Mathematical and computer modeling of automatic control in the presence of disturbances

Authors

  • Mikhail N. Smirnov St. Petersburg State University, 199034, St. Petersburg, Russia Federation
  • Maria A. Smirnova St. Petersburg State University, 199034, St. Petersburg, Russia Federation https://orcid.org/0000-0002-0799-4357

DOI:

https://doi.org/10.21638/11701/spbu10.2024.109

Abstract

One of the most important tasks of the automatic motion control system in real operating conditions is to compensate for the influence of disturbances acting on the object, taking into account the peculiarities of its dynamics. This article presents a method for calculating the coefficients of automatic control, which provides a minimum of the size of the set of reactions to non-deterministic external influences, limited by the norm, and the necessary location of the roots of the characteristic polynomial of a system closed by such control. The specified algorithm is implemented in MATLAB and tested on the example of a specific marine vessel. Based on the simulation results, a conclusion is made about the acceptable quality of the generated algorithm.

Keywords:

control, computer simulation, perturbation

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References

Литература

Зубов В. И. Лекции по теории управления. СПб.: Лань, 2009. 496 с.

Зубов В. И. Математические методы исследования систем автоматического регулирования. Л.: Машиностроение, 1974. 336 с.

Мирошник И. В. Теория автоматического управления. Нелинейные и оптимальные системы. СПб.: Питер, 2005. 271 с.

Олссон Г., Пиани Д. Цифровые системы автоматизации и управления. СПб.: Невский Диалект, 2001. 557 с.

Чернецкий В. И., Дидук Г. А., Потапенко А. А. Математические методы и алгоритмы исследования автоматических систем. Л.: Энергия, 1970. 374 с.

Янушевский Р. Т. Теория линейных оптимальных многосвязных систем управления. М.: Наука, 1973. 464 с.

Bosgra O. H., Kwakernaak H., Meinsma G. Design methods for control systems. Notes for a course of the Dutch Institute of Systems and Control. Delft: Delft University of Technology, 2006. 325 p.

Doyle J., Francis B., Tannenbaum A. Feedback control theory. New York: Macmillan Publ. Co., 1992. 227 p.

Жабко А. П., Жабко Н. А., Яковлев П. В. Метод оптимального демпфирования В. И. Зубова в задаче управления одной гироскопической системой // Вестник Санкт-Петербургского университета. Прикладная математика. Информатика. Процессы управления. 2022. Т. 18. Вып. 2. С. 278–284. https://doi.org/10.21638/11701/spbu10.2022.208

Veremei E. I., Korchanov V. M. Multiobjective stabilization of a certain class of dynamic systems // Automation and Remote Control. 1989. N 49. P. 1210–1219.

Веремей Е. И. Линейные системы с обратной связью. СПб.: Лань, 2013. 448 с.

Веремей Е. И., Корчанов В. М. Многоцелевая стабилизация динамических систем одного класса // Автоматика и телемеханика. 1988. № 9. С. 126–137.

Smirnov M. N., Smirnova M. A., Smirnova T. E., Smirnov N. V. The problem of synthesis the control laws with uncertainties in external disturbances // Lecture Notes in Engineering and Computer Science. 2017. Vol. 2227. P. 276–279.

Smirnov M. N., Smirnova M. A., Smirnova T. E., Smirnov N. V. The issues of multipurpose control laws construction // Lecture Notes in Engineering and Computer Science. 2017. Vol. 2227. P. 194–196.

Smirnova M. A., Smirnov M. N. Multipurpose control laws in trajectory tracking problem // International Journal of Applied Engineering Research. 2016. Vol. 11 (22). P. 11104–11109.

Поляк Б. Т., Щербаков П. С. Робастная устойчивость и управление. М.: Наука, 2002. 303 с.


References

Zubov V. I. Lekcii po teorii upravlenija [Lections on control theory]. St. Petersburg, Lan' Publ., 2009, 496 p. (In Russian)

Zubov V. I. Matematicheskie metody issledovanija sistem avtomaticheskogo regulirovanija [Mathematical methods of research of automatic control systems]. Leningrad, Mashinostroenie Publ., 1974, 336 p. (In Russian)

Miroshnik I. V. Teorija avtomaticheskogo upravlenija. Nelinejnye i optimal'nye sistemy [Automatic control theory. Nonlinear and optimal systems]. St. Petersburg, Piter Publ., 2005, 271 p. (In Russian)

Olsson G., Piani D. Cifrovye sistemy avtomatizacii i upravlenija [Digital systems of automatization and control]. St. Petersburg, Nevskij Dialekt Publ., 2001, 557 p. (In Russian)

Cherneckij V. I., Diduk G. A., Potapenko A. A. Matematicheskie metody i algoritmy issledovanija avtomaticheskih sistem [Mathematical methods and algorithms of automatic systems research]. Leningrad, Jenergija Publ., 1970, 374 p. (In Russian)

Janushevskij R. T. Teorija linejnyh optimal'nyh mnogosvjaznyh sistem upravlenija [The theory of linear optimal multivariable control systems]. Moscow, Nauka Publ., 1973, 464 p. (In Russian)

Bosgra O. H., Kwakernaak H., Meinsma G. Design methods for control systems. Notes for a course of the Dutch Institute of Systems and Control. Delft, Delft University of Technology Publ., 2006, 325 p.

Doyle J., Francis B., Tannenbaum A. Feedback control theory. New York, Macmillan Publ. Co., 1992, 227 p.

Zhabko A. P., Zhabko N. A., Jakovlev P. V. Metod optimal'nogo dempfirovanija V. I. Zubova v zadache upravlenija odnoj giroskopicheskoj sistemoj [Zubov's optimum damping method in the control problem of one gyroscope system]. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Sciences. Control Processes, 2022, vol. 18, iss. 2, pp. 278–284. https://doi.org/10.21638/11701/spbu10.2022.208 (In Russian)

Veremei E. I., Korchanov V. M. Multiobjective stabilization of a certain class of dynamic systems. Automation and Remote Control, 1989, no. 49, pp. 1210–1219.

Veremej E. I. Linejnye sistemy s obratnoj svjaz'ju [Linear systems with feedback]. St. Petersburg, Lan' Publ., 2013, 448 p. (In Russian)

Veremej E. I., Korchanov V. M. Mnogocelevaja stabilizacija dinamicheskih sistem odnogo klassa [Multipurpose stabilisation of one class of dynamic systems]. Automatics and Telemechanics, 1988, no. 9, pp. 126–137. (In Russian)

Smirnov M. N., Smirnova M. A., Smirnova T. E., Smirnov N. V. The problem of synthesis the control laws with uncertainties in external disturbances. Lecture Notes in Engineering and Computer Science, 2017, vol. 2227, pp. 276–279.

Smirnov M. N., Smirnova M. A., Smirnova T. E., Smirnov N. V. The issues of multipurpose control laws construction. Lecture Notes in Engineering and Computer Science, 2017, vol. 2227, pp. 194–196.

Smirnova M. A., Smirnov M. N. Multipurpose control laws in trajectory tracking problem. International Journal of Applied Engineering Research, 2016, vol. 11 (22), pp. 11104–11109.

Polyak B. Т., Shherbakov P. S. Robastnaja ustojchivost' i upravlenie [Robust stability and control]. Moscow, Nauka Publ., 2002, 303 p. (In Russian)

Published

2024-04-16

How to Cite

Smirnov, M. N., & Smirnova, M. A. (2024). Mathematical and computer modeling of automatic control in the presence of disturbances. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 20(1), 109–116. https://doi.org/10.21638/11701/spbu10.2024.109

Issue

Section

Control Processes