Analysis of control programs and climb paths of the hypersonic first stage of an aerospace system

Control programs and flight paths of the hypersonic first stage of an aerospace system in climb with acceleration to hypersonic velocity are analyzed. Two approaches to determining the control programs and flight paths are identified: the "traditional" approach and the "optimization" one. The "traditional" approach implies specifying a typical mission profile with max-q and peak heat flux. In the case of the "optimization" approach the problem of propellant mass minimum is stated and solved using the method of Pontryagin’s maximum principle. It concerns the mass of propellant consumed in hypersonic acceleration for various terminal flight path angles. Optimal control programs and optimal flight paths are determined. Those meeting the max-q and peak heat flux requirements are selected. The results of modeling the motion of a hypersonic booster with typical and optimal angle-of-attack schedules corresponding to the "traditional" and "optimization" approaches are presented and discussed. It is established that less propellant is consumed in the case of optimal control, which is accounted for by more efficient use of the hypersonic booster's aerodynamic performance due to direct control of the angle of attack.