Scientific Journal

Applied Aspects of Information Technology

DISCRETE APPROXIMATION OF CONTINUOUS OBJECTS WITH MATLAB
Abstract:

This work is dedicated to the study of various discrete approximation methods for continuous links, which is the obligatory step  in the digital control systems synthesis for continuous dynamic objects and the guidelines development for performing these opera tions using the MATLAB programming system. The paper investigates such sampling methods as pulse-, step-, and linearly invariant  Z-transformations, substitution methods based on the usage of numerical integration various methods and the zero-pole correspond ence method. The paper presents examples of using numerical and symbolic instruments of the MATLAB to perform these opera tions, offers an m-function improved version for continuous systems discretization by the zero-pole correspondence method, which  allows this method to approach as step-invariant as linearly invariant Z-transformations; programs for continuous objects discrete  approximation in symbolic form have been developed, which allows to perform comparative analysis of sampling methods and sys tems synthesized with their help and to study quantization period influence on sampling accuracy by analytical methods. A compari son of discrete transfer functions obtained by different methods and the corresponding reactions in time to different signals is per formed. Using of the developed programs it is determined that the pulse-invariant Z-transformation can be used only when the input  of a continuous object receives pulse signals, and the linear-invariant transformation should be used for intermittent signals at the  input. The paper also presents an algorithm for applying the Tustin method, which corresponds to the replacement of analogue inte gration by numerical integration using trapezoidal method. It is shown that the Tustin method is the most suitable for sampling of  first-order regulators with output signal limitation. The article also considers the zero-pole correspondence method and shows that it  has the highest accuracy among the rough methods of discrete approximation. Based on the performed research, recommendations  for the use of these methods in the synthesis of control systems for continuous dynamic objects are given. 

Authors:
Keywords
DOI
https://doi.org/10.15276/aait.02.2021.5
References

1. Goodwin, G. Grebe, S. & Salgado, M. “Design of Control Systems” (in Russian). Publ. Binom.  Knowledge Laboratory. 2004. 911 p. 

2. Kotsegub, P. Kh. & Kotsegub, Kh. P. “Theory of Pulsed Electromechanical systems” (in Russian),  Donetsk National Technical University. Donetsk: Ukraine. 2004. 262 p. 

3. Kalechman, M. “Practical MATLAB Applications for Engineers”. CRC Press Taylor & Francis  Group. New-York: USA. 2007. 708 p. 

4. Andrievsky, B. R. & Fradkov, A. L. “Selected Chapters of the Theory of Automatic Control with  Examples in the MATLAB Language” (in Russian). Nauka Publications. 2000. 475 p. 

5. Ishmatov, Z. Sh., Kazakov, E. G. & Mezeushev, D. V. “Modern Control Theory: Laboratory Prac tice”. UPI (Ural Polytechnic Institute). Yekaterinburg: Russian Federation, 2006. 50 p.

6. Eihab B. M. Bashier. “Practical Numerical and Scientific Computing with MATLAB and Python”.  CRC Press Taylor & Francis Group. New-York: USA. 2020. 349 p. 

7. “MATLAB. The Language of Technical Computing”. [Software documentation] / MATLAB – Ac tive link: https://uk.mathworks.com/help/matlab/. 

8. Huei-Huang, L. “Programming and Engineering Computing with MATLAB”. SDC Publications. 2020. 520 p. 

9. “MATLAB. The Language of Technical Computing”. [Software documentation] / MATLAB – Ac tive link: https://uk.mathworks.com/help/control/index.html. 

10. Dingyu, X. & Yang Quan C. “Modeling, Analysis and Design of Control Systems in MATLAB and  Simulink”. Publ. World Scientific. 2015. 580 p. 

11. “MATLAB. The Language of Technical Computing”. [Software documentation] / MATLAB – Ac tive link: https://uk.mathworks.com/help/symbolic/. 

12. Desmond, J., Higham, Nicholas J. Higham “MATLAB Guide”. Third Edition – SIAM-Society for  Industrial and Applied Mathematics. 2018. 502 p. 

