FREQUENCY FEATURES OF THE NUMERICAL METHOD SAMPLING OF DIGITAL CONTROL SYSTEMS

Authors

  • V. I. Moroz Lviv Polytechnic National University, L’viv, Ukraine, Ukraine
  • A. B. Vakarchuk Lviv Polytechnic National University, L’viv, Ukraine, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2022-2-19

Keywords:

Bode diagram, control theory, digital control system, discrete transfer function, linear system, numeric integrators, structure models, z-transform

Abstract

Context. The studies of the frequency properties of the explicit multistep numerical integrators which use for sampling of continuous transfer function in the digital control systems, are conducted in this article. Numerical integrators in such systems implement as an integral parts of the digital regulators.

Objective. The goal of this research is an analysis of the behavior of explicit numerical integrators of different orders, which areused to discretize continuous systems, in order to study their impact on the properties of the synthesized digital system.

Method. Numerical methods of integration are considered as digital filters, the behavior of which is studied by the frequency characteristics method. To do this, the z-transform apparatus was used. Integrators’ discrete transfer functions were found for frequency analysis using the Control Systems Toolbox package of the mathematical application MATLAB. For further analysis, two closed feedback test structures were used: with integrators in the forward channel and in the feedback loop. Both variants of structures were studied by the frequency characteristics method for sampling using numerical integrators of 1st–6th orders.

Results. The inefficiency of using high-order numerical integrators for continuous systems’ discretization is shown. Given the behavior of the frequency characteristics of test systems, the most rational is the use of low-order integrators, namely – the first and second orders. Establishing the cause of this phenomenon requires additional research, in particular, to identify the possible impact of additional zeros and poles of discrete transfer functions of the numerical integrators.

Conclusions. The use of low-order integrators, namely the first and second orders, is the most rational for sampling of digital control systems and the inefficiency of using high-order numerical integrators to sample continuous systems is proven.

Author Biographies

V. I. Moroz, Lviv Polytechnic National University, L’viv, Ukraine

Prof., Dr. Sc., Professor of Institute of Power Engineering and Control Systems

A. B. Vakarchuk, Lviv Polytechnic National University, L’viv, Ukraine

PhD Student of Institute of Power Engineering and Control Systems

References

Åström K., Wittenmark B. Computer-Controlled Systems: Theory and Design, Third Edition. New York, Published by Dover Books on Electrical Engineering, 2013, 578 p. DOI 10.1108/ir.1998.04925fae.003

Dorf R. C., Bishop R. H. Modern Control Systems. 12th Edition. New Jersey, Pearson, 2010, 1104 p. DOI 10.1002/rnc.1054

Jury E. Sampled-data control systems. New York, John Wiley & Sons, Inc., 1958, 453 p. DOI: 10.2307/3007623

Jury E. Theory and Application of the Z-Transform Method. Melbourne, Krieger Pub Co, 1973, 330 p.

MATLAB Environment. [Electronic resource] ©1994–2021. The MathWorks, Inc. Access mode: https://www.mathworks.com/products/matlab.html

Control System Toolbox: Design and analyze control systems. [Electronic resource] ©1994–2021. The MathWorks, Inc. Access mode: https://www.mathworks.com/products/control.html?s_tid=srchtitle

Johnson M., Moradi M. (Editors)PID Control: New Identification and Design Methods. London, ©Springer-Verlag London Limited, 2005, 544 p. DOI: 10.1007/1-84628-148-2

Tou J. Digital and Sampled-Data Control System (McGrawHill Electrical and Electronic Engineering Series). New York, McGraw Hill Book Co, January 1959, 631 p.

Chua L., Pen-Min Lin Computer-aided analysis of electronic circuits: algorithms and computational techniques. Englewood Cliffs, N. J., Prentice-Hall, 1975, 737 p.

Hairer E., Nørsett S., Wanner G. Solving Ordinary Differential Equations I: Nonstiff Problems. Second Edition. Berlin, Нeidelberg, Springer, 2008, 528 p. DOI: 10.1007/978-3-540-78862-1

Ogata Katsuhiko. Discrete-Time Control Systems, 2nd edition. Englewood Cliffs, N. J.: Prentice-Hall, 1995, 760 p.

Kuo B. Digital Control Systems, 2nd Edition (The Oxford Series in Electrical and Computer Engineering. Oxford, Oxford University Press, 1995, 751 p.

Khaitan S., Gupta A. High Performance Computing in Power and Energy Systems, Power Systems Series. Berlin, Heidelberg, Springer-Verlag, 2013, 384 p. DOI 10.1007/978-3-642-32683-7_2

Lozynskyi О., Paranchuk Ya., Moroz V., Stakhiv P. Computer Model of the Electromechanical System of Moving Electrodes of an Arc Furnace with a Combined Control Law, 2019 IEEE 20th International Conference on Computational Problems of Electrical Engineering (CPEE). September 15–18, 2019, proceedings. Lviv, Ukraine. DOI: 10.1109/CPEE47179.2019.8949136

Moroz V. The Numerically-Analytic Method for the RealTime Computer Simulation, 9th International Workshops “Computational Problems of Electrical Engineering”, September 16–20, 2008, proceedings, Volume 1. Ukraine, Alushta (Crimea), pp. 162–164.

Smith J. Mathematical Modeling and Digital Simulation for Engineers and Scientists. Second Edition. New Jersey, Wiley-Interscience, 448 p. DOI: 10.2307/2531888

Moroz V., Vakarchuk A. Numerical Integrators on Electrical Circuits’ Transient Calculation, 22nd International Conference “Computational Problems of Electrical Engineering” (CPEE-2021), September 15–17th, 2021 : proceedings. Šumava, Czech Republic. DOI: 10.1109/CPEE54040.2021.9585266

Moroz V., Vakarchuk A. Why High-Order Integrators Not Rational on Electrical Systems’ Computer Calculation, IEEE 20th International Conference on Modern Electrical and Energy System September 21–24, 2021 : proceedings. Kremenchuk Mykhailo Ostrohradskyi National University,Ukraine. DOI: 10.1109/MEES52427.2021.9598791

Downloads

Published

2022-07-02

How to Cite

Moroz, V. I., & Vakarchuk, A. B. (2022). FREQUENCY FEATURES OF THE NUMERICAL METHOD SAMPLING OF DIGITAL CONTROL SYSTEMS . Radio Electronics, Computer Science, Control, (2), 201. https://doi.org/10.15588/1607-3274-2022-2-19

Issue

No. 2 (2022): Radio Electronics, Computer Science, Control

Section

Control in technical systems

License

Copyright (c) 2022 V. I. Moroz, A. B. Vakarchuk

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.