Skip to main content
SpringerLink
Log in
Book cover

Conference on Non-integer Order Calculus and Its Applications

RRNR 2018: Advances in Non-Integer Order Calculus and Its Applications pp 142–162Cite as

Non-Integer Order Control of PMSM Drives with Two Nested Feedback Loops

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

Abstract

In industrial control applications, the plants are often represented by integer-order models and controlled by proportional-integral-derivative controllers. The control scheme for permanent magnet synchronous motors (PMSM) includes two nested loops, each employing a PI controller: the inner loop is dedicated to control the current, the outer loop is devoted to control the angular speed. The optimum modulus and symmetrical optimum criteria are widely accepted techniques to tune the two PI controllers. However, to obtain improvements, one may think to apply non-integer order controllers. To this aim, if one uses a fractional-order PI (FOPI) controller in the inner loop, the consequent inner feedback system of non-integer order becomes a non-integer order plant in the outer loop. Then, a FOPI controller should be more effective to control a real example of non-integer order plant. This paper proposes an appropriate design approach to obtain performance and robustness specifications by FOPI controllers in both loops. The approach provides analytical formulas to determine the parameters of the controllers, which are characterized by stability, minimum-phase and interlacing properties. The simulation of a real PMSM shows the effectiveness of the approach and could help to increase the confidence in non-integer order controllers.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Arena, P., Caponetto, R., Fortuna, L., Porto, D.: Nonlinear noninteger order circuits and systems - an introduction. In: Chua, L. (ed.) World Scientific Series on Nonlinear Science. Series A, vol. 38. World Scientific, Singapore (2000)

    MATH  Google Scholar 

  2. Åström, K.J., Hägglund, T.: PID Controllers: Theory, Design, and Tuning, 2nd edn. Instrument Society of America, Research Triangle Park (1995)

    Google Scholar 

  3. Caponetto, R., Dongola, G.: A numerical approach for computing stability region of FO-PID controller. J. Franklin Inst. 350(4), 871–889 (2013). https://doi.org/10.1016/j.jfranklin.2013.01.017

    Article  MathSciNet  MATH  Google Scholar 

  4. Caponetto, R., Dongola, G., Fortuna, L., Petráš, I.: Fractional Order Systems: Modeling and Control Applications. World Scientific, Singapore (2010)

    Book  Google Scholar 

  5. Caponetto, R., Dongola, G., Pappalardo, F., Tomasello, V.: Auto-tuning and fractional order controller implementation on hardware in the loop system. J. Optim. Theory Appl. 156(1), 141–152 (2013). https://doi.org/10.1007/s10957-012-0235-y

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, Y.Q.: Ubiquitous fractional order controls? In: Proceedings of the 2nd IFAC Symposium on Fractional Derivatives and Its Applications, Porto, Portugal, vol. 2, pp. 168–173, 19–21 July 2006

    Google Scholar 

  7. Chen, Y.Q., Petras, I., Xue, D.: Fractional order control – a tutorial. In: 2009 American Control Conference, Hyatt Regency Riverfront, St. Louis, MO, USA, 10–12 June 2009

    Google Scholar 

  8. Kalman, R.E.: When is a linear control system optimal? Trans. ASME J. Basic Eng. 86(Series D), 51–60 (1964)

    Article  Google Scholar 

  9. Kessler, C.: Das symmetrische optimum. Regelungstechnik 6, 395–400, 432–436 (1958)

    Google Scholar 

  10. Jalloul, A., Trigeassou, J.-C., Jelassi, K., Melchior, P.: Fractional order modeling of rotor skin effect in induction machines. Nonlinear Dyn. 73(1), 801–813 (2013)

    Article  Google Scholar 

  11. Lino, P., Maione, G.: Loop-shaping and easy tuning of fractional-order proportional integral controllers for position servo systems. Asian J. Control. 15(3), 796–805 (2013). https://doi.org/10.1002/asjc.556

    Article  MathSciNet  MATH  Google Scholar 

  12. Lino, P., Maione, G., Padula, F., Stasi, S., Visioli, A.: Synthesis of fractional-order PI controllers and fractional-order filters for industrial electrical drives. IEEE/CAA J. Autom. Sinica 4(1), 58–69 (2017). https://doi.org/10.1109/JAS.2017.7510325

    Article  MathSciNet  Google Scholar 

  13. Luo, Y., Chen, Y.Q.: Fractional Order Motion Controls. Wiley, Chichester (2013)

    Google Scholar 

  14. Lurie, B.J., Enright, P.J.: Classical Feedback Control: With MATLAB. Control Engineering Series. Munro, N. (ed.) Marcel Dekker, Inc., New York, Basel (2000)

    Google Scholar 

  15. Lutz, H., Wendt, W.: Taschenbuch der Regelungstechnik. 4. Korregierte Auflage, Verlag Harri Deutsch, Frankfurt am Main (2002)

    Google Scholar 

  16. Maione, G., Lino, P.: New tuning rules for fractional \({PI}^\alpha \) controllers. Nonlinear Dyn. 49(1–2), 251–257 (2007). https://doi.org/10.1007/s11071-006-9125-x

