Comparison of PD and LQR Methods for Spacecraft Attitude Control Using Star Trackers

The work contained herein is a comparison of spacecraft attitude control methodologies that use reaction wheels for torque actuation and star trackers to infer spacecraft orientation and angular rate. A Kalman filter was used to estimate Euler angles and angular rate using the measurements from three star trackers. Using the linearized equations of motion for a rigid body in space, the linearized stability, effectiveness and robustness of a linear quadratic regulator (LQR) control design were compared with that of a proportional-derivative (PD) control design. The goal of the study was to determine the degree to which the optimal gains calculated with the LQR control law improve the performance of a spacecraft attitude control system in comparison to the non-optimal gains calculated with the PD control law.