Derivation of Equations of Motion and Model-based Control for 3D Rigid Body Approximation of LUVOIR

The Large UV/Optical/IR Surveyor (LUVOIR) is a conceptual space observatory under development by NASA Goddard Space Flight Center for the Astronomy and Astrophysics Decadal Survey. As with similar space telescopes, e.g., James Webb, this spacecraft will have ultra-stringent pointing stability requirements, i.e., on the order of miliarcseconds. Thus, the design of the LUVOIR attitude control system (ACS) may benefit from a model-based approach. In this document, we present an approximate model of the LUVOIR composed of two 3D rigid bodies connected by a 1-DOF rotary joint. From this model, we derive the nonlinear equations of motion, following the approach of Eric T. Stoneking [1], and linearize them about an arbitrary reference orientation. Using the subsequent state space representation, it is straightforward to compute a set of control gains (e.g., via the ”lqr” or ”place” commands in MATLAB). We conclude this memo with a comparison of our LQR approach with the existing PID slew controller designed by a former NASA intern.