Skip to main content
SpringerLink
Log in

A Tube-Based MPC Structure for Fractional-Order Systems

  • Conference paper
  • First Online:
Advanced, Contemporary Control (PCC 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 708))

Included in the following conference series:

  • 140 Accesses

Abstract

In the paper a new structure to improve the robustness of Fractional-Order Model Predictive Control (FOMPC) are proposed. The method based on the modified Model Following Control (MFC) idea, with the Internal Model Control (IMC) concept, introduced by Skoczowski and Domek in [14]. This leads to a novel, tube-based fractional-order robust predictive control structure, named TFOMPC, which offer an additional degree of freedom in tuning a control loop for higher efficiency. It seems that the proposed TFOMPC approach has potentially great advantages, is simple to implement and easy to tune. Thanks to this, it can be used in many control systems of difficult, inaccurately identified objects, not only of a fractional-order.

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

Access this chapter

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

References

  1. Brunner, F.D., Müller, M.A., Allgöwer, F.: Enhancing output feedback MPC for linear discrete-time systems with set-valued moving horizon estimation. In: Proceedings of IEEE Conference on Decision and Control (2016)

    Google Scholar 

  2. Domek, S.: Robust Model Predictive Control for Nonlinear Processes, vol. 593. Technical University of Szczecin Academic Press, Szczecin (2006). (in Polish)

    Google Scholar 

  3. Domek, S.: Multiple use of the fractional-order differential calculus in the model predictive control. In: 19th International Conference on Methods and Models in Automation and Robotics (MMAR), pp. 359–362 (2014)

    Google Scholar 

  4. Domek, S.: Model-plant mismatch in fractional order model predictive control. In: Domek, S., Dworak, P. (eds.) Theoretical Developments and Applications of Non-Integer Order Systems. LNEE, vol. 357, pp. 281–291. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-23039-9_24

    Chapter  Google Scholar 

  5. Kaczorek, T.: Selected Problems of Fractional Systems Theory. LNCIS, Springer, Berlin (2011). https://doi.org/10.1007/978-3-642-20502-6

    Book  MATH  Google Scholar 

  6. Kögel, M., Findeisen, R.: Robust output feedback MPC for uncertain linear systems with reduced conservatism. IFAC-Papers Online 50, 10685–10690 (2017)

    Article  Google Scholar 

  7. Lorenzetti, J., Pavone, M.: A simple and efficient tube-based robust output feedback model predictive control scheme. In: European Control Conference (ECC), pp. 1775–1782 (2020)

    Google Scholar 

  8. Ławryńczuk, M.: Computationally Efficient Model Predictive Control Algorithms. SSDC, vol. 3. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04229-9

    Book  MATH  Google Scholar 

  9. Mayne, D.Q., Raković, S.V., Findeisen, R., Allgöwer, F.: Robust output feedback model predictive control of constrained linear systems. Automatica 42, 1217–1222 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D., Feliu, V.: Fractional Order Systems and Controls. Springer, London (2010). https://doi.org/10.1007/978-1-84996-335-0

    Book  MATH  Google Scholar 

  11. Oustaloup, A.: La Derivation Non Entiere: Theorie. Synthese et Applications, Hermes, Paris (1995)

    Google Scholar 

  12. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  13. Romero, M., De Madrid, Á.P., Mañoso, C., Vinagre, B.M.: Fractional-order generalized predictive control: formulation and some properties. In: 11th International Conference on Control, Automation, Robotics and Vision, pp. 1495–1500 (2010)

    Google Scholar 

  14. Skoczowski, S., Domek, S.: Robustness of a model following control system. In: Proceedings of International Conference on Mathematical Theory of Networks and Systems (MTNS), CD (2000)

    Google Scholar 

  15. Skoczowski, S., Domek, S., Pietrusewicz, K., Broel-Plater, B.: A method for improving the robustness of PID control. IEEE Trans. Ind. Electron. 52, 1669–1676 (2005)

    Article  Google Scholar 

  16. Sopasakis, P., Sarimveis, H.: Stabilising model predictive control for discrete-time fractional-order systems. Automatica 75, 24–31 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Tatjewski, P.: Advanced Control of Industrial Processes. Springer, London (2007). https://doi.org/10.1007/978-1-84628-635-3

    Book  MATH  Google Scholar 

  18. Tatjewski, P.: Disturbance modeling and state estimation for offset-free predictive control with state-spaced process models. Int. J. Appl. Math. Comput. Sci. 24, 313–323 (2014)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. West Pomeranian University of Technology in Szczecin, ul. Sikorskiego 37, 70-313, Szczecin, Poland

    Stefan Domek

Authors
  1. Stefan Domek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Domek .

Editor information

Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Marek Pawelczyk

  2. Silesian University of Technology, Gliwice, Poland

    Dariusz Bismor

  3. Silesian University of Technology, Gliwice, Poland

    Szymon Ogonowski

  4. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Domek, S. (2023). A Tube-Based MPC Structure for Fractional-Order Systems. In: Pawelczyk, M., Bismor, D., Ogonowski, S., Kacprzyk, J. (eds) Advanced, Contemporary Control. PCC 2023. Lecture Notes in Networks and Systems, vol 708. Springer, Cham. https://doi.org/10.1007/978-3-031-35170-9_10

Download citation

Publish with us

Policies and ethics

Search

Navigation