Skip to main content
SpringerLink
Log in

Model-Plant Mismatch in Fractional Order Model Predictive Control

  • Chapter
  • First Online:
Theoretical Developments and Applications of Non-Integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 357))

Abstract

The effectiveness of model predictive control (MPC) depends on the accuracy of the process model, which is utilized directly to compute the manipulated variable. The effect of various model-plant mismatches on the performance of the classic predictive controller is well known. However, many industrial processes exhibit very complex properties, and determining an adequate model for them is not an easy task. In recent years it has been suggested to employ non-integer order models to describe difficult processes. This leads to fractional order model predictive control (FOMPC) systems. Their properties, e.g. stability, robustness, control quality, have become one of the active research topics in control theory and applications. In the paper, the effect of various plant-model mismatches on the performance of FOMPC is illustrated through a simulation experiment.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
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

Institutional subscriptions

References

  1. Chen, Y.Q., Petráš, I., Xue, D.: Fractional order control. In: American Control Conference, pp. 1397–1410. St. Louis (2009)

    Google Scholar 

  2. Domek, S.: Fractional-Order Differential Calculus in Model Predictive Control. West Pomeranian University of Technology Academic Press, Szczecin (2013)

    Google Scholar 

  3. Domek, S.: Switched state model predictive control of fractional-order nonlinear discrete-time systems. In: Pisano, A., Caponetto, R. (eds.) Advances in Fractional Order Control and Estimation, Asian J. Control, Special Issue, vol. 15, no. 3, pp. 658–668 (2013)

    Google Scholar 

  4. Domek, S.: Fractional-order model predictive control with small set of coincidence points. In: Latawiec, K., Łukaniszyn, M., Stanisławski, R. (eds.) Advances in Modelling and Control of Non-integer Order Systems, Lecture Notes in Electrical Engineering, vol. 320, pp. 135–144. Springer, Opole (2014)

    Google Scholar 

  5. Dzieliński, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Polish Acad. Sci. Tech. Sci. 58(4), 583–592 (2010)

    MATH  Google Scholar 

  6. Kaczorek, T.: Selected Problems of Fractional Systems Theory. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  7. Maciejowski, J.M.: Predictive Control with Constraints. Prentice Hall, Englewood Cliffs (2002)

    Google Scholar 

  8. Nafsun, A.I., Yusoff, N.: Effect of model-plant mismatch on MPC controller performance. J. Appl. Sci. 21(11), 3579–3585 (2011)

    Google Scholar 

  9. Ostalczyk, P.: The non-integer difference of the discrete-time function and its application to the control system synthesis. Int. J. Syst. Sci. 31(12), 1551–1561 (2000)

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  11. Romero, M., Vinagre, B.M., De Madrid, Á.P.: GPC Control of a fractional–order plant: improving stability and robustness. In: 17th IFAC World Congress, pp. 14266–14271. Seoul (2008)

    Google Scholar 

  12. 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. Singapore (2010)

    Google Scholar 

  13. Stanisławski, R., Latawiec, K.: Normalized finite fractional differences—the computational and accuracy breakthroughs. Int. J. Appl. Math. Comput. Sci. 22(4), 907–919 (2012)

    MathSciNet  MATH  Google Scholar 

  14. Wang, Y., Wang, X.: Performance diagnosis of MPC with model-plant mismatch. In: Proceedings of the Chinese Control and Decision Conference, pp. 78–82. Xuzhou (2010)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Control Engineering and Robotics, West Pomeranian University of Technology at 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. Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland

    Stefan Domek

  2. Faculty of Electrical Engineering, West Pomeranian University of Technology, Szczecin, Poland

    Paweł Dworak

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Domek, S. (2016). Model-Plant Mismatch in Fractional Order Model Predictive Control. In: Domek, S., Dworak, P. (eds) Theoretical Developments and Applications of Non-Integer Order Systems. Lecture Notes in Electrical Engineering, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-23039-9_24

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23039-9_24

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23038-2

  • Online ISBN: 978-3-319-23039-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation