Skip to main content

Tuning of Fractional Order Controller and Prefilter in MIMO Robust Motion Control: SCARA Robot

  • Chapter
  • First Online:

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 270))

Abstract

Quite recently, fractional approaches was greatly used in control engineering area. Several methodologies based on fractional controllers tuning has been treated. In this work, a multi-input multi-output (MIMO) quantitative feedback theory (QFT) method is mixed with a fractional order PD\(^{\mu }\) controller and a fractional prefilter to govern multivariable systems. Each obtained sub-systems from the MIMO QFT technique is controlled independently. A new analytic tuning method of fractional order controller is developed in the aim to ensure stability and robustness. After the controller tuning a fractional order prefilter is designed and optimized to reach the desired performances. The proposed method effectiveness will be tested and evaluated based on a real robot model.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   179.99
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. Abel, N.: Solution de quelques problemes a l’aide d’integrales definies. Gesammelte mathematische Werke 1, 11–27 (1881)

    Google Scholar 

  2. Bagley, R.L., Calico, R.A.: Fractional-order state equations for the control of viscoelastic damped structures. J. Guid. Control Dyn. 14, 304–311 (1991)

    Article  Google Scholar 

  3. Bagley, R.L., Torvik, P.: On the appearance of the fractional derivative in the behavior of real materials. J. Appl. Mech. 51, 294–298 (1984)

    Article  Google Scholar 

  4. Chen, Y., Xue, D.: A comparative introduction of four fractional order controllers. In: 4th IEEE World Congress on Intelligent Control and Automatic (WCICA02) (2002)

    Google Scholar 

  5. Dulf, E.-H., Timis, D., Muresan, C.-I.: Robust fractional order controllers for distributed systems. Acta Polytech. Hung. 14, 163–176 (2017)

    Google Scholar 

  6. Euler, L.: Foundations of Differential Calculus. Springer, New York (2000)

    Google Scholar 

  7. Garcia-Sanz, M., Egana, I., Villanueva, J.: Interval modelling of SCARA robot for robust control. In: 10th Mediterranean Conference on Control and Automation - MED (2002)

    Google Scholar 

  8. Horowitz, I.: Synthesis of Feedback Systems. Academic Press, New York (1963)

    MATH  Google Scholar 

  9. Horowitz, I.: Survey of quantitative feedback theory (qft). Int. J. Control 53, 255–291 (2001)

    Article  MathSciNet  Google Scholar 

  10. Keyser, R.D., Muresan, C.I., Ionescu, C.M.: A novel auto-tuning method for fractional order pi/pd controllers. ISA Trans. 62, 268–275 (2016)

    Google Scholar 

  11. Letnikov, A.: Theory of differentiation of fractional order. Mat. Sbornik 3, 1–68 (1868)

    Google Scholar 

  12. Liouville, J.: Memoire sur quelques questions de geometrie et de mecanique, et sur un nouveau genre pour resoudre ces questions. J. Ec. Polytech. 13, 1–69 (1832)

    Google Scholar 

  13. Luo, Y., Chen, Y.Q., Wang, C.Y., Pi, Y.G.: Tuning fractional order proportional integral controllers for fractional order systems. J. Process Control 20(7), 823–831 (2010)

    Article  Google Scholar 

  14. Mainardi, F.: Fractional relaxation in anelastic solids. J. Alloys Compd. 211(212), 534–538 (1994)

    Article  Google Scholar 

  15. Melchior, P., Inarn, C., Oustaloup, A.: Path tracking design by fractional prefilter extension to square MIMO systems. In: Proceedings of the ASME 2009 International Design Engineering Technical Conference and Computers and Information in Engineering Conference (2009)

    Google Scholar 

  16. Melchior, P., Robin, G., L’Hostis, S., Levron, F.: Non integer order movement generation in path planning. In: CESA’98 IMACS-IEEE/SMC Multiconference Computational Engineering in Systems Applications (1998)

    Google Scholar 

  17. Metzler, R., Klafter, J.: The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1–77 (2000)

    Google Scholar 

  18. Muresan, C.I.: Fractional calculus: from simple control solutions to complex. In: Nonlinear Systems and Complexity, vol. 6, pp. 113–134. Springer, Cham (2014)

