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Fractional discrete model of an electrical drive with brushless micro-motor

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Języki publikacji
EN
Abstrakty
EN
The use of fractional-order calculus for system modeling is a good alternative to well-known classic integer-order methods, primarily due to the precision with which the modeled object may be mapped. In this study, we created integer and fractional discrete models of a real object – a highspeed brushless micro-motor. The accuracy of the models was verified and compared.
Rocznik
Strony
421--427
Opis fizyczny
Bibliogr. 36 poz., rys., tab.
Twórcy
autor
  • Institute of Applied Computer Science, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924 Łódź, Poland
autor
  • Institute of Applied Computer Science, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924 Łódź, Poland
  • Institute of Applied Computer Science, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924 Łódź, Poland
autor
  • Institute of Applied Computer Science, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924 Łódź, Poland
Bibliografia
  • [1] A.A. Kilbas, H. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, New York, NY, USA: Elsevier Science Inc, 2006.
  • [2] I. Podlubny, Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications, San Diego, California: Academic Press, 1999.
  • [3] K.S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, New York: John Wiley & Sons, 1993.
  • [4] Y. Chen, I. Petráš, and D. Xue, “Fractional order control – A tutorial”, in Proceedings of the American Control Conference, (St. Louis, MO, USA), 2009.
  • [5] A.M. Lopes and J.A. Tenreiro MacHado, “Fractional-order model of a non-linear inductor”, Bull. Pol. Ac.: Tech. 67 (1), 61–67 (2019).
  • [6] P.A. Laski, “Fractional-order feedback control of a pneumatic servo-drive”, Bull. Pol. Ac.: Tech. 67 (1), 53–59 (2019).
  • [7] A. Gligor and T. M. Dulǎu, “Fractional Order Controllers Versus Integer Order Controllers”, in Procedia Eng. 181, 538–545 (2017).
  • [8] L. Majka, “Using Fractional Calculus in an Attempt at Modeling a High Frequency AC Exciter”, in Lecture Notes in Electrical Engineering, vol. 559, pp. 55–71, Springer Verlag, 2020.
  • [9] G.L. Grandi and J.O. Trierweiler, “Tuning of fractional order PID controllers based on the frequency response approximation method”, in IFAC PapersOnLine, pp. 982–987, Elsevier Ltd, 2019.
  • [10] F. Merrikh-Bayat, N. Mirebrahimi, and M.R. Khalili, “Discretetime fractional-order PID controller: Definition, tuning, digital realization and some applications”, Int. J. Control Autom. Syst. 13, 81–90, 2015.
  • [11] O. Aydogdu and M. Korkmaz, “Optimal Design of a Variable Coefficient Fractional Order PID Controller by using Heuristic Optimization Algorithms”, Int. J. Adv. Comp. Sci. Appl. 10 (3), 314–321 (2019).
  • [12] I. Petráš and B.M. Vinagre, “Practical application of digital fractional-order controller to temperature control”, Proc. Acta Montanistica Slovaca 7 (2), 131–137 (2002).
  • [13] P. Ostalczyk and P. Duch, “Closed – Loop system synthesis with the variable-, fractional – Order PID controller”, in 2012 17th International Conference on Methods and Models in Automation and Robotics, MMAR 2012, 2012.
  • [14] J. Baranowski, W. Bauer, M. Zagórowska, and P. Piątek, “On Digital Realizations of Non-integer Order Filters”, Circuits Syst. Signal Process. 35 (6), 2083–2107 (2016).
  • [15] I. Petráš, S. Grega, and L. Dorčák, “Digital Fractional Order Controllers Realized by PIC Microprocessor: Experimental Results”, tech. rep., Department of Informatics and Process Control, 5 2003.
  • [16] P. Ostalczyk, D.W. Brzeziński, P. Duch, M. Łaski, and D. Sankowski, “The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control”, Cent. Eur. J. Phys. 11 (6), 750–759 (2013).
  • [17] A. Rhouma and H. Sami, “A Microcontroller Implementation of Fractional Order Controller”, Int. J. Contr. Syst. Robot. 2, 122–127 (2017).
  • [18] A. Tepljakov, E. Petlenkov, and J. Belikov, “Embedded system implementation of digital fractional filter approximations for control applications”, in Proceedings of the 21st International Conference on Mixed Design of Integrated Circuits and Systems, MIXDES 2014, 2014.
