

Adaptive disturbance compensation in linear systems with state and input delays
https://doi.org/10.17586/0021-3454-2024-67-12-999-1009
Abstract
The problem of adaptive compensation of an external previously unknown disturbance affecting a linear object with delays in state and control signal is solved. The disturbance is not coordinated with the control, and only the output variable under control is accessible for direct measurements. The disturbance is modeled by an autonomous dynamic model with unknown parameters, and the control law is formed based on the principle of the internal model. The special parameterization of the external disturbance and the control error expansion scheme used allow to ensure the limitedness of all signals and asymptotic fulfillment of the control goal. Theoretical statements are illustrated by results of computer simulation
About the Authors
D. N. GerasimovRussian Federation
Dmitry N. Gerasimov - PhD, Associate Professor, Faculty of Control Systems and Robotics
St. Petersburg
A. V. Paramonov
Russian Federation
Alexey V. Paramonov - PhD, Associate professor, Faculty of Control Systems and Robotics
St. Petersburg
V. O. Nikiforov
Russian Federation
Vladimir O. Nikiforov - Dr. Sci., Professor, Vice-Rector for Research
St. Petersburg
References
1. Gu K., Kharitonov V., Chen J. Stability of Time-delay systems, Springer, 2003, 356 р.
2. Richard J.-P. Automatica, 2003, no. 10(39), pp. 1667–1694.
3. Niculescu S.-I., Gu K. Advances in Time-Delay Systems, Berlin Heidelberg, Springer-Verlag GmbH, 2004.
4. Karafyllis I., Krstic M. Predictor Feedback for Delay Systems: Implementations and Approximations, Birkhauser, 2010.
5. Fridmann E. Introduction to Time-Delay Systems. Analysis and Control, Switzerland, Springer International Publishing, 2014.
6. Castillo-Toledo B., Nunez-Perez E. Kybernetika, 2003, no. 4(39), pp. 415–432.
7. Yoon S.Y., Lin Z. Proc. of the 19th IFAC World Congress, 2014, no. 3(47), pp. 9780–9785.
8. Francis D.A., Wonham W.N. Applied Mathematics and Optimization, 1975, no. 4(2), pp. 170–194.
9. Davison E.J. IEEE Trans. on Automatic Control, 1976, no. 1(21), pp. 25–34.
10. Nikiforov V.O., Gerasimov D.N. Adaptive Regulation: Reference Tracking and Disturbance Rejection, Springer, 2022.
11. Bobtsov A.A., Pyrkin A.A. Journal of Computer and Systems Sciences International, 2008, no. 4(47), pp. 513–517.
12. Pyrkin A., Smyshlyaev A., Bekiaris-Liberis N., Krstic M. American Control Conf., San-Francisco, Baltimore, USA, 2010, DOI: 10.1109/ACC.2010.5531131.
13. Pyrkin A., Bobtsov A. IEEE Trans. on Automatic Control, 2016, no. 12(61), pp. 4229–4234.
14. Bobtsov A.A., Pyrkin A.A. et al. Automation & Remote Control, 2015, no. 12(76), pp. 2124–2142.
15. Basturk H., Krstic M. Automatica, 2015, vol. 58, рр. 131–138.
16. Gerasimov D.N., Paramonov A.V., Nikiforov V.O. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, no. 6(16), pp. 1023–1030. (in Russ.)
17. Gerasimov D.N., Paramonov A.V., Nikiforov V.O. Intern. J. of Control, 2020, no. 7(93), pp. 1596–1604.
18. Gerasimov D.N., Miliushin A.S., Nikiforov V.O. Intern. J. of Adaptive Control and Signal Processing, 2019, pp. 900–912, DOI:10.1002/acs.2999.
19. Gerasimov D.N., Miliushin A.S., Paramonov A.V., Nikiforov V.O. Journal of Instrument Engineering, 2019, no. 9(62), pp. 772–781. (in Russ.)
20. Gerasimov D., Paramonov A., Nikiforov V. Intern. J. of Control, 2020, no. 7(93), pp. 1596–1604.
21. Nikiforov V.O., Paramonov A.V., Gerasimov D.N. IFAC-PapersOnLine, 2023, no. 2(56), pp. 9179–9184.
22. Basturk H. Automatica, 2017, vol. 76, рр. 169–176.
23. Van Huan B., Margun A., Kremlev A.S., Dobriborsci D. Proc. of the 20th Intern. Conf. on Informatics in Control, Automation and Robotics, 2023, vol. 2, рр. 236–243.
24. Van Huan B. Metod otsenivaniya vektora peremennykh sostoyaniya dlya klassa nelineynykh nestatsionarnykh sistem v usloviyakh neopredelennostey (Method of Estimating the Vector of State Variables for a Class of Nonlinear Nonstationary Systems under Uncertainty), Candidate’s thesis, St. Petersburg, 2024. (in Russ.)
25. Gerasimov D.N., Paramonov A.V., Nikiforov V.O. Proc. of European Control Conference (ECC), St. Petersburg, Russia, 2020, рр. 65–70.
26. Thowsen A. Intern. J. of Systems Science, 1981, no. 12(12), pp. 1485–1492.
27. Zhou B. Automatica, 2014, vol. 50, рр. 1434–1443.
28. Narendra K., Annaswamy A. Stable Adaptive Systems, NJ, Prentice Hall, 1989.
29. Ioannou P., Sun J. Robust Adaptive Control, NJ, Prentice–Hall, 1996.
30. Paramonov A.V., Gerasimov D.N., Nikiforov V.O. Proc. of the European Control Conference (ECC), Delft, Netherlands, 2021, рp. 2169–2174.
31. Isidori A. Lectures in Feedback design for Multivariable Systems, Springer, 2017, 413 р.
Review
For citations:
Gerasimov D.N., Paramonov A.V., Nikiforov V.O. Adaptive disturbance compensation in linear systems with state and input delays. Journal of Instrument Engineering. 2024;67(12):999-1009. (In Russ.) https://doi.org/10.17586/0021-3454-2024-67-12-999-1009