• actuation algorithm
• actuation stiffness
• LISA
• ESA
• NASA
• gravitational waves
• drag free
• control

LISA, the Laser Interferometer Space Antenna, and its technology-demonstrating LISA Pathfinder forms a cooperative mission between ESA and NASA aiming to detect and measure gravitational waves. The measurement bandwidth over which LISA operates is 0.1 mHz–1 Hz with a goal to extending the measurements down to 30 μHz. This measurement bandwidth is where much of the most interesting gravitational wave sources are emitting, and is directly complementary to a number of planned ground-based interferometers (LIGO, VIRGO, TAMA 300 and GEO600) that will observe gravitational waves over the higher frequency regime (10–1000Hz). The two main categories of gravitational wave sources detectable by LISA are galactic binaries and the massive black holes expected to exist at the centre of most galaxies.
The LISA space segment consists of three spacecrafts flying in a quasi-equilateral triangular formation, in an Earth-trailing orbit at some 20 degrees behind or in front of the Earth. Each of the three identical spacecraft carries a V-shaped payload which is a measurement system consisting of: two Gravity Reference Sensors (basically two free-flying test masses that will undergo displacement due to the passage of gravitational waves), the associated laser interferometer measurement systems and the electronics. The two arms of the V-shaped payload of the spacecraft at one corner of the triangle together with the corresponding single arms of the other two spacecrafts constitute one of the three Michelson-type interferometers. These interferometers are able to detect gravitational waves through the measurement of changes in the length of the optical path between the two reflective test masses of one arm of the interferometer relatively to the other arm. In order to detect the extremely small displacement caused by the passage of the gravitational waves the test masses have to be maintained in a drag-free environment well shielded from the other external noise effects.
Nevertheless, caused by the LISA geometrical configuration, a pure drag-free strategy for both the test masses in each spacecraft cannot be performed. This results in a extremely fine control system able to maintain the test masses relative position and their orientation respect to the spacecraft, and able to perform the drag-free along, at least, the direction of the interferometer arms. For this reason, some electrostatic forces are applied to the test masses by means of voltages applied to the electrodes that surround them.
This thesis, starting from the current status of the LISA Pathfinder mission, proposes an alternative Gravity Reference Sensor actuation strategy for the generation of the voltages on the electrodes. The analytical analysis of the stiffness and the noise induced by the new actuation strategy as well the main issues connected with the Gravity Reference Sensor electronics are presented. Detailed simulation are needed in order to ensure the mission success, for this reason an End-to-End Simulator is under development. This work includes the implementation of the Gravity Reference Sensor model in the LISA End-to-End Simulator. Simulation are done in order to validate the GRS model implementation and the feasibility of the proposed actuation strategy.