Решение задачи терминального управления для плоской системы с учетом ограничений заменой плоского выхода

Решение задачи терминального управления для плоской системы…

ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 6

133

Белинская Юлия Сергеевна

— аспирант кафедры «Математическое моделирование»

МГТУ им. Н.Э. Баумана (Российская Федерация, 105005, Москва, 2-я Бауманская ул.,

д. 5).

Просьба ссылаться на эту статью следующим образом:

Белинская Ю.С. Решение задачи терминального управления для плоской системы с уче-

том ограничений заменой плоского выхода // Вестник МГТУ им. Н.Э. Баумана.

Сер. Естественные науки. 2016. № 6. C. 122–134. DOI: 10.18698/1812-3368-2016-6-122-134

SOLUTION TO POINT-TO-POINT STEERING PROBLEM

FOR CONSTRAINED FLAT SYSTEM BY CHANGING THE FLAT OUTPUT

Yu.S. Belinskaya

usbelka@mail.ru

Bauman Moscow State Technical University, Moscow, Russian Federation

Abstract

Keywords

This article presents a solution to point-to-point steering

problem for constrained flat system. Constraints arise from

the physical formulation of the problem. The proposed

approach is based on the replacement of the flat output of

the system by the one with the range of possible values

within the feasible set. This work analyses the system

describing the motion of the four rotor mini-rotorcraft and

proves the flatness of such a dynamic system. Author

designed the dynamic feedback linearizing the system. The

maneuver for a point-to-point steering problem is the

following: the mini-rotorcraft moves in a corridor from

takeoff, through the horizontal flight, around the corner and

to the landing. Thus, its movement is restricted by the floor,

ceiling and walls. The solution of such a complex point-to-

point steering problem can be divided into several steps. The

first step is the problem of a small height lift and its solution.

Then the flat output of the system is changed in order to

satisfy all the constraints. In the beginning of the second step

the trajectory deviates insignificantly from the planned one.

It happens because of the replacement of the flat output and

switching the control. Other steps do not have any

deviation. The article demonstrates the effectiveness of the

proposed approach by showing the results of numerical

simulation

Flat systems, flat output, point-

to-point steering problem, dynamic

feedback, constrained dynamic

systems

REFERENCES

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flatness of nonlinear systems.

IEEE Trans. Automat. Control

, 1999, vol. 44, no. 5, pp. 922–937.

[2] Krishchenko A.P. Stabilization of programmed motion of nonlinear systems.

Izvestiya AN

SSSR

Tekhnicheskaya kibernetika

, 1985, no. 6, pp. 103–112 (in Russ.).