Robust nonlinear feedback guidance for an aerospace plane: A geometric approach

Single-stage-to-orbit vehicles using airbreathing propulsion--referred to as aerospace planes--hold promise for more economical delivery of payloads to low Earth orbit. Feedback guidance logic is developed for efficiently and effectively steering such a vehicle through the atmosphere and into orbit. Accurate and robust regulation of the vehicle translational dynamics is considered first. A nonlinear design approach drawing from singular perturbations, feedback linearization, and variable structure control is employed to synthesize regulators which lead to similar dynamic behavior over the entire flight envelope. The design approach provides for a systematic way to counter disturbance effects as well as modeling uncertainties. Differential geometry provides a common framework for the three nonlinear feedback control methodologies.;The two-time-scale behavior present in the vehicle translational dynamics allows the state space to be decomposed into an invariant slow manifold and an invariant foliation of fast manifolds. Feedback guidance logic with robust performance is obtained by synthesizing a composite feedback control from a slow control for the regulation of the nominal slow dynamics along the slow manifold 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 stabilization problems along the fast foliation, using the feedback linearization methodology. In the presence of boundable disturbances, uniform ultimate boundedness of the exactly linearized fast dynamics can be ensured through application of a smoothed variable structure controller.;The two-time-scale decomposition also provides the basis for developing feedback guidance logic for steering and accelerating an aerospace plane along the super- and hypersonic segments of a near-minimum-fuel ascent trajectory. Accurate solutions of the minimum-fuel ascent problem show the effects of dynamic pressure, axial load, and heating rate constraints and establish a basis for the development and assessment of the guidance logic. The minimum-fuel ascent trajectories are found to track the ascent corridor constraints. This characterization permits the formulation of the robust near-minimum-fuel ascent guidance problem as a robust tracking problem, which is amenable to the geometric feedback synthesis approach.