Optimal observer-based feedback control for linear fractional-order systems with periodic coefficients

Arman Dabiri, Eric Butcher

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper proposes a new technique to design an optimal observer-based feedback control for linear fractional-order systems with constant or periodic coefficients. The proposed observer-based feedback control assures the fastest convergence of the closed-loop system’s states. For this purpose, a state-transition operator is defined in a Banach space and approximated using the fractional Chebyshev collocation method. It is shown that periodic gains of the controller and observer can be independently tuned by minimizing the spectral radius of their associated state-transition operators. The validity and efficiency of the proposed method are demonstrated through two illustrative examples.

Original languageEnglish (US)
JournalJVC/Journal of Vibration and Control
DOIs
StatePublished - Jan 1 2019

Fingerprint

Feedback control
Banach spaces
Closed loop systems
Mathematical operators
Controllers
Optimal design

Keywords

  • fractional Chebyshev collocation method
  • Fractional-order systems
  • optimal control
  • optimal observer-based feedback control
  • periodic differential equations
  • spectral method

ASJC Scopus subject areas

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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abstract = "This paper proposes a new technique to design an optimal observer-based feedback control for linear fractional-order systems with constant or periodic coefficients. The proposed observer-based feedback control assures the fastest convergence of the closed-loop system’s states. For this purpose, a state-transition operator is defined in a Banach space and approximated using the fractional Chebyshev collocation method. It is shown that periodic gains of the controller and observer can be independently tuned by minimizing the spectral radius of their associated state-transition operators. The validity and efficiency of the proposed method are demonstrated through two illustrative examples.",
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AB - This paper proposes a new technique to design an optimal observer-based feedback control for linear fractional-order systems with constant or periodic coefficients. The proposed observer-based feedback control assures the fastest convergence of the closed-loop system’s states. For this purpose, a state-transition operator is defined in a Banach space and approximated using the fractional Chebyshev collocation method. It is shown that periodic gains of the controller and observer can be independently tuned by minimizing the spectral radius of their associated state-transition operators. The validity and efficiency of the proposed method are demonstrated through two illustrative examples.

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