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.

Control programs and flight paths of a hypersonic vehicle in climb are analyzed. Two approaches to solving the task of 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 of a hypersonic vehicle. In order to maximize the specific impulse (optimize the performance of the propulsion system) the vehicle moves along the line of peak dynamic pressing. In the case of the optimization approach the minimum fuel problem is stated and solved using the method of Pontryagins maximum principle. It concerns the mass of fuel consumed in hypersonic acceleration. Optimal control programs and optimal flight paths are determined. The results of modeling the motion of a hypersonic vehicle with angle-of-attack schedules corresponding to the traditional and optimization approaches are presented and discussed. It is established that less fuel is consumed in the case of optimal control, which is accounted for by more efficient use of the hypersonic vehicle aerodynamic performance due to direct control of the angle of attack.

Disturbed motion of the hypersonic first stage of an aerospace system in climb is analyzed. Deviations of atmospheric density from standard values and deviations of aerodynamic force coefficients from reference values are taken as disturbances. Disturbance motion of the hypersonic first stage of a hypersonic vehicle with the optimal angle-of-attack schedule obtained for reference atmosphere and nominal aerodynamic characteristics is modeled. Deviations of terminal conditions of disturbed motion from the target values of velocity, altitude and flight path inclination are determined. The problem of minimum propellant mass consumed in the climb with acceleration to hypersonic velocity is solved for disturbed motion by the method of Pontryagin’s maximum principle. Optimal angle-of-attack schedules, optimal flight paths and finite values of the mass of the hypersonic first stage are determined. Comparative analysis of optimal control programs and flight paths for disturbed and undisturbed motion is made.

Disturbed motion of a hypersonic vehicle in climb is analyzed. Deviations of atmospheric density from standard values and deviations of aerodynamic force coefficients from nominal values are taken as disturbances. Disturbed motion of a hypersonic vehicle with the optimum angle-of-attack schedule and nominal flight characteristics is modeled. Deviations of terminal conditions of disturbed motion from the target values of velocity, altitude and path inclination are determined. Using the method of Pontryagin’s maximum principle the problem of fuel mass minimum consumed in hypersonic acceleration climb is solved for disturbed motion. Optimal angle-of-attack schedules, optimal flight paths and finite values of the hypersonic vehicle’s mass are determined. Comparative analysis of optimal control programs and flight paths obtained for disturbed and undisturbed motion is carried out.

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