  This paper introduces a novel reconfigurable and power-efficient FPGA
(Field-Programmable Gate Array) implementation of an operator splitting
algorithm for Non-Terrestial Network's (NTN) relay satellites model predictive
orientation control (MPC). Our approach ensures system stability and introduces
an innovative reconfigurable bit-width FPGA-based optimization solver. To
demonstrate its efficacy, we employ a real FPGA-In-the-Loop hardware setup to
control simulated satellite dynamics. Furthermore, we conduct an in-depth
comparative analysis, examining various fixed-point configurations to evaluate
the combined system's closed-loop performance and power efficiency, providing a
holistic understanding of the proposed implementation's advantages.
