Long-term deorbiting control for an electrodynamic tether system exploiting periodic solutions

Abstract

This paper focuses on the nonlinear dynamics and control problem of deorbiting an electrodynamic tethered satellite system in an inclined elliptical orbit. Considering the perturbing Lorenz forces, a set of modified equinoctial elements is employed to describe the slow-varying orbital dynamics. In addition, the fast-varying attitude dynamics of the system is incorporated into dynamic modeling by adopting an assumption of a dumbbell model. To circumvent the difficulties in computation of a real-time optimal control law for a long-term deorbiting process, a compound control scheme is proposed. A time-scale separation method is adopted to facilitate the controller design. In the scheme, a nonlinear optimal control law accounting for system constraints and nonlinear dynamics is first proposed to find an initial nominal periodic orbit without considering the variations of orbital elements. Subsequently, a closed-loop feedback control law based on energy rate is presented to track the periodic solutions for several orbits by considering the overall dynamics. Notably, the periodic solution will be re-computed after each tracking procedure to account for the slow variation in orbital elements. Comparative studies are presented to demonstrate the advantages of the proposed control law in reducing computational costs.