Optimization of control gains for three dimensional retrieval dynamics of tethered satellites

Abstract

Introduction Dynamics and control of tethered satellites during deployment and retrieval phases have been studied by numerous authors. Following the suggestion of the tension control law by Hupp, many nonlinear feedback tension control laws based on Liapunov functions have been proposed. Determination of the tension control law through this route is possible only by trial and error because Liapunov functions are nonunique. In this paper an alternate method, a linear state variable feedback control law is proposed for retrieval of tethered satellites. The control gains are determined by using theorems in analytical mechanics. This method results in a minimum number of state variables that need to be fed back to stabilize the system because it is possible to set some of the controller gains to zero. Simulation of the nonlinear system over the nonzero gain space results in a robust controller that meets the performance specifications set by the designer. The study concludes with the effect of structured uncertainties in the initial conditions. All the initial conditions are perturbed and the simulations are carried out once again with the same control law. The result is very encouraging: large variations in the initial conditions can be tolerated before degradation in the system response. 'presently. Engineer, Vikram Sarabhai Space Centre, Thiruvananthapuram, India t Assistant Professor, Member, AIAA '•presently, Engineer, Vikram Sarabhai Space Centre, Thiruvananthapuram, India Copyright ©1998 by the American Institute of Aeronautics and Astronautics, Inc., All rights reserved. Tethered satellites deployed from the Space Shuttle have been proposed for diverse applications such as creation of artificial gravity, gravity gradient stabilization, minimization of impact loads during spacecraft docking, electrodynamic drives and power generators for spacecraft, exploration of the upper atmosphere, orbital transfer, retrieval of stranded astronauts and ailing satellites, aerodynamic deceleration of satellites to prepare for reentry, as part of space escalators, creation of artificial gravity in the Space Station and long wavelength radio astronomy interferometry. A fundamental issue in the utilization of tethers is quick deployment/retrieval of the attached payload. Inordinate librations of the tether during deployment/retrieval are undesirable. The structural damping present in the system is too low to contain the librations. Deployment and retrieval of tethers are difficult to deal with analytically, because they lead to coupled nonlinear time varying differential equations. Rupp in 1975 proposed to control the tether reel located in the parent spacecraft to alter the tension in the tether, which in turn changes the stiffness and the damping of the system. Implementation of such a tension control law requires sensing the tether tension, rate of tether deployment/retrieval and the tether length. The control law will determine the amount of tension required to augment the requiste amount of stiffness and damping. Baker applied the tension control law to a model which included out of plane motion. Modi