Optimal command control of hypersonic aircraft flight path in conditions of atmospheric disturbances

Abstract

Disturbed flight of a hypersonic vehicle in accelerated climb is analyzed. Disturbances are deviations of atmospheric density from the values of a standard model. The following concepts and definitions are used in the paper. The nominal optimal angle-of-attack control program is the angle-of-attack control program obtained in solving the task of minimizing fuel consumption for a model of standard atmosphere (hereafter nominal program). The disturbed nominal optimal program is the angle-of-attack control program obtained in solving the task of minimizing fuel consumption for a model of disturbed atmosphere on the condition that the disturbances are known (hereafter disturbed program. The command optimal program is the angle-of-attack control program obtained in solving the task of minimizing fuel consumption for a model of disturbed atmosphere on the condition that the disturbances are unknown (hereafter command program, command control). A multi-step control process is accepted. At each step of control the angle-of-attack control program is defined using the method of Pontryagins maximum principle. The nominal control program is used at the first step. The results of modeling disturbed motion with angle-of-attack command control are presented for maximum rarefied and maximum dense atmosphere. In the case of rarefied atmosphere the angle-of-attack restriction is violated at the end of the flight segment under consideration in solving the boundary value problem, while the prescribed terminal velocity, altitude and flight path inclination conditions are satisfied. In the case of dense atmosphere the terminal altitude and flight path inclination conditions are satisfied, but the terminal velocity condition is not. Since there is no violation of the above-mentioned control and phase coordinate restrictions in the case of the disturbed program, further line of research in the area of optimal command control is related to the improvement of the algorithm of solving the boundary value problem.

Keywords

• hypersonic aircraft
• climb
• acceleration
• atmospheric disturbances
• optimal angle-of-attack control program
• fuel mass minimum
• pontryagin’s maximum principle