    Google Scholar 

  19. Muresan, C.-I., Folea, S., Mois, G., Dulf, E.-H.: Development and implementation of an fpga based fractional order controller for a DC motor. Mechatronics 23, 798–804 (2013)

    Article  Google Scholar 

  20. Osler, T.J.: The integral analog of the leibniz rule. Math. Comp. 26, 903–915 (1972)

    MathSciNet  MATH  Google Scholar 

  21. Oustaloup, A.: Systèmes asservis linéaires d’ordre fractionnaire. Masson, Paris (1983)

    Google Scholar 

  22. Oustaloup, A.: La commande CRONE. Hermes, Paris (1991)

    MATH  Google Scholar 

  23. Oustaloup, A.: La dérivation non entière: théorie, synthèse et applications. Hermes, Paris (1995)

    MATH  Google Scholar 

  24. Pan, I., Das, S., Gupta, A.: Handling packet dropouts and random delays for unstable delayed processes in ncs by optimal tuning of \(pi^{\lambda }d^{\mu }\) controllers with evolutionary algorithms. ISA Trans. 50, 557–572 (2011)

    Article  Google Scholar 

  25. Patil, M.D., Nataraj, P., Vyawahare, V.: Design of robust fractional-order controller and prefilters for multivariable system using interval constraint satisfaction technique. Int. J. Dynam. Control 5, 145–158 (2016)

    Google Scholar 

  26. Podlubny, I.: Fractional order systems and \(pi^{\lambda }d^{\mu }\) controllers. IEEE Trans. Autom. Control 44, 208–214 (1999)

    Article  MathSciNet  Google Scholar 

  27. Riemann, B.: Versuch einer allgemeinen auffassung der integration und differentiation. Gesammelte Mathematische Werke und Wissenschaftlicher 1, 331–344 (1876)

    Google Scholar 

  28. Ross, B.: Fractional calculus and its applications. In: Proceedings of the International Conference held at the University of New Haven. Springer, New York (1974)

    Google Scholar 

  29. Xue, D., Chen, Y.: A comparative introduction of four fractional order controllers. In: 4th IEEE World Congress on Intelligent Control and Automation (2002)

    Google Scholar 

  30. Xue, D., Zhao, C., Chen, Y.Q.: Fractional order PID control a DC-motor with elastic shaft: a case study. In: Proceedings of the American Control Conference (2006)

    Google Scholar 

  31. Yousfi, N., Melchior, P., Rekik, C., Derbel, N., Oustaloup, A.: Comparison between h\(_{\infty }\) and crone control combined with qft approach to control multivariable systems in path tracking design. Int. J. Comput. Appl. 45, 1–9 (2012a)

    Google Scholar 

  32. Yousfi, N., Melchior, P., Rekik, C., Derbel, N., Oustaloup, A.: Path tracking design based on Davidson-Cole prefilter using a centralized crone controller applied to multivariable systems. Nonlinear Dyn. 71, 701–712 (2013)

    Google Scholar 

  33. Yousfi, N., Melchior, P., Rekik, C., Derbel, N., Oustaloup, A.: Path tracking design by fractional prefilter using a combined qft/h\(_{\infty }\) design for tdof uncertain feedback systems. J. Appl. Nonlinear Dyn. 1, 239–261 (2012b)

    Google Scholar 

  34. Zhao, C., Yang, D., Xue, Q.C.: A fractional order PID tuning algorithm for a class of fractional order plants. In: IEEE International Conference on Mechatronics and Automation (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mohamed Allagui .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Allagui, M., Yousfi, N., Derbel, N., Melchior, P. (2020). Tuning of Fractional Order Controller and Prefilter in MIMO Robust Motion Control: SCARA Robot. In: Ghommam, J., Derbel, N., Zhu, Q. (eds) New Trends in Robot Control. Studies in Systems, Decision and Control, vol 270. Springer, Singapore. https://doi.org/10.1007/978-981-15-1819-5_1

Download citation

Publish with us

Policies and ethics