A feedback control for the advanced launch system

Abstract

A robust feedback algorithm is presented for a near-minimum-fuel ascent of a two-stage launch vehicle operating in the equatorial plane. The development of the algorithm is based on the ideas of neighboring optimal control and can be derived into three phases. In phase 1, the formalism of optimal control is employed to calculate fuel-optimal ascent trajectories for a simple point-mass model. In phase 2, these trajectories are used to numerically calculate gain functions of time for the control(s), the total flight time, and possibly, for other variables of interest. In phase 3, these gains are used to determine feedback expressions for the controls associated with a more realistic model of a launch vehicle. With the Advanced Launch System in mind, all calculations are performed on a two-stage vehicle with fixed thrust history, but this restriction is by no means important for the approach taken. Performance and robustness of the algorithm is found to be excellent.