Optimal Control of a Librating Electrodynamic Tether Performing a Multirevolution Orbit Change

摘要

Satellites that use low-thrust propulsion systems for maneuvering, although efficient, can take a long time toncomplete significant orbit changes. Determining the nonlinear optimal controls for such multirevolution maneuversnusing the instantaneous orbital state dynamics can be riddled with numerical errors and are often subject to longncomputation times, due to the large number of discretization nodes required by the optimization algorithm. Annapproach to optimal control of an electrodynamic tether is examined using averaged orbital state dynamics asnconstraints instead of instantaneous dynamic constraints.Amean-square libration state is introduced in the dynamicnmodel that captures the average of the out-of-plane libration of the tether. A sample long-termoptimal orbit changenmaneuver of a librating electrodynamic tether subject to atmospheric drag is investigated. Themethod of averagingnis employed to transformthe optimal control problemfromthe time domain into Fourier space, inwhich the complexnproblemis significantly reduced to aZermelo-type problemthat is solved using a pseudospectralmethod.To validatenthe dynamic model of averaged states, the instantaneous states are propagated from the initial conditions using thenresulting optimal controls.