Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

Download PDF
9 pages

Loading next page...
 
/lp/de-gruyter/chaos-suppression-in-fractional-order-permanent-magnet-synchronous-B4iRfqAlF0
Publisher
de Gruyter
Copyright
© 2017 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2016-0059
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

Journal

Nonlinear Engineering – de Gruyter

Published: Jun 27, 2017

References

  • Codimension - two Bifurcations In Indirect Field Oriented Control of Induction Motor Drives of Bifurcation and Chaos pp
    Salas
  • A New Approach To Generalized Fractional Derivatives Bull Issue pages
    Katugampola
  • Bispectral analysis of systems possessing chaotic motions of Sound and Vibration vol no pp
    Pezeshki
  • and Yu Dynamic analysis of a fractional - order Lorenz chaotic system Chaos Solutions Volume Issue Pages
    Yu
  • note on the fractional - order Chua s system Chaos Solitons and
    Petras
  • Fractional order state equations for the control of viscoelastically damped structures Journal of Guidance Control and Dynamics Vol No pp
    Bagley
  • Bifurcations and chaos in a permanent - magnet synchronous motor IEEE Circuits and Systems I Theory and Applications
    Li
  • Electromagnetic Theory ( New York
    Heaviside
  • Fractional order systems without equilibria Chin
    Li
  • Chaos and hyperchaos in the fractional - order Rössler equations Physica A : Statistical Mechanics and its Applications Volume Pages
    Li
  • Review of wind turbine control
    Salle
  • Hopf bifurcations in indirect field oriented control of induction motors : Designing a robust PI controller Proceedings of the th Conference on Decision and Control Phoenix Arizona
    Bazanella
  • u note on the fractional - order Chen system Chaos Solutions Volume Issue Pages
    Chen
  • Zero - Hopf Bifurcation in Indirect Field Oriented Control of Induction Motors First IFAC Conference on Analysis and Control of Chaotic Systems
    Reginatto