Skip to main content
Log in

Path tracking design based on Davidson–Cole prefilter using a centralized CRONE controller applied to multivariable systems

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

To perfectly govern MIMO (Multi-Input Multi-Output) processes, a fully populated matrix controller has been developed due to its flexibility. Taking into account the plant uncertainties, the CRONE (Commande Robuste d’Ordre Non Entier) control approach is used with the non-diagonal quantitative feedback theory (QFT) procedure. The MIMO-QFT robust synthesis methodology has been used in order to generate the appropriate equivalent MISO (Multi-Input Single-Output) system structure from the MIMO plant. For each MISO structure, the CRONE control approach based on third-generation CRONE methodology is used to find the diagonal elements of the controller of the plant while considering the plant uncertainties. The non-diagonal part of the controller is determined to reach the aim of minimizing the coupling effects. After that, a fractional prefilter synthesis approach is developed to find the non-integer prefilter expression satisfying the tracking specifications. A SCARA robot manipulator has been used to verify the designed controller performances.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Oustaloup, A.: Fractional order sinusoidal oscillators: optimization and their use in highly linear F.M. modulation. IEEE Trans. Circuits Syst. 8(10), 1007–1009 (1981)

    Article  Google Scholar 

  2. Oustaloup, A.: The CRONE control. In: Proceedings of the European Control Conference (ECC 91), Grenoble, France, 2–5 July (1991)

    Google Scholar 

  3. Sabatier, J., Oustaloup, A., Garcia Iturricha, A., Lanusse, P.: CRONE control: principles and extension to time-variant plants with asymptotically constant coefficients. Nonlinear Dyn. 29, 363–385 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Oustaloup, A., Mathieu, B., Lanusse, P.: Intégration non entière complexe et contours d’Isoamortissement. Autom. Prod. Inform. Ind. 29(1), 177–202 (1995)

    Google Scholar 

  5. Lanusse, P.: De la commande CRONE de première génération à la commande CRONE de troisième génération. PhD thesis, Bordeaux I University, France (1994)

  6. Kempfle, S., Schäfer, I., Beyer, H.: Fractional calculus via functional calculus: theory and applications. Nonlinear Dynamics 29(1–4), 99–127 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Oustaloup, A., Mathieu, B.: La Commande CRONE: du Scalaire Au Multivariable. Hermès, Paris (1999)

    MATH  Google Scholar 

  8. Oustaloup, A., Mathieu, B., Lanusse, P., Sabatier, J.: La Commande CRONE. Hermès, Paris (1999)

    MATH  Google Scholar 

  9. Lanusse, P., Nelson Gruel, D., Sabatier, J., Lasnier, R., Oustaloup, A.: Synthèse multivariable d’une commande CRONE décentralisée. In: Automatique et Informatique Appliquée. Académie Roumaine, pp. 159–166 (2009)

    Google Scholar 

  10. Melchior, P., Inarn, C., Oustaloup, A.: Path tracking design by fractional prefilter extension to square MIMO systems. In: The Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (ASME 2009), California, USA, 30 August–2 September (2009)

    Google Scholar 

  11. Mohammad, S., Alavi, M., Khaki Sedigh, A., Labibi, B.: Pre-filter design for tracking error specifications in MIMO-QFT. In: The 44th IEEE Conference on Decision and Control, and the European Control Conference (CDC-ECC 2005), Seville, Spain, 12–15 December (2005)

    Google Scholar 

  12. Boje, E.: Non-diagonal controllers in MIMO quantitative feedback design. Int. J. Robust Nonlinear Control 12(4), 303–320 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zenghui, W., Zengqiang, C., Qinglin, S., Zhuzh, Y.: Multivariable decoupling predictive control based on QFT theory and application in CSTR chemical process. Chin. J. Chem. Eng. 14(6), 765–769 (2006)

