Design And Analysis Of A Fractional-Order State-Space Adaptive Controller For Second-Order Systems

Souad ANTEUR; Rochdi BACHIR BOUIADJRA; Mohammed Benmadani   DEBBAT; Ramon VILANOVA ARBOS; Marwa  GAIDI; Fatima Zohra   HACENE

doi:10.66950/yt8vhk96

Authors

Souad ANTEUR University Mustapha Stambouli of Mascara Author https://orcid.org/0009-0009-9054-854X
Rochdi BACHIR BOUIADJRA University Mustapha Stambouli of Mascara Author https://orcid.org/0000-0002-7514-2025
Mohammed Benmadani DEBBAT University Mustapha Stambouli of Mascara Author https://orcid.org/0000-0002-8637-8607
Ramon VILANOVA ARBOS Universitat Autònoma de Barcelona Author https://orcid.org/0000-0002-8035-5199
Marwa GAIDI University Mustapha Stambouli of Mascara Author https://orcid.org/0000-0001-8116-9470
Fatima Zohra HACENE University Mustapha Stambouli of Mascara Author https://orcid.org/0009-0007-3749-8278

DOI:

https://doi.org/10.66950/yt8vhk96

Keywords:

Fractional Order Systems, Adaptive Control, State-Space Model, Second-Order Systems

Abstract

This article proposes an adaptive control method for a class of second-order fractional-order dynamic systems characterized by distinct eigenvalues in the state space. The control scheme developed is a generalization of the MRAC (Model Reference Adaptive Control) framework to scalar systems with fractional derivatives. To ensure accurate tracking of a reference model that is also fractional, an adaptive state feedback controller is designed. This is based on the tracking error between the outputs of the system and the model, incorporating a fractional-order adaptation law to ensure parameter convergence. Numerical simulations validate the effectiveness of the proposed approach and, through comparison with conventional MRAC control, highlight its superior performance in terms of tracking accuracy and robustness in the presence of uncertainties.

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