Stabilization of tethered tug–debris system with residual liquid fuel

The combination of the tug, tether, and debris is called the tethered tug–debris system, or tethered towing system. A study is conducted to investigate the stabilization aspects of the tethered tug–debris system. The debris is an upper stage with residual liquid fuel, and the control adopted is the wave-based control. The study’s objective is to suppress libration of the combination, tumbling of the debris, and sloshing of the liquid fuel simultaneously. Complete and simplified dynamics for tethered towing of upper stages with residual liquid fuel are derived and compared. Open-loop and closed-loop controllers for a crane system with a triple pendulum are designed by using the wave-based control method. Equivalent conditions between the simplified towing system and the crane system are established, and the wave-based closed-loop controller is modified and applied to the complete towing system.