanar is said to be singular. In this configuration, it is impossible to obtain the component of the required dynamic moment orthogonal to this plane. In the case of a setup including three CMGs in a trirectangular trihedron, the maximum achievable kinetic moment is 2.45 h, but singular configurations appear along certain directions as soon as the modulus of the kinetic moment of the cluster reaches 0.41 h. This limits considerably the advantage of this structure, because only 17% of the maximum kinetic moment can be used safely.
Setups including four or more CMGs do not suppress singularities, but there is then an infinity of paths of the precession angles which generate the required kinetic or dynamic moment, and this redundancy is used to avoid singular configurations. Some of these configurations are easily avoided by a standard least squares algorithm, but others are attractive and locally unavoidable. For instance, in a tetrahedral setup for which the maximum achievable kinetic moment is 3.26 h, any kinetic moment below this maximum (even zero) can be achieved by an infinity of configurations, of which up to 16 may be singular. Since locally unavoidable attractive singularities are present only for moduli of the kinetic moment equal to or above 1.15 h, a simple command allows use of 35.4% of the maximum kinetic moment. In [1] we propose a general guidance algorithm based on an optimisation method using dynamic programming, which allows the use of the total maximum kinetic moment.
The structure with four CMGs offers the best price/performance ratio. Our research work is focused on the improvement of the global guidance process to make it suitable for on-board use and on the enhancement of local guidance laws. We are also collaborating on CMG attitude control research in the frame of contracts tended by CNES to the companies MMS (Matra Marconi Space) and Alcatel Space Industries (formerly Aerospatiale Cannes). In order to have an experimental support for our theoretical research, we have designed and built (with funding from DGA/Spoti and the Midi-Pyrénées Region) an inverted gyroscopic pendulum and a CMG attitude control test bench. These facilities are now operational and help us to visualise the singular behaviours and validate our simulation models.
CMG attitude control test bench. A platform representing a satellite
is articulated by a three-axis free suspension. It is equipped
with sensors giving its attitude. It supports four CMGs in an adjustable pyramid setup.
Each 7.5 Nms CMG is supported by the tilt motor-reduction gear.
The platform attitude is controlled by controlling the CMG tilt rates.
(High resolution image : 120 Ko )
