Synthesis and implementation of fractional-order controllers in a current curcuit of the motor with series excitation

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.161352

Keywords:

fractional calculus, regulators with fractional order of differentiation and integration, series excitation motor

Abstract

We have synthesized and investigated fractional-order regulators, which provide for a series of technological processes the best indicators for the quality of transient process, specifically DC motors with series excitation. Given the dependence of magnetic flux on the armature current and saturation of the magnetic system, a motor armature circuit turns into a system with significant nonlinear properties under static and dynamic modes. However, it can be described with high accuracy by the transfer function of fractional order. Owing to the appropriate fractional integral-differentiating regulators, it becomes possible to obtain the quality of transient processes that is better than when using classic methods.

We have considered standard methods to synthesize the coefficients of regulators and established that such settings result in deterioration of transients due to the saturation of regulators, caused by power supply voltage limitation. Therefore, it has been proposed, for a closed circuit with different structures of fractional regulators, to use a genetic algorithm for determining the optimal values of the coefficients of regulators based on the criterion for the shortest time of first harmonization and minimum overshoot.

Experimental study into different structures of regulators has been performed conducted for settings on the module optimum and a fractional order of astatism from 0.35 to 1.5. Based on the results obtained, it can be argued that the best indicators are demonstrated by regulators at astatism 1+μco, 1.5. The overshoot is then actually less than 2 %. It has been also shown that astatism 1+μco ensures high-quality of transient processes in the unsaturated zone of magnetic system as well.

The research results could be used primarily in the systems of closed control in DC motors with series excitation, as well as with objects in which power laws are observed

Author Biographies

Victor Busher, Odessa National Polytechnic University Shevchenka avе., 1, Odessa, Ukraine, 65044

Doctor of Technical Sciences, Professor

Department of Electromechanical Systems with Computer Control

 

Lubov Melnikova, Odessa National Polytechnic University Shevchenka avе., 1, Odessa, Ukraine, 65044

PhD, Associate Professor

Department of Electromechanical Systems with Computer Control

Vasiliy Horoshko, Odessa National Polytechnic University Shevchenka avе., 1, Odessa, Ukraine, 65044

