Dynamics-Informed hierarchical sliding mode control for libration of partial space elevators in cargo transportation

Abstract

This study presents an original analysis of out-of-plane libration dynamics and its control in partial space elevator cargo transportation. A comprehensive three-dimensional dynamic model of the partial space elevator has been derived to examine the effects of out-of-plane libration. To ensure a stable in-plane configuration, a coupling-free analytical speed function is developed that cancels out the coupling effects stemming from out-of-plane libration. A novel approach is developed to introduce a thrust control strategy for the elimination of out-of-plane libration using a virtual dynamic-based hierarchical sliding mode control law. By employing a new combined channel implementation mode, it is demonstrated that in and out-of-plane libration can be controlled with a single thruster, resulting in reduced fuel consumption. The stability of the proposed control strategy is proven within the Lyapunov framework. Numerical simulations validate the effectiveness of the control strategy and highlight its significance. Results show that out-of-plane libration increases the magnitude of in-plane libration, while climber movement amplifies out-of-plane libration. The control strategy successfully eliminates out-of-plane libration using limited control input, ensuring stable cargo transportation in the partial space elevator.