LISA satellite formation control

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.