New geometric formulation for libration dynamics and suppression of partial space elevator by fuzzy logic and thrust vectoring control.

This study proposes a new control strategy for mitigating the libration in a partial space elevator (PSE). First, a libration-free or coupling-free analytical speed function is derived by assuming no in-plane and out-of-plane libration in the cargo transportation phase. Subsequently, a thrust is applied at the PSE's end body to counter any libration during this phase. A new set of geometric measures - bending and departure angles - are introduced to characterize the libration motion in PSE's dynamic equation. Based on these measures, two separate proportional-derivative (PD) stabilizing feedback laws are proposed. These PD laws individually control the bending and departure angles by thrust at the end body to suppress the libration that deviates from the libration-free trajectory. Due to the dynamic coupling between the bending and departure modes, they dominate alternatively. Accordingly, a novel fuzzy logic control law is proposed to switch between two PD controls based on the state of these two angles. Finally, a thrust vectoring control is proposed to combine in-plane and out-of-plane thrusting into a single actuation control. The asymptotic stability of the proposed control scheme is proved by Lyapunov's stability theory. Comprehensive numerical analyses demonstrate the effectiveness of the new geometric representation of the libration and the proposed new control strategy, highlighting their ability to suppress libration with bounded control inputs efficiently. • Derived new coupling-free analytical speed function for libration-free cargo transfer trajectory. • Introduced a new set of geometric measures, bending and departure angles, to describe libration motion. • Proposed a Fuzzy logic law to switch control between bending and departure angles. • Proposed a thrust vectoring control to combine in-plane and out-of-plane thrusting into one actuation. [ABSTRACT FROM AUTHOR]