novtexmechМехатроника, автоматизация, управлениеMekhatronika, Avtomatizatsiya, Upravlenie1684-64272619-1253Commercial Publisher «New Technologies»10.17587/mau.24.167-177novtexmech-1725Research ArticleСИСТЕМНЫЙ АНАЛИЗ, УПРАВЛЕНИЕ И ОБРАБОТКА ИНФОРМАЦИИSYSTEM ANALYSIS, CONTROL AND INFORMATION PROCESSINGНепрямое адаптивное управление каскадными системами на основе метода скоростного биградиентаIndirect Model Reference Adaptive Control of Cascade Systems Based on the Speed-Bigradient MethodНгуенТ. Т.NguyenC. T.

Нгуен Ти Тхань - канд. техн. наук, доц.

Ханой

Nguyen Chi Thanh - Сand. Tech. Sc., Associate Professor.

Hanoi, 240000

chithanh@lqdtu.edu.vnФиношинА. В.FinoshinA. V.

Канд. техн. наук, доц.

Москва

Сand. Tech. Sc., Associate Professor.

Moscow, 105005

earlov@gmail.comТехнический университет им. Ле Куй ДонаВьетнамLe Quy Don Technical UniversityViet NamМГТУ им. Н. Э. БауманаРоссияBauman Moscow State Technical UniversityRussian Federation202510042025264167177Copyright © Commercial Publisher «New Technologies», 20252025Commercial Publisher «New Technologies»Commercial Publisher «New Technologies»https://mech.novtex.ru/jour/about/submissions#copyrightNoticehttps://mech.novtex.ru/jour/article/view/1725

Рассматривается задача слежения для линейных каскадных систем, состоящих из двух подсистем, в условиях параметрической неопределенности. Для повышения точности слежения и робастных свойств предлагается модификация метода скоростного биградиента Ю. И. Мышляева за счет расширения размерности выходного каскада путем добавления интегратора, формирования информационного выхода в виде линейной комбинации ошибки слежения и ее производных и синтеза виртуального управления в виде локальной обратной связи по информационному выходу. Описывается четырехэтапная процедура синтеза алгоритма непрямого адаптивного управления на основе метода скоростного биградиента с интегральным виртуальным управлением. Решение задачи слежения обосновывается методом функций Ляпунова. Доказывается достижение поверхности скольжения и информационного выхода за конечное время.

Исследуются идентифицирующие свойства алгоритма. Приводится процедура синтеза алгоритма слежения и результаты компьютерного моделирования замкнутой системы управления на примере линейной системы третьего порядка.

The adaptive tracking control problem for the linear cascade system consisting of two subsystems is considered. The modification of the Speed bi-gradient method is proposed to improve both the accuracy and the robust property. The considered modification is performed by an extending the dimension of the output subsystem of a cascade system, and forming the information output as the generalized tracking error dynamics, and the virtual control synthesis as the local feedback of an information output. The fourstage design procedure of the indirect adaptive control is proposed. The achievement of the tracking control objective is proved by a Lyapunov method. The finite-time stability of the sliding manifold and the information output is ensured. Identification properties of a control law are investigated. Both the control law design and simulation results for the third order cascade control plant are presented.

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The authors declare that there are no conflicts of interest present.