    Article  MATH  Google Scholar 

  17. Maciejowski, J.M.: Multivariable Feedback Design. Addison-Wesley, Wokingham (1989)

    MATH  Google Scholar 

  18. Maione, G.: Continued fractions approximation of the impulse response of fractional order dynamic systems. IET Control Theory Appl. 2(7), 564–572 (2008). https://doi.org/10.1049/iet-cta:20070205

    Article  MathSciNet  Google Scholar 

  19. Maione, G.: Conditions for a class of rational approximants of fractional differentiators/integrators to enjoy the interlacing property. In: Bittanti, S., Cenedese, A., Zampieri, S. (eds.) Proceedings of the 18th IFAC World Congress (IFAC WC 2011), Università Cattolica del Sacro Cuore, IFAC Proceedings, Milan, Italy, 28 August–2 September 2011, vol. 18, Part 1, pp. 13984–13989 (2011). https://doi.org/10.3182/20110828-6-IT-1002.01035

    Article  Google Scholar 

  20. Mansouri, R., Bettayeb, M., Djennoune, S.: Approximation of high order integer systems by fractional order reduced-parameters models. Math. Comput. Model. 51, 53–62 (2010)

    Article  MathSciNet  Google Scholar 

  21. Monje, C.A., Calderon, A.J., Vinagre, B.M., Feliu, V.: The fractional order lead compensator. In: Proceedings of the 2nd IEEE International Conference on Computational Cybernetics (ICCC 2004), Vienna, Austria, 30 August–1 September 2004, pp. 347–352 (2004)

    Google Scholar 

  22. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D., Feliu, V.: Fractional-Order Systems and Controls: Fundamentals and Applications. Springer, London (2010)

    Book  Google Scholar 

  23. Monje, C.A., Vinagre, B.M., Feliu, V., Chen, Y.Q.: Tuning and auto-tuning of fractional order controllers for industry applications. Control Eng. Pract. 16, 798–812 (2008)

    Article  Google Scholar 

  24. Oldenbourg, R.C., Sartorius, H.: A uniform approach to the optimum adjustments of control loops. In: Oldenburger, R. (ed.) Frequency Response. The Macmillan Co., New York (1956)

    Google Scholar 

  25. Oldham, K.B., Spanier, J.: The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press, New York (1974)

    MATH  Google Scholar 

  26. Ortigueira, M.D.: Fractional Calculus for Scientists and Engineers. Springer, Dordrecht (2011)

    Book  Google Scholar 

  27. Oustaloup, A.: La Commande CRONE. Command Robuste d’Ordre Non Entiér. Editions Hermés, Paris (1991)

    Google Scholar 

  28. Podlubny, I.: Fractional-order systems and \({PI}^\lambda {D}^\mu \) controllers. IEEE Trans. Autom. Control. 44(1), 208–214 (1999)

    Article  MathSciNet  Google Scholar 

  29. Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calc. Appl. Anal. 5, 367–386 (2002)

    MathSciNet  MATH  Google Scholar 

  30. Retiere, N.M., Ivanès, M.S.: Modeling of electrical machines by implicit derivative half order systems. IEEE Power Eng. Rev. 18(9), 62–64 (1998)

    Google Scholar 

  31. Retiere, N.M., Ivanès, M.S.: An introduction to electrical machines modeling by non integer order systems. Application to double-cage induction machine. IEEE Trans. Energy Convers. 14(4), 1026–1032 (1999)

    Article  Google Scholar 

  32. Shah, P., Agashe, S.: Review of fractional PID controller. Mechatronics 38, 29–41 (2016). https://doi.org/10.1016/j.mechatronics.2016.06.005

    Article  Google Scholar 

  33. Valério, D., Sá da Costa, J.: Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Process. 86, 2771–2784 (2010)

    Article  Google Scholar 

  34. Voda, A.A., Landau, I.D.: A method for auto-calibration of PID controllers. Automatica 31(1), 41–53 (1995)

    Article  MathSciNet  Google Scholar 

  35. Yu, W., Luo, Y., Pi, Y., Chen, Y.Q.: Fractional-order modeling of a permanent magnet synchronous motor velocity servo system: method and experimental study. In: Proceedings of the 2014 International Conference on Fractional Differentiation and Its Applications, Catania, Italy, 23–25 June 2014

    Google Scholar 

  36. Zhao, C., Xue, D., Chen, Y.Q.: A fractional order PID tuning algorithm for a class of fractional order plants. In: Proceedings of the IEEE International Conference on Mechatronics and Automation, Niagara Falls, Canada, 29 July–1 August 2005, vol. 1, pp. 216–221 (2005)

    Google Scholar 

Download references

Acknowledgement

This paper is based upon work from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).

Author information

Authors and Affiliations

  1. Department of Electrical and Information Engineering, Polytechnic University of Bari, Via E. Orabona, 4, 70125, Bari, Italy

    Paolo Lino & Guido Maione

Authors
  1. Paolo Lino
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guido Maione
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guido Maione .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Lino, P., Maione, G. (2020). Non-Integer Order Control of PMSM Drives with Two Nested Feedback Loops. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_11

Download citation

Publish with us

Policies and ethics

Search

Navigation