Postgraduate student

Department of Electromechanical Systems with Computer Control

References

  1. Vasil'ev, V. V., Simak, L. A. (2008). Drobnoe ischislenie i approksimacionnye metody v modelirovanii dinamicheskih sistem. Kyiv, 256.
  2. Uchaykin, V. V. (2008). Metod drobnyh proizvodnyh. Ul'yanovsk: Izdatel'stvo «Artishok», 512.
  3. Uchaikin, V. V. (2013). Fractional Derivatives for Physicists and Engineers. Springer, 385. doi: https://doi.org/10.1007/978-3-642-33911-0
  4. Tarasov, V. E. (2010). Fractional Dynamics. Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Heidelberg, 505.
  5. Oldham, K. B., Spanier, J. (Eds.) (1974). The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Elsevier, 322. doi: https://doi.org/10.1016/s0076-5392(09)x6012-1
  6. Hilfer, R. (2000). Applications of Fractional Calculus in Physics. World Scientific, 472. doi: https://doi.org/10.1142/3779
  7. Novikov, V. V., Wojciechowski, K. W., Komkova, O. A., Thiel, T. (2005). Anomalous relaxation in dielectrics. Equations with fractional derivatives. Materials Science-Poland, 23 (4), 977–984.
  8. Petrushin, V., Bendahmane, B., Yahiaoui, B., Yakimets, A. (2017). Influence of magnetic circuit saturation and skin effects on the adjustable induction motor characteristics. International Journal of Hydrogen Energy, 42 (48), 29006–29013. doi: https://doi.org/10.1016/j.ijhydene.2017.07.221
  9. Doradla, S. R., Sen, P. C. (1978). Time ratio control (TRC) scheme for a DC series motor Part II: Commutation circuit analysis. Canadian Electrical Engineering Journal, 3 (2), 44–48. doi: https://doi.org/10.1109/ceej.1978.6591134
  10. Sen, P. C., Doradla, S. R. (1978). Time ratio control (TRC) scheme for a DC series motor Part I: Performance. Canadian Electrical Engineering Journal, 3 (2), 39–43. doi: https://doi.org/10.1109/ceej.1978.6591133
  11. Alexandridis, A. T., Konstantopoulos, G. C. (2014). Modified PI speed controllers for series-excited dc motors fed by dc/dc boost converters. Control Engineering Practice, 23, 14–21. doi: https://doi.org/10.1016/j.conengprac.2013.10.009
  12. Rengifo Rodas, C. F., Castro Casas, N., Bravo Montenegro, D. A. (2017). A performance comparison of nonlinear and linear control for a DC series motor. Ciencia en Desarrollo, 8 (1), 41–50. doi: https://doi.org/10.19053/01217488.v8.n1.2017.5455
  13. Farooq, U., Gu, J., Asad, M. U., Abbas, G. (2014). Robust Takagi-Sugeno fuzzy speed regulator for DC series motors. 2014 12th International Conference on Frontiers of Information Technology. doi: https://doi.org/10.1109/fit.2014.24
  14. Valluru, S. K., Singh, M., Kumar, N. (2012). Implementation of NARMA-L2 Neuro controller for speed regulation of series connected DC motor. 2012 IEEE 5th India International Conference on Power Electronics (IICPE). doi: https://doi.org/10.1109/iicpe.2012.6450518
  15. Petrás, I. (2009). Fractional – order feedback control of a dc motor. Journal of Electrical Engineering, 60 (3), 117–128. Available at: https://pdfs.semanticscholar.org/a033/af254d22cc8bfc979341bd8af6e3c76a07a6.pdf
  16. Copot, C., Muresan, C. I., De Keyser, R. (2013). Speed and position control of a DC motor using fractional order PI-PD control. 3rd International Conference on Fractional Signals and Systems. Ghent. Available at: https://core.ac.uk/download/pdf/55870474.pdf
  17. Heidarpoor, S., Tabatabaei, M., Khodadadi, H. (2017). Speed control of a DC motor using a fractional order sliding mode controller. 2017 IEEE International Conference on Environment and Electrical Engineering and 2017 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe). doi: https://doi.org/10.1109/eeeic.2017.7977822
  18. Tajbakhsh, H., Balochian, S. (2014). Robust Fractional Order PID Control of a DC Motor with Parameter Uncertainty Structure. International Journal of Innovative Science, Engineering & Technology, 1 (6), 223–229. Available at: http://www.ijiset.com/v1s6/IJISET_V1_I6_37.pdf
  19. Petras, I. (2011). Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab. Engineering Education and Research Using MATLAB. doi: https://doi.org/10.5772/19412
  20. Das, S., Pan, I. (2012). Fractional Order Signal Processing. SpringerBriefs in Applied Sciences and Technology. Springer. doi: https://doi.org/10.1007/978-3-642-23117-9
  21. Marushchak, Y. Y., Kopchak, B. L. (2017). Synthesis fractional order controllers for electromechanical systems. Elektrotekhnichni ta kompiuterni systemy, 25, 26–33. Available at: http://nbuv.gov.ua/UJRN/etks_2017_25_6
  22. Busher, V., Aldairi, A. (2018). Synthesis and technical realization of control systems with discrete fractional integral-differentiating controllers. Eastern-European Journal of Enterprise Technologies, 4 (2 (94)), 63–71. doi: https://doi.org/10.15587/1729-4061.2018.139892
  23. Kuvshinov, A. A. (2009). Teoriya elektroprivoda. Ch. 1. Orenburg, 197.
  24. Rutkovskaya, D., Pilin'skiy, M., Rutkovskiy, L. (2006). Neyronnye seti, geneticheskie algoritmy i nechetkie sistemy. Moscow, 452.

Downloads

Published

2019-04-02

How to Cite

Busher, V., Melnikova, L., & Horoshko, V. (2019). Synthesis and implementation of fractional-order controllers in a current curcuit of the motor with series excitation. Eastern-European Journal of Enterprise Technologies, 2(2 (98), 63–72. https://doi.org/10.15587/1729-4061.2019.161352

Issue

Vol. 2 No. 2 (98) (2019): Information technology. Industry control systems

Section

Industry control systems

License

Copyright (c) 2019 Victor Busher, Lubov Melnikova, Vasiliy Horoshko

Creative Commons License

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

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.