Adaptive control with a guarantee of a given performance

Cover Page

Cite item

Full Text

Abstract

The paper presents a modification of the classical output adaptive control algorithm in order to guarantee that the output signal belongs to a given set specified by the developer at any time. Unlike classical adaptive control schemes, where it is impossible to influence control performances, including transient and steady-state performance, it is proposed here to supplement the classical adaptive control procedure with a nonlinear control law to solve these problems. The nonlinear control law is based on the special coordinate transformation of the output variable so that the problem with constraints is reduced to the problem without constraints. For a transformed system without constraints, any existing adaptive control schemes can be applied to stabilize it. Moreover, in new coordinates, it is not required to guarantee the specified performance of transient processes at any time, and the value of the marginal error is not important. This is due to the fact that inverse transformations will always guarantee that the original signals are within the limits specified by the developer. The problem for plants with a relative degree one is solved in order to avoid cumbersome conclusions. However, all the results obtained can be directly extended to plants with an arbitrary relative degree. An example is given that illustrates the effectiveness of the proposed method and confirms the theoretical conclusions.

About the authors

Igor Borisovich Furtat

Institute of Problems of Mechanical Engineering RAS

Author for correspondence.
Email: cainenash@mail.ru
St.Peterburg

Pavel Aleksandrovich Gushchin

Institute of Problems of Mechanical Engineering RAS

Email: guschin.p@mail.ru
St.Peterburg

Ba Huy Nguyen

Institute of Problems of Mechanical Engineering RAS

Email: leningrat206@gmail.com
St.Peterburg

Nikita Sergeevich Kolesnik

Institute of Problems of Mechanical Engineering RAS

Email: nik.kolesnik.1998@mail.ru
St.Peterburg

References

  1. Еремин Е. Л. Алгоритм адаптивной системы управления с явно-эталонной моделью для строго минимально-фазового объекта // Информатика и системы управления. – 2004. – №2, Т. 8. – С. 157–166.
  2. Мирошник И. В., Никифоров В. О., Фрадков А. Л. Нелинейное и адаптивное управление сложными динамическими системами. – СПб.: Наука, 2000.
  3. Фрадков А. Л. Кибернетическая физика: принципы и примеры. – СПб.: Наука, 2003.
  4. Фуртат И. Б., Гущин П. А. Управление динамическими объектами с гарантией нахождения регулируемого сигнала в заданном множестве // Автоматика и телемеханика. – 2021. – №4. – С. 121–139.
  5. Халил Х. К. Нелинейные системы. – М.–Ижевск: НИЦ «Регулярная и хаотическая динамика», Институт компьютерных исследований, 2009.
  6. Anderson B. D. O. Adaptive systems, lack of persistency of excitation and bursting phenomena // Automatica. – 1985. – Vol. 21, No. 3. – P. 247–258.
  7. Annaswamy A. M., Skantze F. P., Loh A.-P. Adaptive control of continuous time systems with convex/concave parametrization // Automatica. – 1998. – Vol. 34, No. 1. – P. 33–49.
  8. Arslan G., Basar T. Disturbance attenuating controller design for strict-feedback systems with structurally unknown dynamics // Automatica. – 2001. – Vol. 37, No. 8. – P. 1175–1188.
  9. Campion G., Bastin G. Analysis of an adaptive controller for manipulators: Robustness versus flexibility // Systems & Control Letters. – 1989. – Vol. 12, No. 3. – P. 251–258.
  10. Chopra N., Spong M. W. Output synchronization of nonlinear systems with relative degree one // Recent Advances in Learning and Control. – Springer, London, 2008. – Vol. 371. – P. 51–64.
  11. Farza M., M’saad M., Maatoug T., Kamoun M. Adaptive observers for nonlinearly parameterized class of nonlinear systems // Automatica. – 2009. – Vol. 45, No. 10. – P. 2292–2299.
  12. Furtat I. B. Robust synchronization of the structural uncertainty nonlinear network with delay and disturbances // IFAC Proc. Volumes (IFAC-PapersOnline), 11th IFAC Int. Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP–2013. – 2013. – P. 227–232.
  13. Furtat I., Gushchin P. Nonlinear feedback control providing plant output in given set // Int. Journal of Control. – 2021. – DOI: https://doi.org/10.1080/00207179.2020.1861336.
  14. Goodwin G. C., Mayne D. Q. A parameter estimation perspective of continuous time model reference adaptive control // Automatica. – 1987. – Vol. 23, No. 1. – P. 57–70.
  15. Hashim Z. S., Ibraheem I. K. A relative degree one modified active disturbance rejection control for four-tank level control system // Int. Review of Applied Sciences and Engineering. – 2021. – Vol. 8, No. 2. – P. 157–166.
  16. Ioannou P. A., Sun J. Robust Adaptive Control. – Courier Corporation, 2012.
  17. Narendra K. S., Annaswamy A. M. Stable Adaptive Systems. – Courier Corporation, 2012.
  18. Polycarpou M. M., Ioannou P. A. A robust adaptive nonlinear control design // Automatica. – 1996. – Vol. 32, No. 3. – P. 423–427.
  19. Rifai K. E., Youcef-Toumi K. Robust adaptive control of switched system. – InTech, Switched Systems, 2009.
  20. Tao G. Multivariable adaptive control: A survey // Automatica. – 2014. – Vol. 50, No. 11. – P. 2737–2764.
  21. Zhao G., Chen G., Mi J. Overcoming a fundamental limitation of linear systems with generalized first order reset element // Proc. of the 37th Chinese Control Conference (CCC). – 2018. – doi: 10.23919/ChiCC.2018.8483381.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).