Optimal Control of Electrodynamic Tether Orbit Transfers Using Timescale Separation

摘要

Electrodynamic tether systems have the potential to allow orbital maneuvers to be undertaken with little or nonpropellant. However, when operated in this mode, the current must be modulated on a fast timescale compared withnthe variation in the average orbital elements. This paper introduces a new numerical technique for calculatingnoptimal trajectories for general dynamical systems for which the dynamics evolve on multiple timescales. Thenmethod combines quadrature and pseudospectral methods using the Chebyshev–Gauss–Lobatto points, which arenshown to be ideal for handling timescale separation. The resulting nonlinear programming problem generates ansignificantly reduced problem size compared with solving the full-scale problem. Numerical results for a problemnwith an analytic solution show that the method achieves high accuracy. Results generated for hanging and spinningnelectrodynamic tethers demonstrate that spinning electrodynamic tethers can be more efficient for orbitalnmaneuvering.