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Fractional-Order Model Reference Adaptive Controllers for First-Order Integer Plants

  • Manuel A. Duarte-MermoudEmail author
  • Norelys Aguila-Camacho
  • Javier A. Gallegos
  • Juan C. Travieso-Torres
Chapter

Abstract

In this chapter, we extend the ideas of the model reference adaptive control (MRAC), developed for integer-order plants with integer-order adaptive laws, to the case of integer-order plants but with fractional-order adaptive laws. Two cases are analyzed in detail; the direct MRAC (DMRAC) and the combined MRAC (CMRAC). In both cases, boundedness of all the signals in the resultant adaptive scheme is theoretically proved and a discussion on the error, and parameter convergence is provided in each case. The study is performed for scalar first-order time-invariant plants, since extensions to the vector case are currently under investigation.

Notes

Acknowledgements

The results reported in this chapter have been financed by CONICYT- Chile, under the Basal Financing Program FB0809 “Advanced Mining Technology Center”, FONDECYT Project 1150488, “Fractional Error Models in Adaptive Control and Applications”, and FONDECYT 3150007, “Postdoctoral Program 2015”.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Manuel A. Duarte-Mermoud
    • 1
    Email author
  • Norelys Aguila-Camacho
    • 1
  • Javier A. Gallegos
    • 2
  • Juan C. Travieso-Torres
    • 3
  1. 1.Department of Electrical Engineering and AMTCUniversity of ChileSantiagoChile
  2. 2.Department of Electrical EngineeringUniversity of ChileSantiagoChile
  3. 3.Department of Industrial TechnologiesUniversity of Santiago de ChileSantiagoChile

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