Model Predictive Control for Drag-Free Operation in Next Generation Gravity Mission (NGGM)

Following the success of the European GOCE mission, which provided a static global map of the Earth’s gravity field, the European Space Agency started several studies for a Next Generation Gravity Mission (NGGM). The objective of this mission is to measure the temporal variations of the Earth’s gravitational field over a long period with a level of accuracy never achieved before. NGGM will consist of two satellites flying drag-free in a low-altitude inclined orbit. Variations in the distance between the two satellites, which will be measured by laser interferometry, corrected by measurements of non gravitational acceleration, represent gravity anomalies. This thesis focuses on a fundamental aspect of the mission, i.e. linear drag-free. The purpose of the control system, which aims to achieve a drag-free condition, is to compensate for non-gravitational accelerations measured by precise GOCE-like accelerometers. In detail, after having explored the Embedded Model Control system already developed for GOCE, the implementation of the Model Predictive Control was tested, verifying that it could achieve the same performance as the first. This was carried out by developing two simplified state-space-matrix models of the systems with the two types of control, and then extracting and analyzing the transfer functions between the following inputs: thruster noise, accelerometer noise, atmospheric disturbances and the output, i.e. the residual non-gravitational acceleration at the output of the plant. The simplified model with MPC system was also exploited to implement performance budget allocation in the frequency domain. This analysis was performed by analyzing the influence on the error of the three inputs in different frequency bands, then allocating the requirement value between the three disturbances according to known performances and margin policies. Finally, to validate the simplified models and to test the actual performance of the developed control system, the results were compared with simulations carried out in the Simulink environment. Future work could focus on the development of a more precise system, thus implementing the internal models of the thruster and accelerometer with their transfer functions. The discussion could also be extended to attitude control, retracing the same steps that have been taken in this thesis. This thesis was based on previous research work of Politecnico di Torino and developed in collaboration with GNC group of Thales Alenia Space Italia (TAS-I), Torino site, on the Next Generation Gravity Mission.