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Impulse Response of a Generalized Fractional Second Order Filter

[+] Author Affiliations
Zhuang Jiao

Tsinghua University, Beijing, China; Utah State University, Logan, UT

YangQuan Chen

Utah State University, Logan, UT

Paper No. DETC2011-47867, pp. 303-310; 8 pages
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 3: 2011 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5480-8
  • Copyright © 2011 by ASME


The impulse response of a generalized fractional second order filter of the form (s2α + asα + b)−γ is derived, where 0 < α ≤ 1, γ > 0. The asymptotic properties of the impulse responses are obtained for two cases, and similar properties are shown for these two cases when we change the value of γ. It is shown that only when (s2α + asα + b)−1 has the critical stability, the generalized fractional second order filter (s2α + asα + b)−γ has different properties as we change the value of γ. Finally, numerical examples to illustrate the impulse response are provided to verify the proposed concepts.

Copyright © 2011 by ASME



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