Feedback control of tethered satellites using Lyapunov stability theory
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This paper treats the three-dimensional aspects of tethered satellite deployment and retrieval. Feedback control laws with guaranteed closed-loop stability are obtained using the second method of Lyapunov. Tether mass and aerodynamic effects are not included in the design of the control laws. First, a coordinate transformation is presented that partially uncouples the in-plane and out-of-plane dynamics. A combination of tension control as well as out-of-plane thrusting is shown to be adequate for fast retrieval. Next, a unified control design method based on an integral of motion (for the coupled system) is presented. It is shown that the controller designed by the latter, method is superior to that of the former, primarily from the out-of-plane thrust usage point of view. A detailed analysis of stability of the closed-loop system is presented and the existence of limit cycles is ruled out if out-of-plane thrusting is used in conjunction with tension control. Finally, a tether rate control law is also developed using the integral of motion mentioned previously. The control laws developed in the paper can also be used for stationkeeping. © 1991 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.
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