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Energy Stored in Fractional-Order Elements With Constant Inputs

[+] 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. DETC2015-47450, pp. V009T07A044; 9 pages
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 9: 2015 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5719-9
  • Copyright © 2015 by ASME


The internal efficiency of the energy storage in a general fractional-order circuit element is analyzed. By use of distributed-circuit representations, integral expressions are derived for the energy stored in a fractional-order integrator or a fractional-order differentiator for any given profile of the distributed state. For either constant-current or constant-voltage charging, these expressions for the stored energy are evaluated and compared with the energy supplied at the terminals of the element, so that the efficiency of the charging process is determined. The result is found to verify a published conjecture on the constant-input charging efficiency of the fractional-order elements.

Copyright © 2015 by ASME



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