As fractional-order systems are becoming more widely accepted and their usage is increasing, it is important to understand their energy storage and loss properties. Fractional-order operators can be implemented using a distributed state representation, which has been shown to be equivalent to the Riemann–Liouville representation. In this paper, the distributed state for a fractional-order integrator is represented using an infinite resistor–capacitor network such that the energy storage and loss properties can be readily determined. This derivation is repeated for fractional-order derivatives using an infinite resistor–inductor network. An analytical example is included to verify the results for a half-order integrator. Approximation methods are included.
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November 2015
Research-Article
Energy Storage and Loss in Fractional-Order Systems
Tom T. Hartley,
Tom T. Hartley
Department of Electrical and Computer Engineering,
e-mail: thartley@uakron.edu
University of Akron
,Akron, OH 44325-3904
e-mail: thartley@uakron.edu
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Jean-Claude Trigeassou,
Jean-Claude Trigeassou
IMS-LAPS,
e-mail: jean-claude.trigeassou@ims-bordeaux.fr
University of Bordeaux 1
,Talence Cedex 33405
, France
e-mail: jean-claude.trigeassou@ims-bordeaux.fr
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Nezha Maamri
Nezha Maamri
Search for other works by this author on:
Tom T. Hartley
Department of Electrical and Computer Engineering,
e-mail: thartley@uakron.edu
University of Akron
,Akron, OH 44325-3904
e-mail: thartley@uakron.edu
Jean-Claude Trigeassou
IMS-LAPS,
e-mail: jean-claude.trigeassou@ims-bordeaux.fr
University of Bordeaux 1
,Talence Cedex 33405
, France
e-mail: jean-claude.trigeassou@ims-bordeaux.fr
Carl F. Lorenzo
Nezha Maamri
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 30, 2014; final manuscript received December 27, 2014; published online April 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.
J. Comput. Nonlinear Dynam. Nov 2015, 10(6): 061006 (8 pages)
Published Online: November 1, 2015
Article history
Received:
April 30, 2014
Revision Received:
December 27, 2014
Online:
April 9, 2015
Citation
Hartley, T. T., Trigeassou, J., Lorenzo, C. F., and Maamri, N. (November 1, 2015). "Energy Storage and Loss in Fractional-Order Systems." ASME. J. Comput. Nonlinear Dynam. November 2015; 10(6): 061006. https://doi.org/10.1115/1.4029511
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