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A Gallery of Root Locus of Fractional Systems

[+] Author Affiliations
J. A. Tenreiro Machado

Institute of Engineering of Polytechnic of Porto, Porto, Portugal

Paper No. DETC2013-12470, pp. V004T08A018; 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


The root locus (RL) is a classical tool for the stability analysis of integer order linear systems, but its application in the fractional counterpart poses some difficulties. Therefore, researchers have mainly preferred to adopt frequency based methods. Nevertheless, recently the RL was considered for the stability analysis of fractional systems. One first method is by tacking advantage of commensurable expressions that occur when truncating fractional orders up to a finite precision. The second method consists of searching the complex plane for solutions of the characteristic equation using a numerical procedure. The resulting charts are insightful about the characteristics of the closed-loop system that outperform the frequency response methods. Given the limited know how in this particular topic and the shortage of literature, this study explores several types of fractional-order transfer functions and presents the corresponding RL.

Copyright © 2013 by ASME



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