A Comparative Analysis of Control Techniques for Formation Flying Spacecraft in an Earth/Moon-Sun L2 Centered LISSAJOUS Orbit

Abstract

In this thesis, several control techniques are applied to an occulter satellite for a given formation flying mission. This research is in collaboration with the Flight Dynamics Analysis branch at the NASA Goddard Space Flight Center in Greenbelt, Maryland. The spacecraft is part of a leader-follower configuration which orbits about the Earth/Moon-Sun L2 libration point in a lissajous orbit. A controller is required to maintain a distance of 50,000 km between the occulter and the leader satellite in the radial direction with respect to the orbit. The occulter is allowed a tolerance range of 10 m within the "shadow" of the leader. In addition, the controller must also minimize the fuel usage (Deltav) needed to maintain the occulter's trajectory. The control techniques analyzed in this paper consist of several linear (PID, Linear Quadratic Regulator, and Hinfinity) and one nonlinear controller (Sliding Mode Control). All control techniques are compared based on the overall minimization of trajectory error and fuel usage, ease of implementation, and robustness against disturbances and perturbations such as solar radiation pressure and thruster misalignments. The results of this research show that of the control techniques analyzed, the Linear Quadratic Regulator (LQR) and Sliding Mode Control (SMC) satisfy the mission requirements. While LQR uses less fuel to satisfy given mission requirements, the SMC would also be a suitable choice of control if a mission weighted accuracy over fuel usage.