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On the Energy Stored in Fractional-Order Electrical Elements

[+] Author Affiliations
Tom T. Hartley, Robert J. Veillette, Jay L. Adams

University of Akron, Akron, OH

Carl F. Lorenzo

NASA Glenn Research Center, Cleveland, OH

Paper No. DETC2013-13498, pp. V004T08A032; 6 pages
  • ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 4: 18th Design for Manufacturing and the Life Cycle Conference; 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Portland, Oregon, USA, August 4–7, 2013
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5591-1
  • Copyright © 2013 by ASME


In this paper, fractional-order electrical elements are considered as energy storage devices. They are studied by comparing the energy available from the element to do future external work, relative to the energy input into the element in the past. A standard circuit realization is used to represent the fractional-order element connected to an inductor with a given initial current. This circuit realization is used to determine the energy returned by both capacitive and inductive fractional-order elements of order between zero and one. Plots of the energy stored versus time are provided. The major conclusion is that fractional-order elements tend to rapidly dissipate much of their input energy leaving less energy for doing work in the future.

Copyright © 2013 by ASME



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