Effect of tether flexibility on the tethered Shuttle subsatellite stability and control

TLDR

The study examines how tether flexibility affects in‑plane stability during station‑keeping and proposes an alternate optimal control law with additional vibrational‑mode feedback, as well as a nonlinear retrieval control law. The authors develop two control strategies: an alternate optimal law incorporating first‑mode vibrational feedback, and a nonlinear retrieval law using tether length and swing‑angle feedback. Simulations reveal that flexible tethers yield smaller stability regions, but the proposed control laws markedly improve transient swing and vibration responses, reducing in‑plane and out‑of‑plane swing amplitudes and highlighting the importance of vibrational‑mode amplitudes in gain selection.

Abstract

This paper investigates the effect of tether flexibility on the (in-plane) stability regions as a function of tether tension control parameters during stationkeeping. It is found that the size of the stability regions for the flexible tether is reduced considerably as compared with that for the rigid massive tether for some control parameters. An alternate optimal control law, which includes additional feedback of the first vibrational mode and its rate, is introduced; the results of stationkeeping simulations show that the transient responses of both the in-plane swing angle and vibrations are improved as compared with previously developed control laws. For retrieval a typical nonlinear control law, which includes the nonlinear feedback of the tether length, in-plane and out-of-plane swing angles and their rates, is developed. Simulation results show that the amplitudes of the in-plane and out-of-plane swing angles could be reduced significantly; also, it is demonstrated that the amplitudes of the tether vibrational modes should be considered for the selection of the control gains.