Trajectory optimization and guidance law development for transatmospheric vehicles

The problems of on-board trajectory optimization and real-time guidance law synthesis are addressed for an air-breathing, single-stage-to-orbit vehicle. The particular objective of fuel-optimal ascent is examined in the hypersonic regime using a simple vehicle model representative of the aerospace plane concept. This model includes a dual-mode propulsion system composed of SCRAMJET and rocket engines. An energy state approximation is applied to a four-state dynamic model for flight of a point mass in a vertical plane over a spherical non-rotating Earth. Optimal climb profiles for the unconstrained and dynamic pressure constrained cases result from further reduction in model order. An analytic switching condition is derived for optimal transition to rocket powered flight as orbital velocity is approached. Simple feedback guidance laws for both the unconstrained and dynamic pressure constrained cases are derived via a combination of singular perturbation and feedback linearization techniques. Lastly, the performance of the resulting nonlinear feedback guidance laws is presented in a numerical simulation of ascent to orbit.