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Stabilizing Periodic Orbits of the Fractional Order Chaotic Van Der Pol System

[+] Author Affiliations
Mohammad A. Rahimi, Hasan Salarieh, Aria Alasty

Sharif University of Technology, Tehran, Iran

Paper No. IMECE2010-40165, pp. 175-183; 9 pages
doi:10.1115/IMECE2010-40165
From:
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME

abstract

In this paper, stabilizing the unstable periodic orbits (UPO) in a chaotic fractional order system called Van der Pol is studied. Firstly, a technique for finding unstable periodic orbit in chaotic fractional order systems is stated. Then by applying this technique to the van der Pol system, unstable periodic orbit of system is found. After that, a method is presented for stabilization of the discovered UPO based on theories stability of the linear integer order and fractional order systems. Finally, a linear feedback controller was applied to the system and simulation is done for demonstration of controller performance.

Copyright © 2010 by ASME

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