IDENTIFICATION OF THE MATHEMATICAL MODELS OF THE TECHNOLOGICAL OBJECTS FOR ROBUST CONTROL SYSTEMS

Authors

  • N. M. Lutska National University of Food Technology, Kiev, Ukraine
  • A. P. Ladanyuk National University of Food Technology, Kiev, Ukraine
  • T. V. Savchenko National University of Trade and Economics, Kiev, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2019-3-18

Keywords:

Іdentification, production object, robust control, mathematical models, area of uncertainty

Abstract

Context. The problem of identification of the mathematical models of the technological objects on the basis of which the robust
control system is subsequently synthesized has been considered. The methods of identification of the mathematical models of the
technological objects for robust control are the target of the research.
Objective. The purpose of the research is to develop recommendations for the existing methods of identifying the mathematical
models of the technological objects for robust control to allow the effective application of the robust control systems as well as to
increase the energy efficiency of the system as a whole.
Method. The suggested recommendations for the identification of the mathematical models of the technological objects aimed at
the further synthesis of robust control are divided into two types – with a known and an unknown area of uncertainty. For the former with the mathematical model which is identified only in the nominal mode the existing methods for identifying the continuous models in accordance with the experimentally obtained data are preferable. Taking the multidimensionality and multiplicity of most technological objects into account, the structure of the model in the space of time variables is recommended. It has been suggested to reduce the area of uncertainty to the additive or multiplicative form for the identification of the mathematical models for which, in addition to the nominal model, identification of the area of uncertainty is stipulated. In this case, several models in different operating object modes are used, while the uncertainty is calculated as the distance between the nominal and other models on the frequency grid with the further approximation of the filters of the preassigned order.
Results. The suggested algorithm for identifying the mathematical models with the area of uncertainty has been implemented and
investigated for a production object – the subsystem of the levels of the diagonal extraction plant of a sugar-mill.
Conclusions. The performed experiments have confirmed the efficiency of the proposed calculation of the area of uncertainty of
the mathematical models of the technological objects, while the proposed recommendations for the identification of the mathematical models for robust control can be used in practice. Further research is aimed at identifying the area of uncertainty of the closed control systems.

Author Biographies

N. M. Lutska, National University of Food Technology, Kiev

PhD, Associate Professor of Department of Integrated Automated Control Systems

A. P. Ladanyuk, National University of Food Technology, Kiev

Dr. Sc., Professor of Department of Integrated Automated Control Systems

T. V. Savchenko, National University of Trade and Economics, Kiev

PhD, Associate Professor of Department of Program Engineering and Cybersecurity, Kyiv

References

Lutska N. M., Ladanyuk A. P. Optymal’ni ta robastni systemy keruvannja technolohichnymy ob’jektamy: monohrafija. Kyiv, Vydavnyctvo “Lira-K”, 2015, 288 p. [in Ukrainian]

Mackenroth U. Robust control systems. Theory and case studies. Berlin, Springer-Verlag Berlin Heidelberg, 2004, 520 p. DOI: 10.1007/978-3-662-09775-5

Ljung L. System identification: theory for the user. Second Ed. New Jersey, Prentice Hall PTR, 1999, 609 р.

Ljung L., Vicino A. Special issue on system identification, IEEE Transactions on Automatic Control, 2005, Vol. 50, No. 10, P. 1473. DOI: 10.1109/TAC.2005.856638

Soderstrom T., Van Den Hof P., Wahlberg B. et al. Introduction to the special issue on data-based modeling and system identification, Automatica, 2005, Vol. 41, pp. 357–358. DOI: 10.1016/j.automatica.2004.11.004

Douma S. G., Van Den Hof P. Relations between uncertainty structures in identification for robust control,

Automatica, 2005, Vol. 41, pp. 439–457. DOI:10.1016/j.automatica.2004.11.005

Douma S. G., Van Den Hof P. On the choice of uncertainty structure in identification for robust control, IEEE conference on decision and control: 41st international conference, Desember 2002: proceeding. Las Vegas, IEEE, 2002, pp. 4197–4202.

Douma S. G., Van Den Hof P. An alternative paradigm for probabilistic uncertainty bounding in prediction error identification, IEEE conference on decision and control, and the European Control: 44st international conference, 12–15 December 2005: proceeding. Seville, IEEE, 2005, pp. 4970–4975.

Chen J., Gu G. Control oriented system identification. New York, Wiley, 2000, 421 p. DOI: 10.1002/rnc.733

Milanese M., Vicino A. Optimal estimation theory for dynamic systems with set membership uncertainty: an overview, Automatica, 1991, Vol. 27 (6), pp. 997–1009. DOI: 10.1016/0005-1098(91)90134-N

Makila P. M., Partington J. R., Gustafsson T. K. Worst-case control-relevant identification, Automatica, 1995, Vol. 31

(12), pp. 1799–1819. DOI: 10.1016/0005-1098(95)00106-3

Oppenheim A. V., Schafer R. W. Digital signal processing. New Jersey, Prentice Hall, 1975, 585 p.

Boyd S., Vandenberghe L. Convex optimization. Cambridge University Press, 2004, 727 p. DOI:10.1017/CBO9780511804441

Downloads

Published

2019-10-01

How to Cite

Lutska, N. M., Ladanyuk, A. P., & Savchenko, T. V. (2019). IDENTIFICATION OF THE MATHEMATICAL MODELS OF THE TECHNOLOGICAL OBJECTS FOR ROBUST CONTROL SYSTEMS. Radio Electronics, Computer Science, Control, (3), 163–172. https://doi.org/10.15588/1607-3274-2019-3-18

Issue

No. 3 (2019): Radio Electronics, Computer Science, Control

Section

Control in technical systems

License

Copyright (c) 2019 N. M. Lutska, A. P. Ladanyuk, T. V. Savchenko

Creative Commons License

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

Creative Commons Licensing Notifications in the Copyright Notices

The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.

The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.

The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.