novtexmechМехатроника, автоматизация, управлениеMekhatronika, Avtomatizatsiya, Upravlenie1684-64272619-1253Commercial Publisher «New Technologies»10.17587/mau.23.146-151novtexmech-1150Research ArticleРОБОТЫ, МЕХАТРОНИКА И РОБОТОТЕХНИЧЕСКИЕ СИСТЕМЫROBOT, MECHATRONICS AND ROBOTIC SYSTEMSАнализ системы "маятник—тележка" при внешнем гармоническом воздействии на основе критериальной матрицы системыAnalysis of a Cart-Inverted Pendulum System with Harmonic Disturbances Based on its Criterion MatrixЛонгXоанг ДыкLongHoang Duc

аспирант

Санкт-Петербург

Hoang Duc Long, Ph.D. Student, Faculty of Control Systems and Robotics

Saint Petersburg

longhd@mta.edu.vnДударенкоН. А.DudarenkoN. A.

канд. техн. наук, доц.

Санкт-Петербург

 

Cand. of Sc., Associate Professor

Saint Petersburg

dudarenko@mail.ifmo.ruУниверситет ИТМОРоссияITMO UniversityRussian Federation202206032022233146151Copyright © Commercial Publisher «New Technologies», 20222022Commercial Publisher «New Technologies»Commercial Publisher «New Technologies»https://mech.novtex.ru/jour/about/submissions#copyrightNoticehttps://mech.novtex.ru/jour/article/view/1150

Управление перевернутым маятником на тележке является классической задачей теории управления. Динамика перевернутого маятника схожа с динамикой многих реальных систем, представляющих практический интерес, таких как маятниковые системы, ракетные пусковые установки, сигвеи и многие другие. Управление такой системой является сложной задачей в силу неустойчивости и нелинейности системы. Кроме того, физические ограничения, накладываемые на систему, также усложняют процесс проектирования системы управления. Большая часть нелинейностей обусловлена как самой конструкцией системы, так и влиянием внешних возмущений различного характера. В статье представлен подход к анализу системы "маятник—тележка", функционирующей в условиях внешних гармонических воздействий. Предлагаемый подход основан на исследовании характеристического показателя критериальной матрицы системы, именуемого функционал вырождения. Функционал вырождения, сконструированный на спектре сингулярных чисел критериальной матрицы системы, используется как качественный показатель, позволяющий определить диапазон частот гармонического воздействия, на котором система функционирует как единое целое. Для управления системой перевернутого маятника на тележке используется линейно-квадратичный регулятор. Предлагаемый подход иллюстрируется примером.

The control of an inverted pendulum is a classical benchmark control problem. Its dynamics resemble that of many real-world systems of interest like pendulous, missile launchers, segways, and many more. The control of this system is challenging as it is a highly unstable, highly non-linear, non-minimum phase system, and underactuated. Furthermore, the physical constraints on the track position also pose complexity in its control design. A great deal of nonlinearity is present inherently and as well as affected by the surrounding external disturbances. The paper presents an approach for analysis of a cart-inverted pendulum system with harmonic disturbances. The approach is based on the index of the criterion matrix of the system named a degeneration factor. The degeneration factor is constructed with the singular values of the criterion matrix of the system and allows us to find frequency range, where the system operates as a whole. A linear-quadratic regulator is used to control the cart-inverted pendulum system. The results are supported with an example.

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