Design of Model Predictive Control to Angular Drag-Free and Pointing Control in the Next Generation Gravity Mission (NGGM)

Following the achievements of the European GOCE mission, which produced a high-resolution static global model of Earth’s gravity field, the European Space Agency has initiated several studies on a Next Generation Gravity Mission (NGGM). The primary objective of NGGM is to observe temporal variations of Earth’s gravitational field over long time scales with an unprecedented level of accuracy. The mission consists of two satellites flying in a long-distance formation along a low-altitude inclined orbit, with each satellite is controlled to achieve drag- free condition. Gravity field anomalies will be estimated from variations in the inter-satellite distance, measured by means of laser interferometry and corrected through precise measurements of non-gravitational accelerations. This thesis is mainly related to the design of attitude and pointing control systems, which are included in the GNC (Guidance, Navigation and Control) on-board software. The main objective of the system is to guarantee a drag-free condition while also fulfilling demanding pointing requirements. The control strategy relies on a multi-hierarchical design that achieves command decoupling through inner and outer control loops. Model Predictive Control (MPC) was subsequently tested, demonstrating that it can achieve performance comparable to the first approach. In detail, the mathematical models used in the design of the Embedded Model Control (EMC) for angular drag-free dynamics, attitude predictor, and FLOF (Formation Local Orbital Frame) predictor are analysed separately. This is carried out through the development of three linear time-invariant (LTI) state-space systems, with two control strategies applied to the pointing control law. The individual blocks are exploited to perform a preliminary analysis of the subsystems’ transfer functions, with the objective of characterizing their intrinsic behavior. As the next step, the simplified models are combined into a single state-space-matrix model to simulate the system under the total control command. The transfer functions corresponding to three inputs—thruster noise, accelerometer noise, and atmospheric disturbances—are then computed and analysed with respect to the output, i.e. the residual non-gravitational angular acceleration at the plant output. By exploiting the simplified model with MPC, the effects of the three inputs on the error are investigated through a frequency-domain analysis. Finally, a sensitivity analysis is conducted to evaluate the system’s robustness through Matlab simulations, in which some parameters are varied to assess their impact on system performance. 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.