VESTNIK of Samara University. Aerospace and Mechanical EngineeringVESTNIK of Samara University. Aerospace and Mechanical Engineering2542-04532541-7533Samara National Research University776910.18287/2541-7533-2020-19-1-41-50UnknownOptimal command control of hypersonic aircraft flight path in conditions of atmospheric disturbancesKrikunovM. M.<p><span lang="EN-US">Candidate of Science (Engineering), <br />Senior Research Associate</span></p>krikunov.mm@ssau.ruhttps://orcid.org/0000-0002-0379-7372Samara National Research University2005202019141501905202019052020Copyright © 2020, VESTNIK of Samara University. Aerospace and Mechanical Engineering2020<p>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.</p>Гиперзвуковой самолётнабор высотыразгонатмосферные возмущенияоптимальная программа угла атакишаг управленияминимум массы топливапринцип максимума ПонтрягинаHypersonic aircraftclimbaccelerationatmospheric disturbancesoptimal angle-of-attack control programfuel mass minimumPontryagin’s maximum principle[1. Buzuluk V.I. Optimizatsiya traektoriy dvizheniya aerokosmicheskikh letatel'nykh apparatov [Optimization of aerospace vehicle flight paths]. Moscow: Central Aerohydrodynamic Institute Publ., 2008. 476 p.][2. Nechaev Yu.N. Silovye ustanovki giperzvukovykh i vozdushno-kosmicheskikh letatel'nykh apparatov [Power units of hypersonic and space-air vehicles]. Moscow: Rossiyskaya Akademiya Kosmonavtiki Publ., 1996. 214 p.][3. Nechaev Yu.N., Polev A.S., Nikulin A.V. Modelirovanie usloviy raboty parovodorodnogo RTD v sostave silovoy ustanovki giperzvukovogo letatel'nogo apparata. Vestnik Akademii kosmonavtiki. Nauchno-tekhnicheskie problemy kosmonavtiki. Vypusk 2. Materialy nauchnykh dokladov na zasedaniyakh napravleniya v 1996-1997 gg. Moscow: Rossiyskaya Akademiya Kosmonavtiki Publ., 1998. P. 159-191. (In Russ.)][4. Balakin V.L., Krikunov M.M. Analysis of control programs and flight paths of a hypersonic vehicle in climb. Vestnik of Samara University. Aerospace and Mechanical Engineering. 2018. V. 17, no. 4. P. 18-26. (In Russ.). DOI: <a href='http://doi.org/10.18287/2541-7533-2018-17-4-18-26'>10.18287/2541-7533-2018-17-4-18-26</a>][5. Balakin V.L., Krikunov M.M. Disturbed motion of a hypersonic vehicle in climb. Vestnik of Samara University. Aerospace and Mechanical Engineering. 2019. V. 18, no. 2. P. 7-20. (In Russ.). DOI: <a href='http://doi.org/10.18287/2541-7533-2019-18-2-7-20'>10.18287/2541-7533-2019-18-2-7-20</a>][6. Pontryagin L.S., Boltyanskiy V.G., Gamkrelidze R.V., Mishchenko E.F. Matematicheskaya teoriya optimal'nykh protsessov [Mathematical theory of optimal processes]. Moscow: Nauka Publ., 1983. 393 p.][7. Shkol'nyy E.P., Mayboroda A. Atmosfera i upravlenie dvizheniem letatel'nykh apparatov [Atmosphere and aircraft motion control]. Leningrad: Gidrometeoizdat Publ., 1973. 308 p.][8. Krylov V.I., Bobkov V.V., Monastyrnyy P.I. Vychislitel'nye metody. T. II [Computational methods]. Moscow: Nauka Publ., 1977. 400 p.]