Reduced Order Models for Precision Thermal Control of Earth Observation Telescope

Abstract Thermal control is critical for space telescopes, as thermo-elastic deformation can significantly degrade imaging performance. This imposes stringent specifications on temperature range, thermal gradient, and temporal temperature stability. While most frameworks focus on offline thermal optimization, online control approaches include PID controllers and predictive control using compact thermal models. However, PID-based methods cannot naturally incorporate temperature constraints or thermal gradient specifications, while compact-models fail to capture spatial variations. Although, standard model predictive control (MPC) using detailed thermal models can address these limitations, solving the resulting constrained optimization problem in real-time is computationally prohibitive. This work presents the first application of MPC for thermal control of a simulated Cassegrain telescope located in a 500 km sun-synchronous orbit. We employ a reduced-order model constructed via proper orthogonal decomposition that enables real-time MPC implementation. Thermal gradient constraint (1°C maximum difference across the telescope structure) and stability constraint (2°C maximum variation during 800 s imaging sessions) are directly encoded into the MPC formulation. Simulation results demonstrate that this reduced-order MPC (ROMPC) approach achieves 38% improvement in temperature stability over PID control and 24% over bang-bang control during stabilized operation. For critical optics components, ROMPC reduces thermal gradients compared to PID and bang-bang control. Furthermore, transient analysis reveals that ROMPC improves temporal temperature stability by avoiding the large overshoots (±6°C), a key limitation of PID control. Thus, ROMPC provides superior thermal performance than traditional controllers by leveraging global spatio-temporal awareness.