Modeling and Design for the Attitude Control Phase of the LISA drag-free Mission

The Laser Interferometer Space Antenna (LISA) is a Space mission led by ESA now entering its phase A. LISA will be the first observatory in space to explore the Gravitational Universe. It will gather revolutionary information about the dark universe. The new LISA mission envisaged as a joint ESA-NASA mission to observe astrophysical and cosmological sources of low frequency gravitational waves. The primary objective of the LISA mission is to detect and observe gravitational waves emitted from massive black holes and galactic binaries in the low-frequency band which ranges from 0:1mHz up to 1Hz with a goal of extending the measurements down to 30mHz. The underlying measurement principle is a laser interferometry system built up with three satellites that are flying in a triangular constellation with an edge length of 2:5Mkm. These will detect low frequency gravitational waves through the measurement of changes in the length of the optical path between the two reflective proof masses of one arm of the interferometer relative to the other arm. In order to ensure that the test masses are flying in a disturbance-free motion along their geodesics, so that an extremely small displacement due to the passage of gravitational waves is detectable, challenging performance requirements with respect to internal and external disturbance rejection must be satisfied by an overall Drag-Free-System. This provides the relatively undisturbed environment for the test-masses which form the references for the measurement of the gravitational waves. Without it the effect of gravitational waves would be not detectable. This thesis is written in the context of the space mission Laser Interferometer Space Antenna (LISA) and its technology demonstration precursor mission LISA Pathfinder. The research carried out led to the development of a simulator and a preliminary control model of the LISA attitude control system to assess its feasibility. Technological risk assessment in general, as well as that associated with the LISA mission, is also considered. The main focus of this thesis is the modeling and control of the drag free LISA scenario. The first part of the work brought to a set up of nonlinear equations of the overall system dynamics in order to produce a simulator for the LISA spacecraft complete dynamic. The mathematical modeling allowed to better understand the behavior of the system and the related interaction within the scope of the mission. The effects of gravitational waves on any system are incredibly small, even for a system designed to detect them. For this reason disturbance effects which could, in any other system, be disregarded, must be taken into account as they may produce unacceptable noise levels. Therefore, a fundamental part of the modeling phase has been the characterization of noises and disturbances from sensors, actuators and environment. The second part applies a preliminary study on the control system structure needed to meet the requirements of the mission. General considerations about the modes in which the spacecraft must work are made in a control design perspective. The general study of the plants is then followed by the first controller applied on the attitude of the satellite and on attitude and position of the test masses. The designed control system even if simple, demonstrates to meet the requirements of the phases simulated. Extensive simulations are performed to verify the effectiveness of the proposed approach.