Nonlinear Control with J2 and Drag Perturbations for Nanosatellite Formation Flight

摘要

Formation flying at large distances in Low Earth Orbit (LEO) requires the consideration of nonlinearities in dynamics and differential perturbations such as J_2 and atmospheric drag. This paper formulates the nonlinear relative orbital dynamics with osculating orbital elements including the nonlinear differential J_2 and drag. Two control methodologies for formation control are investigated, viz., the State Dependent Riccati Equation (SDRE) and nonlinear Model Predictive Control (NMPC). For SDRE control, the tracking is done by error regulation using a novel chatter-free State Dependent Coefficient (SDC) matrix. The NMPC methodology is similarly implemented for the tracking problem with a terminal cost, state constraints, and thrust constraints. The SDRE and NMPC methodologies are then simulated for a large projected circular orbit (PCO) acquisition scenario in context of the Telematics Observation Mission (TOM). A performance comparison based on fuel budget, time of acquisition and computational time for the two control schemes is presented.