  • [19] MathWorks, “System Identification for PID Control – MATLAB\Simulink”.
  • [20] A. Tepljakov, E. Petlenkov, and J. Belikov, “FOMCON: a MATLAB Toolbox for Fractional-order System Identification and Control”, Int. J. Microelectron. Comp. Sci. 2 (2), 51–62 (2011).
  • [21] A. Tepljakov, E. Petlenkov, and J. Belikov, “Closed-loop identification of fractional-order models using FOMCON toolbox for MATLAB”, in Proceedings of the Biennial Baltic Electronics Conference, BEC, 2014.
  • [22] B.B. Alagoz, A. Tepljakov, A. Ates, E. Petlenkov, and C. Yeroglu, “Time-domain identification of One Noninteger Order Plus Time Delay models from step response measurements”, International Journal of Modeling, Simulation, and Scientific Computing 10 (1), 19410112 (2019).
  • [23] K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag Berlin Heidelberg, 2010.
  • [24] L. Dorčák, “Numerical Models for the Simulation of the Fractional-Order Control Systems”, Slovak Academy of Sciences, Institute of Experimental Physics, 1994.
  • [25] A. Oustaloup, La dérivation non entière: théorie, synthèse et applications, Paris: Hermes, 1995.
  • [26] P. Ostalczyk, P. Duch, and D. Sankowski, “Fractional-Order Backward-Difference Grünwald-Letnikov and Horner Simplified Forms Evaluation Accuracy Analysis”, Automatyka 15 (3), 443–453 (2011).
  • [27] D.W. Brzeziński and P. Ostalczyk, “The Grünwald-Letnikov formula and its equivalent Horner’s form accuracy comparison and evaluation for application to fractional order PID controllers”, in 2012 17th International Conference on Methods and Models in Automation and Robotics, MMAR 2012, 2012.
  • [28] D.W. Brzeziński and P. Ostalczyk, “About accuracy increase of fractional order derivative and integral computations by applying the Grünwald-Letnikov formula”, Commun. Nonlinear Sci. Numer. Simul. 40, 151–162 (2016).
  • [29] P. Ostalczyk, “Remarks on five equivalent forms of the fractional-order backward-difference”, Bull. Pol. Ac.: Tech. 62 (2), 271–278 (2014).
  • [30] STMicroelectronics, “STM32F745xx STM32F746xx ARM-based Cortex-M7 32b MCU+FPU, 462DMIPS up to 1MB Flash/320+16+4KB RAM, USB OTG HS/FS, ethernet, 18TIMs, 3ADCs, 25 com itf, cam & LCD Datasheet – production data”, 2016, [Online]. Available: https://www.st.com/resource/en/datasheet/stm32f746zg.pdf [Accessed: 17-Apr-2020].
  • [31] Omron, “E6B2-CWZ6C 1000P/R 2M | OMRON Industrial Automation”, 2019, [Online]. Available: http://www.ia.omron.com/product/ item/2450/ [Accessed: 17-Apr-2020].
  • [32] ABC-RC, “A2212 – 1000KV BLDC Brushless Motor 2-3S –135W”, 2020, [Online]. Available: https://abc-rc.pl/product-pol-6764-Silnik-ABC-Power-A2212-1000KV-2-3S-135W-ciag-820g.html [Accessed: 17-Apr-2020].
  • [33] S. Kamalasadan and A. Hande, “A PID Controller for Real-Time DC Motor Speed Control using the C505C Microcontroller”, 17 th International Conference of Computer Applications in Industry and Engineering 850, 34–39 (2004).
  • [34] A. Tepljakov, E. Petlenkov, and J. Belikov, “FOMCON: Fractional-Order Modeling and Control Toolbox for MATLAB”, in MIXDES 2011, 18th International Conference “Mixed Design of Integrated Circuits and Systems”, Gliwice, Poland, 2011, pp. 684–689.
  • [35] W.Y. Svrcek, D.P. Mahoney, and B.R. Young, A Real-Time Approach to Process Control, John Wiley & Sons, Ltd, 2nd ed., 2007.
  • [36] M. Matusiak, M. Bąkała, and R. Wojciechowski, “Optimal Digital Implementation of Fractional-Order Models in a Microcontroller”, Entropy 22, 366 (2020).
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-28b57b7e-6ae6-4ebd-a5ed-5ed9cc791b05
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