Spacecraft High Precision Optimized Control Design for Free-falling Test Mass Tracking in Lisa-Pathfinder Mission

LISA (Laser Interferometer Space Antenna) will be the first space mission for the in-flight detection of gravitational waves. In order to reduce the mission risk, some of the key technologies needed for LISA will be tested by means of the LISA Test-flight Package (LTP) on board the LISA Pathfinder mission (SMART- 2). The goal of the LISA Pathfinder is to provide in- flight testing of the free-fall level of a reference Test Mass (TM) to within a factor 10 from the LISA top- science requirement. One of the critical technologies to be tested is the Test Masses Drag-Free and Attitude Control System (DFACS), which is the system that has to provide the test masses inertial insulation through satellite relative position control up to the nanometer level. The system analyzed in the paper is modelled as a multibody made of the satellite, actuated through thrusters, and two test masses, kept at a fixed relative distance by using a capacitive actuation. The paper presents a new control design procedure for this MIMO system. The procedure, based on a multi- objective optimization, yields to controllers that achieve the prescribed levels of performance in terms of disturbance rejection, robustness and phase margin.