13. Popovich, M. G. & Kovalchuk, O. V “Theory of Automatic control” (in Russian). Publ. Libid, Kiev:  Ukraine. 2007. 656 p.  

14. Miroshnik, I. V. “Automatic Control theory. Linear Systems”(in Russian). SPb.-Peter: Russian  Federation. 2005. 336 p. 

15. Phillips, C. A., Nagle, H. & Chakrabortty. А. “Digital Control System Analysis & Design”. [4th  Edition]. Publ. Pearson. 1995. 528 p. 

16. Peresada, S. M., Kovbasa, S. M. & Zaichenko, Yu. M. “Dynamic Performances of the Shunt Active  Power Filter Control System”. Applied Aspects of Information Technology. Publ. Nauka i Tekhnika. 2021;  Vol.4 No.1: 47–56. DOI: https://doi.org/10.15276/aait.01.2021.4. 

17. Ogata, K. “Discrete-Time Control Systems”. [ 2nd Edition]. Pearson. 1995. 745 p. 18. Ogata K. “Solving Control Engineering Problems with MATLAB (MATLAB Curriculum Series)”.  Englewood Cliffs. NJ: Prentice Hall. 2014. 527 p. 

19. Tolochko, O. I. “Analysis and Synthesis of Electro-Mechanical Systems for the Support of the  State” (in Russian). Donetsk: Ukraine. Nord-Press. 2004. 298 p.  

20. Tolochko. O. I. & Rozkaryaka, P.I. “Analysis of the Shortfalls in the up-to-date Discrete Systems in  the MATLAB Package” (in Russian). Journal Elektrotekhnika and Elektroenergetika. Zaporizhzhya: Ukraine. ZNTU (Zaporizhzhya National Technical University). 2006; No.1: 10–14.  

21. Tolochko, O. I., Kaluhin, D. V., Palis, Stefan & Oshurko, S. V. “Field Weakening Control for In duction Motors Based on Copper and Iron Losses Minimization”. Applied Aspects of Information Technolo gy. Publ. Nauka i Tekhnika. 2020; Vol.3 No.2: 44–57. DOI: https://doi.org/10.15276/aait.02.2020.3.

22. Sadovoi, O. V., Klyuyev, O. V., Sokhina, Yu. V. & Filin, I. V. “Information System of Minimiza tion Consumption Reactive Power in Asynchronous Electric Drive with Vector Control”. Applied Aspects of  Information TechnologyPubl. Nauka i Tekhnika. 2020; Vol.3 No.2: 74–84. DOI: https://doi.org/10.15276/  aait.02.2020.5. 

23. Tolochko, O. I. & Rozkaryaka, P. I. “A Digital Setting Device for Optimal Control on Positional  Electric Drives” (in Russian). Proceedings of Donetsk National Technical University. Donetsk: Ukraine. 2010; No.1: 97–109.  

24. Sinchuk, O. N., Kozakevych, I. А. & Vornikov, D. N. “Control System of Wind Generator Based  onSwitched Reluctance Motor”. Applied Aspects of Information Technology. Publ. Nauka i Tekhnika. 2019;  Vol.2 No.3: 230–242. DOI: https://doi.org/10.15276/aait.03.2019.5. 

25. Arsirii, O. O., Yadrova, M. V., Kondratyev,S. B. & Stelmakh, D. E. “Development of the Intelligent  Softwareand Hardware Subsystem Forcapturing an Object by Robotmanipulator”. Herald of Advanced In formation TechnologyPubl. Nauka i Tekhnika. 2020; Vol.3 No.2: 42–51. DOI: https://doi.org/10.15276/ hait.02.2020.4. 

26. Starostin, S. S. & Tolochko, O. І. “The Value of Parameters in Digital Controllers of Electric Drives  by Design Methods of Continuous Systems” (in Russian). Collection of Scientific works of DSTU (Dnipro  State Technical University). Dneprodzerzhinsk: Ukraine. 2007. p. 179–182.
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Last download:
22 Oct 2021

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