A new tension control law for deployment of tethered satellites

Abstract

Tethered satellites have been proposed for a variety of uses such as creation of artificial gravity, gravity gradient stabilization, minimization of impact loads during spacecraft docking, electrodynamic drives for spacecraft, power generators for spacecraft, exploration of the upper atmosphere, orbital transfer, aerodynamic deceleration of satellites to prepare for reentry, and as part of space escalators. The issue of deployment and retrieval of tethers from orbiting spacecraft (the Space Shuttle is the currently used the parent spacecraft) is critical to the success of the tethered satellite mission. The problem of deployment and retrieval of tethers from the Space Shuttle is extremely complicated because it leads to nonlinear time varying differential equations. One of the methods proposed for deployment and retrieval of tethered satellites is the tension control law [1]. In this method, the tension in the tether is varied in accordance with s predetermined control law to extend or retrieve the tether to the required length, while minimizing the oscillations of the tether. The governing equations being nonlinear, Liapunov's second method may be used to determine the tension control law. This approach has two drawbacks: firstly, Liapunov functions can be found only by trial and error, and consequently, the experience of the analyst plays a major role in the selection of the control law. The relaxation of any one of the assumptions made in the derivation of the equations would lead to a new set of governing equations, which in turn implies a new problem as far as the determination of the Liapunov function is concerned. Secondly, the procedure leads to a nonlinear control law. Despite these limitations, Vadali [2] and Fujii and Ishijima [3] have successfully employed this technique.