LISA satellite formation control
2007Citations per year
Abstract: (Elsevier)
The joint ESA–NASA Laser Interferometer Space Antenna (LISA) mission consists of a triangular formation of three satellites aiming at detecting gravitational waves. In linear approximation the LISA satellites describe a circle around a reference point, maintaining a fixed position with respect to each other. The reference point, the center of the triangle, orbits the Sun in a circular orbit, trailing the Earth at twenty degrees. In reality the distance between the satellites will vary by about one to two percent and the angle between the arms of the antenna will vary by about 0.5° over the course of one year for the nominal LISA satellite configuration. For measurement accuracy it is desirable that the pointing offset of the telescopes be kept small. This makes it necessary to actuate the telescopes or to control the formation.
It was assumed that the LISA satellites are equipped with six μN engines that would allow to keep the two cubical proof masses within each satellite in almost perfect free fall. It was found that control forces up to about 700 μN are required for maintaining the absolute triangular LISA formation, leading to unacceptable excursions of the proof masses from free fall. However, these forces compensate predominantly very low frequency variations of the arm lengths and angles of the triangle, which are then to be compensated by the telescope actuators. The variations are outside the aimed LISA measurement bandwidth (10 −4 –0.1 Hz).
In addition, the effect of thruster noise, orbit determination errors and orbit injection errors was examined. The effect of these error sources on the arm lengths and orientation angles between the LISA satellites was assessed both in open loop and in closed loop, where the closed loop was based on a proportional-derivative (PD) controller. It was found that orbit determination errors of the order of a few km in position and a few mm/s in velocity lead to negligible closed loop control forces. In addition, orbit injection errors of the order of 10 km in position and 1 cm/s in velocity could be eliminated after a few days when thrusting at levels of 200–500 μN. Even for a high estimated level of thruster noise below 10 −4 Hz (equivalent to about 2 μN random thrusts once an hour), the closed loop controller effectively reduced the effect on the angles of the triangle to below 30 nrad.- LISA
- PD control
- mu N propulsion
- formation control
- μN propulsion
- Formation control
- injection: error
- laser: interferometer
- approximation: linear
- satellite
References(9)
Figures(0)
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