Selection of stable design solutions for unmanned aerial vehicle under conditions of uncertainty factors action

DOI: 10.34759/vst-2022-1-57-66

Аuthors

Balyk V. M.^*, Borodin I. D.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: balikv@gmail.com
**e-mail: iibbdd@yandex.ru

Abstract

Currently, the role of unmanned aerial vehicles (UAV) has risen sharply in the field of aircraft building, and the scope of their application herewith is regularly expanding. This type of aerial vehicles is not at a stop, and has been actively developing in recent years. One of the ways of the UAV development consists in enhancing its resistance to the multifactor uncertainty. Multifactor uncertainty is being understood as uncertainty, stipulated by the uncontrolled factors action. It is worth noting that uncontrollable factors incur a significant impact on the design procedures results and design as a whole. In the most general case, the set of possible states of the uncontrollable factors vector will generate an equal to itself by the size set of optimal solutions.

In retrospect, this problem was being solved for the UAVs and aircraft in general by introducing a number of assumptions and special project regulations being formed based on the experience and designer’s subjective perception. The “standard atmosphere” model, rated values of the materials strength etc. may serve as an example of such approach, though, objectively, there are always certain differences from these conditions. For such difference compensation and possible degradation of the aircraft operation, an excess (safety margin) is being admittedly provided in the aircraft capabilities with respect to the design conditions, which frequently leads to the aircraft weight and cost increase. These safety margins are not scientifically substantiated and being elaborated purely empirically. In general, this approach is distinguished by subjectivity. This subjectivism may be eliminated to a certain extent, if the UAV possesses the properties of uncontrollable factors resistance.

There is a whole number of stability studying methods, however, the most convenient and widespread method is Lyapunov function method, though it is imperfect and has a number of disadvantages. The most grave disadvantage of Lyapunov theory consists in the fact that in the general case the Lyapunov function should be guessed. The direct Lyapunov’s method in the stability theory is basic for the stability studying of dynamic systems. However, the Lyapunov function definition does not directly relate to structural properties of the system under study, and, thus, there are still no exhaustive regular ways to its construction according to the given equations of the aircraft motion.

This work novelty lies in the fact that the UAV stability is being studied by a new constructive method of the Lyapunov function statistical synthesis. The statistical synthesis method is being applied to restore functional dependencies from the statistical data. Actually, the original problem of the UAV stability studying is being reduced to a nonlinear programming problem with a statistical stability criterion, by which the optimal design solution is being selected. Statistical synthesis is based on the three basic elements such as statistical sampling, basis functions and statistical criteria. As the result of the conducted study, the following results were obtained:

1. A method of stability studying for a wide class of the UAV-type aircraft has been developed.

2. The stability of the UAV movement was studied according to the developed statistical criterion.

Keywords:

stability to multifactorial indetermination, uncontrollable factors of artificial origin, statistical synthesis of the Lyapunov function, statistical stability criterion, quadratic form of the basis function

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