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Algebraic bound for the phase–frequency response of the commande robuste d'ordre non-entier approximation of fractional differentiators and its applications in control systems analysis

Neshat, K ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1177/1077546320987767
  3. Publisher: SAGE Publications Inc , 2022
  4. Abstract:
  5. This article deals with analyzing the phase–frequency response of commande robuste d'ordre non-entier approximations of fractional-order differentiators. More precisely, an algebraic tight upper bound is derived for the phase of the approximations obtained from the commande robuste d'ordre non-entier method. Then, some applications for this achievement are discussed in the viewpoint of control systems analysis. These applications include usefulness of the obtained upper bound in stability preservation analysis during the commande robuste d'ordre non-entier–based approximation process and applicability of such a bound in finding necessary or sufficient conditions for test of positive realness/negative imaginariness of a fractional-order transfer function. © The Author(s) 2021
  6. Keywords:
  7. Approximation ; Fractional-order controllers ; Negative imaginary systems ; Positive real systems ; Stability analysis ; Control system analysis ; Frequency response ; Systems analysis ; Approximation process ; Fractional differentiators ; Fractional order transfer function ; Fractional-order differentiators ; ITS applications ; Positive realness ; Upper Bound ; Algebra
  8. Source: JVC/Journal of Vibration and Control ; Volume 28, Issue 9-10 , 2022 , Pages 1074-1085 ; 10775463 (ISSN)
  9. URL: https://journals.sagepub.com/doi/10.1177/1077546320987767