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Application of Fractional-Order Calculus to Improve the Mathematical Model of a Two-Mass System with a Long Shaft

Author

Listed:
  • Andriy Lozynskyy

    (Institute of Power Engineering and Control Systems, Lviv Polytechnic National University, 79-013 Lviv, Ukraine)

  • Andriy Chaban

    (Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland)

  • Tomasz Perzyński

    (Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland)

  • Andrzej Szafraniec

    (Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland)

  • Lidiia Kasha

    (Institute of Power Engineering and Control Systems, Lviv Polytechnic National University, 79-013 Lviv, Ukraine)

Abstract

Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

Suggested Citation

  • Andriy Lozynskyy & Andriy Chaban & Tomasz Perzyński & Andrzej Szafraniec & Lidiia Kasha, 2021. "Application of Fractional-Order Calculus to Improve the Mathematical Model of a Two-Mass System with a Long Shaft," Energies, MDPI, vol. 14(7), pages 1-15, March.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:7:p:1854-:d:524985
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    Citations

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    Cited by:

    1. Jacek Kabziński & Przemysław Mosiołek, 2021. "Integrated, Multi-Approach, Adaptive Control of Two-Mass Drive with Nonlinear Damping and Stiffness," Energies, MDPI, vol. 14(17), pages 1-23, September.
    2. Jacek Kabziński & Przemysław Mosiołek, 2022. "Observer-Based, Robust Position Tracking in Two-Mass Drive System," Energies, MDPI, vol. 15(23), pages 1-28, November.
    3. Andrzej Popenda & Andrzej Szafraniec & Andriy Chaban, 2021. "Dynamics of Electromechanical Systems Containing Long Elastic Couplings and Safety of Their Operation," Energies, MDPI, vol. 14(23), pages 1-18, November.
    4. Karol Wróbel & Kacper Śleszycki & Krzysztof Szabat & Seiichiro Katsura, 2021. "Application of Multilayer Observer for a Drive System with Flexibility," Energies, MDPI, vol. 14(24), pages 1-19, December.
    5. Karol Wróbel & Kacper Śleszycki & Amanuel Haftu Kahsay & Krzysztof Szabat & Seiichiro Katsura, 2023. "Robust Speed Control of Uncertain Two-Mass System," Energies, MDPI, vol. 16(17), pages 1-17, August.
    6. Andriy Lozynskyy & Tomasz Perzyński & Jacek Kozyra & Yurii Biletskyi & Lidiia Kasha, 2021. "The Interconnection and Damping Assignment Passivity-Based Control Synthesis via the Optimal Control Method for Electric Vehicle Subsystems," Energies, MDPI, vol. 14(12), pages 1-17, June.
    7. Piotr Derugo & Krzysztof Szabat & Tomasz Pajchrowski & Krzysztof Zawirski, 2022. "Fuzzy Adaptive Type II Controller for Two-Mass System," Energies, MDPI, vol. 15(2), pages 1-24, January.
    8. Andriy Chaban & Zbigniew Łukasik & Andrzej Popenda & Andrzej Szafraniec, 2021. "Mathematical Modelling of Transient Processes in an Asynchronous Drive with a Long Shaft Including Cardan Joints," Energies, MDPI, vol. 14(18), pages 1-17, September.

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