Dynamic Model and Closed-loop Attitude Control for a Starshade Orbiting the L2 Point

Abstract

The goal of this project is to develop a closed-loop attitude control system for a starshade in a halo orbit about the L2 point. The attitude control of the starshade will keep its fundamental plane normal to the telescope-target star vector, allowing it to effectively occult starlight for exoplanet observation. Since the starshade is part of a two-spacecraft system, the dynamics for each craft must be modeled. The telescope’s translational equations of motion are derived from the Circular Restricted Three-Body Problem (CRTBP). Based on the separation distance from the telescope and direction of the target star, the starshade’s motion can be solved for analytically. Rotational motion is modeled for the starshade based on the calculated external torques resulting from gravity and solar radiation. Control torques can be applied to counteract the effects of these external torques and keep the starshade at the desired attitude. The optimal controller for this system is a Linear Quadratic Regulator (LQR). The quaternion-based rotational equations of motion are first linearized about the desired attitude to calculate the controller gain matrix. Since this controller is quaternion-based, there are no singularity risks. The starshade can be commanded to any attitude and point to any target star. Although the main objective for the starshade mission is to maintain target star pointing during 8-hour science modes, this quaternion-based controller extends the starshade’s functionality and provides broadened potential for starshade missions.