Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 517.977.1
NUMERICAL ESTIMATIONS OF MAXIMUM DEVIATIONS FOR AIRCRAFT TRAJECTORIES IN THE ATMOSPHERE
A. N. Rogalyov [1]*, A. A. Rogalyov [2]
[1] Institute of Computational Modeling, Siberian Branch of Russian Academy of Sciences 50/44, Akadmegorodok, Krasnoyarsk, 660036, Russian Federation [2] Siberian Federal University, Institute of Space and Information Technologies 26, Kirenskogo Str., Krasnoyarsk, 660074, Russian Federation *E-mail: rogalyov@icm.krasn.ru
In this article we study guaranteed methods for solving differential equations systems with control actions and its application for problems of aircrafts trajectories maximum deviations estimating. The problem statement of maximum deviations estimating is caused by the necessity to evaluate reliability of complex nonlinear controlled systems that operate under the influence of perturbations. The example of such system is an aircraft: an airplane, a rocket, a spacecraft. We should emphasize the research of an airplane movement during an autoland approach among problems of maximum deviations estimating. This research gives an answer whether a violation of restrictions imposed on the kinematic parameters of an airplane touching down a runway is possible or not. The problems of limit deviations evaluating also include estimating of the possibility of an aircraft motion stability’s loss for a given time interval. The greatest difficulty in solving such problems arises in the case when flight conditions are not fixed, for example, when considering the descent into the atmosphere of a spacecraft orbiter. In this case the loss of stability criteria themselves are not formulated, if we do not confine ourselves to the simplest case of a linear system, for which the Routh-Hurwitz conditions can be used. Some threshold or critical value of one of the parameters of an airplane can serve as a simplistic criterion of stability loss. For example, the angle of attack or slip angle can be taken as such parameter. Reachable sets (collections of all the trajectories of controlled systems) make a figure in such problems. These sets are used in problems of guaranteed or minimax estimation of solutions of dynamical systems if external perturbations that influence on a system and observation errors are enclosed within a certain range (constrained by limitations). The analysis of works that estimate reachable sets indicates that the reliable estimation of reachable sets of controlled systems under uncertainty, if the right-hand sides of these systems depend nonlinearly on the control actions, is not always possible. Therefore the possibility of the guaranteed methods based on symbolic representation of solutions for reachable sets evaluation will be useful for specialists in control. The article presents the results of the application of the numerical methods based on the construction of symbolic formulas of solutions and evaluating all of its possible values.
maximum deviations, aircraft, critical values of parameters, guaranteed method of estimating, symbolical formula.
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Rogalyov Alexey Nikolaevich – Cand. Sc., Docent, senior researcher, Institute of Computational Modeling, SB RAS. E-mail: rogalyov@icm.krasn.ru

Rogalyov Alexander Alexeevich – postgraduate student, Institute of Space and Information Technologies, Siberian Federal University. E-mail: ran@akadem.ru