Non linear Control Design and High-Fidelity Modeling of the Gravitational Reference Sensor for the LISA ESA Mission

This thesis, carried out in collaboration with Thales Alenia Space, addressed the design, implementation, and validation of control strategies for the Drag-Free and Attitude Control System (DFACS) of the Laser Interferometer Space Antenna (LISA) mission. LISA is a space observatory based on three Spacecrafts (SC) that will use laser interferometry to detect and measure gravitational waves by precisely monitoring the relative positions of six free-falling test masses across separate spacecraft. The mission requires that, per each SC, two Test Masses (TM) remain in the so called drag-free condition, as free as possible from all non-gravitational forces. LISA presents three particularly critical phases: con- stellation acquisition, test mass (TM) release, and drag-free science operations. Among these, TM release remains a delicate and essential process, even after the in-flight demonstration by the LISA precursor, LISA Pathfinder (LPF), which revealed its complexity from multiple perspectives. The TM can be in two states: mechanically blocked or electrostatically controlled. Both the states are enabled by the Gravitation Reference Sensor (GRS) which is an electrostatical system with 12 capacitance that works both as sensor and actuator. DFACS plays a key role in the success of the TM release phase, whose objective is to guide the TM from a released state to an electrostatically controlled one. The mechanical release performed by the GRS imparts momentum to the TM, leaving conditions unsuitable for scientific measurement and introducing uncertainties in its initial linear and angular position and velocity. The release is managed by a specific mode of the GRS, the Wide Range (WR) mode, which provides high control authority through the electrostatic actuators in order to capture the TM and guide it toward the center of its housing. Once the TM is sufficiently stabilized, the system can switch to High Resolution (HR) mode, where the control authority is lower but applied with much higher precision, creating the extremely stable conditions required for interferometric measurements. This work focused on the development of the controller and the validation of a high-fidelity model of the GRS to verify compliance with ESA requirements for the TM release. A detailed model of the GRS and the TM dynamics was implemented in MATLAB/Simulink to perform simulations under realistic conditions, incorporating SC perturbations, actuation disturbances, and sensing noise. Sliding Mode Control (SMC) law with boundary layer is used to ensure a robustly stable release while trying to mit- igate chattering effect. GRS commanding algorithm based on the decoupling of the 12 capacitance is designed and tested. DFACS robustness was validated through extensive Monte Carlo simulations that accounted for uncertainties and variable parametric con- ditions. Results demonstrate controller capability to bring the TM dynamics into stable conditions suitable for switching between control modes. In the final part of the work, the results were analyzed to identify the strengths and limitations of the proposed approach, providing a clear understanding of aspects that may require further refinement.