Dynamics and control of a space station based Tethered Elevator System

Abstract

A mathematical model is proposed for studying planar dynamics of a space station based Tethered Elevator System. The model accounts for finite dimensions of the station, offset of the tether attachment point from the station's mass center, and crawling motion of the elevator to or from a platform supported by the fixed length tether. The tether, assumed massless but elastic, is modeled as a double pendulum, while the elevator, end platform and moving offset attachment are treated as point masses. The system center of mass is assumed to follow an arbitrary elliptic orbit. The governing equations of motion, obtained using the Lagrangian procedure, are coupled, nonlinear, nonautonomous, and rather lengthy. Numerical results are given for the rigid tether model with the system mass center following a circular orbit. Simulation of the uncontrolled dynamics suggests that elevator maneuvers can excite unacceptably large amplitude station and tether pitch oscillations, which persist due to the absence of damping. An optimal Linear Quadratic Regulator control strategy is applied in conjunction with two distinctly different types of actuators: (i) thruster control ( T α , T γ ); and (ii) offset-thruster control ( E x , T y ); in presence of the station based momentum gyro output M ψ . Results show that both the schemes are effective during stationkeeping, but the elevator thruster ( T α ) is required during its rapid retrieval. A hybrid controller which utilizes both the thruster and offset strategies offers advantages from safety considerations.