Robust adaptive control system with unknown delay compensation under nonstationarity and external disturbances

Authors

  • Михайло Петрович Лисиця Poltava National Technical Yuri Kondratyuk University Pershotravnevyi avenue, 24, Poltava, Ukraine, 36011, Ukraine https://orcid.org/0000-0002-9484-7098
  • Павел Михайлович Лисица Poltava National Technical Yuri Kondratyuk University Pershotravnevyi avenue, 24, Poltava, Ukraine, 36011, Ukraine https://orcid.org/0000-0001-5462-2284

DOI:

https://doi.org/10.15587/1729-4061.2015.42814

Keywords:

robust control system, variable delay, non-stationary object model, observer of pseudoderivatives

Abstract

Robust control system of non-stationary object with unknown variable limited state delay under disturbances was synthesized using only the measured value of the object output signal and calculated values of the observer of derivatives of additional loop and observer of pseudoderivatives of the main loop.

The idea of calculation of pseudoderivatives lies in using the calculation formula of derivatives with the introduction of additional corrective matrix, which in the last line, at the observer matrix dimension of ³2, includes the values, accordingly depending on the number m, determining the gain of pseudoderivatives.

Based on the proposed calculation algorithm of pseudoderivatives instead of the algorithm of derivatives of the observer of the main control loop, object control error with the specified uncertainty class of up to 7×10-4, which is by 37 times less than the error of the current system with the same value of the coefficient m was reduced. Comparative transients confirm the effectiveness of the proposed adaptive control method of non-stationary objects of the given uncertainty class based on the observer of pseudoderivatives.

Author Biographies

Михайло Петрович Лисиця, Poltava National Technical Yuri Kondratyuk University Pershotravnevyi avenue, 24, Poltava, Ukraine, 36011

PhD, Associate professor

The department of automation and electric drives

Павел Михайлович Лисица, Poltava National Technical Yuri Kondratyuk University Pershotravnevyi avenue, 24, Poltava, Ukraine, 36011

PhD, Associate professor

The department of automation and electric drives

References

  1. Kharitonov, V. L. (1978). Asimptoticheskaya ustoichivost’ semeystva sistem differentsial’nykh uravneniy. Differentsial’nye uravneniуa, 14 (11), 2086–2088.
  2. Polуak, B. Т., Shcherbakov, P. S. (2002). Robastnaуa ustoychivost’ i upravlenie. Мoscow: Nauka, 303.
  3. Miroshnik, I. V., Nikiforov, V. O., Fradkov, A. L. (2000). Nelineynoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami. SPb.: Nauka, 549.
  4. Tsykunov, А. М. (2000). Adaptivnoe upravlenie s kompensatsiey vliyaniya zapazdyvaniya v upravlyayushchem vozdeystvii. Izvestiya RAN. Teoriya i sistemy upravleniya, 4, 78-81.
  5. Tsykunov, А. М. (2002). Adaptivnyy prediktor i ego primenenie v sistemakh upravleniya s zapazdyvaniem. Sb. «Avtomatika i elektromekhanika». Astrakhanskiy gosudarstvennyy tekhnicheskiy universitet,112-116.
  6. Starosel’skiy, A. V. (2014). Bystrodeystvuyushchiy adaptivnyy nablyudatel’ v sisteme kompensatsii neizvestnogo zapazdyvaniya. Moskovskiy gosudarstvennyy institut elektroniki i matematiki. Moscow. Available at: http://www.nostras.ru/matematika/adaptivnaya_sistema_kompensacii.html
  7. Imangazieva, A. V. (2011). Robastnaya sistema avtomaticheskogo upravleniya s kompensatsiey zapazdyvaniya v usloviyakh nestatsionarnosti. Vestn. Astrakhan. gos. tekhn. un-ta. Seriya: Upravlenie, vychisl. tekhn. inform., 2, 30–36.
  8. Furtat, I. B. (2007). Adaptivnoe upravlenie po vykhodu dlya sistem s zapazdyvaniem po upravleniyu na osnove modifitsirovannogo algoritma adaptatsii vysokogo poryadka. Trudyi VI Mezhdunarodnoy konferentsii «Identifikatsiya sistem i zadachi upravleniya». Мoscow, 595–606.
  9. Khalil, H. K. (2000). Universal integral controllers for minimum-phase nonlinear systems. IEEE Transactions on Automatic Control, 45 (3), 490–494. doi: 10.1109/9.847730
  10. Doyle, J. C., Glover, K., Khargonekar, P. P., Francis, B. A. (1989). State-space solutions to standard H/sub 2/ and H/sub infinity / control problems. IEEE Transactions on Automatic Control, 34 (8), 831–847. doi: 10.1109/9.29425
  11. Glover, K. (1986). Robust stabilization of linear multivariable systems: relations to approximation. International Journal of Control, 43 (3), 741–766. doi: 10.1080/00207178608933499
  12. Hassan, L., Zemoucke, A., Boutayer, M. (2011). H¥ unknown input observers design for a class of nonlinear time-delay systems. Preprints of 18th IFAC Word Congress, 3879–3884. doi: 10.3182/20110828-6-it-1002.01583
  13. Han, Q.-L. (2002). Robust stability of uncertain delay-differential systems of neutral type. Automatica, 38 (4), 719–723. doi: 10.1016/s0005-1098(01)00250-3
  14. Ivănescu, D., Niculescu, S.-I., Dugard, L., Dion, J.-M., Verriest, E. I. (2003). On delay-dependent stability for linear neutral systems. Automatica, 39 (2), 255–261. doi: 10.1016/s0005-1098(02)00227-3
  15. Nguang, S. K. (2000). Robust stabilization of a class of time-delay nonlinear systems. IEEE Transactions on Automatic Control, 45 (4), 756–762. doi: 10.1109/9.847117
  16. Gao, H., Chen, T., Lam, J. (2008). A new delay system approach to network-based control. Automatica, 44 (1), 39–52. doi: 10.1016/j.automatica.2007.04.020
  17. Liu, J., Liu, X., Xie, W.-C. (2008). Delay-dependent robust control for uncertain switched systems with time-delay. Nonlinear Analysis: Hybrid Systems, 2 (1), 81–95. doi: 10.1016/j.nahs.2007.04.001

Downloads

Published

2015-06-23

How to Cite

Лисиця, М. П., & Лисица, П. М. (2015). Robust adaptive control system with unknown delay compensation under nonstationarity and external disturbances. Eastern-European Journal of Enterprise Technologies, 3(9(75), 39–45. https://doi.org/10.15587/1729-4061.2015.42814

Issue

Vol. 3 No. 9(75) (2015): Information and controlling system

Section

Information and controlling system

License

Copyright (c) 2015 Михайло Петрович Лисиця, Павел Михайлович Лисица

Creative Commons License

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

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.