Geometric synthesis of aerospace plane ascent guidance logic

Abstract

A single-stage vehicle using airbreathing propulsion holds promise for a more economical delivery of payloads to orbit. The utility of the vehicle is contingent on having a guidance capability for flying a near minimum-fuel ascent trajectory. In this paper, feedback guidance logic is developed for the hypersonic ascent phase. The two-time-scale behavior present in the vehicle translation dynamics allows the corresponding state space to be decomposed approximately into an invariant slow manifold and an invariant foliation of fast manifolds. Robust near-optimal guidance is synthesized as a composite of the minimum-fuel control on the slow manifold—as determined by the dynamic pressure and heat rate constraints—and a fast control for robust tracking of the slow manifold in the presence of atmospheric disturbances and modeling errors. The tracking problem is solved as a family of regulation problems on the fast foliation, using feedback linearization and a bandwidth-limited variable structure controller. Simulations indicate the effectiveness of the guidance logic.