    Article  Google Scholar 

  14. Horowitz, I.: Survey of quantitative feedback theory (QFT). Int. J. Robust Nonlinear Control 11(10), 887–921 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control, Analysis and Design. Wiley, New York (1996)

    Google Scholar 

  16. Yousfi, N., Melchior, P., Rekik, C., Derbel, N., Oustaloup, A.: Path tracking design by fractional prefilter using a combined QFT/H∞ design for TDOF uncertain feedback systems. J. Appl. Nonlinear Dyn. 1(3), 239–261 (2012)

    Google Scholar 

  17. Garcia-Sanz, M., Egana, I.: Quantitative non-diagonal controller design for multivariable systems with uncertainty. Int. J. Robust Nonlinear Control 12, 321–333 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Garcia-Sanz, M., Egana, I., Barreras, M.: Design of quantitative feedback theory non-diagonal controllers for use in uncertain multiple-input multiple-output systems. IEE Proc., Control Theory Appl. 152(2), 177–187 (2005)

    Article  Google Scholar 

  19. Barreras, M., Villegas, C., Garcia-Sanz, M., Kalkkuhl, J.: Robust QFT tracking controller design for a car equipped with 4-wheel steer-by wire. In: Proceedings of the 2006 IEEE International Conference on Control Applications (CCA 2006), Munich, Germany, 4–6 October (2006)

    Google Scholar 

  20. Horowitz, I.: Improved design technique for uncertain multiple input-output feedback systems. Int. J. Control 36, 977–988 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  21. Franchek, M., Herman, P., Nwokah, O.: Robust non-diagonal controller design for uncertain multivariable regulating systems. J. Dyn. Syst. Meas. Control 119, 80–85 (1997)

    Article  MATH  Google Scholar 

  22. Oustaloup, A., Mathieu, B., Lanusse, P.: The CRONE control of resonant plants: application to a flexible transmission. Eur. J. Control 1(2), 113–121 (1995)

    Google Scholar 

  23. Lanusse, P., Oustaloup, A., Mathieu, B.: Robust control of LTI square MIMO plants using two CRONE control design approaches. In: IFAC Symposium on Robust Control Design (ROCOND 2000), Prague, Czech Republic, 11–13 September (2000)

    Google Scholar 

  24. CRONE Research Group: CRONE Control Design Module User’s Guide. Version 4.0 (2010)

  25. Nelson Gruel, D., Lanusse, P., Oustaloup, A.: Decentralized CRONE control of multivariable system with time-delay. In: New Trends in Nanotechnology and Fractional Calculus Applications, pp. 377–391. Springer, Berlin (2009)

    Google Scholar 

  26. Nelson Gruel, D., Lanusse, P., Oustaloup, A.: Robust control design for multivariable plants with time-delays. Chem. Eng. J. 146, 414–427 (2009)

    Article  Google Scholar 

  27. Orsoni, B., Melchior, P., Oustaloup, A.: Davidson–Cole transfer function in path tracking design. In: The 6th IEEE European Control Conference (IEEE-ECC 2001), Porto, Portugal, 4–7 September (2001)

    Google Scholar 

  28. Garcia-Sanz, M., Egaña, I., Villanueva, J.: Interval modeling of a SCARA robot for robust control. In: The 10th Mediterranean Conference on Control and Automation (MED 2002), Lisbon, Portugal, 9–13 July (2002)

    Google Scholar 

  29. Oustaloup, A., Melchior, P., Lanusse, P., Cois, O., Dancla, F.: The CRONE toolbox for Matlab. In: IEEE International Symposium on Computer-Aided Control-System Design (CACSD 2000), Anchorage, USA, 25–27 September, (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Najah Yousfi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yousfi, N., Melchior, P., Rekik, C. et al. Path tracking design based on Davidson–Cole prefilter using a centralized CRONE controller applied to multivariable systems. Nonlinear Dyn 71, 701–712 (2013). https://doi.org/10.1007/s11071-012-0695-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-012-0695-5

Keywords

Navigation