Test Mass Release for LISA ESA mission: Control Design and MonteCarlo Analysis

This thesis is focused on a second order controller named Super Twisting Sliding Mode Control (STW SMC) designed for the Laser Interferometer Space Antenna (LISA) mission. This ESA space mission, which will be launched on 2034, will be used as in-space observatory for a lifetime of five years to detect gravitational waves generated from sources like binary stars systems and merging of supermassive black holes. The space observatory consists in three satellites in a triangular constellation at 1 AU from the Sun on a heliocentric orbit. The distance between spacecrafts will have to be fixed and each small variation will be assigned to possibly gravitational waves. In detail, the sensor instrument is composed by a laser interferometer and two Optical Assembly (OA) clusters on each spacecraft, which are composed by a telescope, an optical bench for the laser interferometer and an electrostatic suspension system which houses suspended cubic Test Mass (TM). The electrostatic suspension system is the actuation system involved in the control design. The main purpose of this work is to develop a robust controller to stabilize the TMs to their own cages center in a noisy space environment with high disturbances during the TMs release, a very critical transient phase in which the TMs are unlocked and released in their proper cages after the constellation acquisition. High levels of stability and precision are required to obtain optimal initial conditions to switch to the scientific in-orbit operations. The proposed control system is tested in terms of performance such as stability, maximum overshoot, settling time, violation time, steady-state error, and accuracy (3σ) through a MonteCarlo simulation campaign. The results are analysed for two hundred runs at different configurations, randomly defined in a wide range of values fixed by ESA documents for noises, disturbances and initial conditions. As reference data to compare the obtained outcomes in respect of the required performance and constraints, reports are given from the previous LISA Pathfinder mission, which had the purpose to verify and test different technologies which will be implemented on LISA itself such as measurement instrumentation. The analysis involves two operative modes: (1) “Wide Range” (WR) and (2) “High resolution” (HR). In the first mode, the TMs are caught and stabilized after their release from plungers with a coarse precision to obtain good initial conditions to switch to the HR mode. The second mode allows a better control and performance within ESA requirements to reach good initial conditions for the science mode, with a converging time within 5000s. In the WR mode, the reduced control authority and the higher magnitude of noises and disturbances are a challenging configuration for the control design. The solution proposed consists in a STW SMC, which is a nonlinear technique applied to obtain a precise and robust control for both position and attitude to effectively counteract the strong disturbances in the challenging space environment and high uncertainties given by on-board sensors and actuators. The mathematical model defines a coupled nonlinear dynamics between the spacecraft and TMs, but there is no coupling between the two TMs. Finally, a second reduced MonteCarlo campaign is proposed to compare the implemented STW SMC and a first order SMC controller to highlight the different properties of the two algorithms in terms of advantages and drawbacks.