A Fractional Model Predictive Control for Fractional Order Systems

Chapter

Abstract

This paper presents a new approach to model predictive control (MPC) that uses fractional order system representation in the MPC to describe the dynamics of plant used to construct the control law. The use of the fractional model guarantees stability and performance of the closed-loop especially with the present of noise. Simulation results are presented to show that the use of fractional order MPC achieves better control performance when compared to those of the conventional MPC that uses integer order models.

References

  1. 1.
    Shantanu D (2008) Functional fractional calculus for system identification and controls. Springer, BerlinMATHGoogle Scholar
  2. 2.
    Valério D, da Costa JSá (2006) Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Process 86:2771–2784Google Scholar
  3. 3.
    Guzmán JL, Berenguel M, Dormido S (2005) Interactive teaching of constrained generalized predictive control. IEEE Contr Syst Mag 25:52–66CrossRefGoogle Scholar
  4. 4.
    Camacho EF, Bordóns C (2004) Model predictive control. Springer, BerlinMATHCrossRefGoogle Scholar
  5. 5.
    Clarke T, Achar BNN, Hanneken JW (2004) MittagLeffler functions and transmission lines, J Mol Liq 114:159–163CrossRefGoogle Scholar
  6. 6.
    Rossiter JA (2003) Model-based predictive control: A practical approach. CRC Press, Boca Raton, FLGoogle Scholar
  7. 7.
    Maciejowski J (2002) Predictive control with constraints. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  8. 8.
    Kulish VV, Lage JL (2000) Fractional-diffusion solutions for transient local temperature and heat flux. Trans ASME 122:372–376CrossRefGoogle Scholar
  9. 9.
    Podlubny I (1999) Fractional-order systems and PIΛ Dμ controllers. IEEE Trans Automat Contr 44:208–214MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Podlubny I (1999) Fractional differential equations: An introduction to fractional derivatives, fractional differential equations to methods of their solution and some of their applications. Academic Press, San DiegoMATHGoogle Scholar
  11. 11.
    Richalet J (1993) Industrial applications of model based predictive control. Automatica 29:1251–1274MathSciNetCrossRefGoogle Scholar
  12. 12.
    Miller KS, Ross B (1993) An introduction to the fractional calculus and fractional differential equations. Wiley, New YorkMATHGoogle Scholar
  13. 13.
    Chareff A, Sun HH, Tsao YY, Onaral B (1992) Fractional system as represented by singularity function. IEEE Trans Automat Contr 37:1465–1470CrossRefGoogle Scholar
  14. 14.
    Oustaloup A (1991) La commande CRONE: commande robuste d´ordre non entier. Hermès, ParisMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Laboratory of Automatics and Informatics of Guelma (LAIG), Department of Electrical EngineeringUniversity of GuelmaGuelmaAlgeria
  2. 2.Department of ElectrotechniqueUniversity of SkikdaSkikdaAlgeria

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