Evaluation of integral funnel in aircraft dynamics on exposure to uncontrolled factors

Theoretical mechanics


Аuthors

Zaitsev V. V.

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

e-mail: vlad128gp@yandex.ru

Abstract

Consider a dynamic system under limited uncontrolled factors impact is under consideration. A problem of aircraft movement study in many cases narrows down to such systems research. Uncontrolled factors of no little significance can be aircraft aerodynamic characteristics approximation errors, forces and moments allowing for wind impact, atmosphere characteristics deviation from normal (and corresponding disturbance in aerodynamic characteristics).

It is common knowledge that solutions for non-linear systems can be obtained in special cases. Thus, the problem of a system phase flow evaluation arises (in a corresponding definition — evaluation of system integral funnel).

This work considers the system with the same critical points nonoccurrence for all parameters, or system critical points nonoccurrence in the region under consideration.

The main problem of the known method of comparison is lack of comparison systems building algorithms for common non-linear systems.

The paper considers corresponding comparison systems building for systems with «drift» and estimation improvement issues. Comparison systems are developed using various generalizations of Lyapunov special functions (the system of functions with equiscalar surfaces distorted by hyperplanes in particular). The temporal separation of the integral funnel under study is evaluated (in particular) as an intersection of sets, bounded by Lyapunov special functions surfaces. The possibility of obtaining high-accuracy evaluations is demonstrated in some suppositions.

The paper gives examples of system solutions evaluation for planar motion in a vertical plane for the problem of estimation of errors impact while aerodynamic performance characterization on the system phase flow.

Methods and corresponding algorithms for a dynamic system integral funnel estimation suggested in this work can be effectively implemented in theory of differential equations (solutions evaluation), control theory (attainability domains estimation), aircraft and spacecraft dynamics applications (allowance for aerodynamic coefficients errors, wind impact, etc.), as well as for motion ballistics and dynamics of submersible craft in games theory dynamic problems.

The indisputable advantage of the suggested techniques consists in obtaining analytical functions describing estimations and high efficiency of algorithms. The result of the suggested technique presents warranted estimations contrary to direct integration (which allow integrate finite number of trajectories, and using additionally methods of integrating results processing obtain some heuristic evaluations).

Keywords:

dynamic system flow estimation, comparison systems, uncontrolled factors impact, aircraft dynamics

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