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Chaos suppression of Fractional order Willamowski–Rössler Chemical system and its synchronization using Sliding Mode Control

Chaos suppression of Fractional order Willamowski–Rössler Chemical system and its synchronization... Abstract Most of the Real systems shows chaotic behavior when they approach complex states. Especially in physical and chemical systems these behaviors define the character of the system. The control of these chaotic behaviors is of very high practical importance and hence mathematical models of these chaotic systems proves vital in deciding the control structures. One such model of chemical reactors is the Willamowski–Rössler system (WR). In this paper we derive a fractional order sliding mode control scheme where the states of the WR system are driven back to the defined equilibrium points. We have also synchronized master and slave fractional order WR system using sliding mode control. As the entire control law is defined in fractional order, we derived a new methodology to prove the stability of the controller. The numerical simulation and analysis are achieved with LabVIEW. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Chaos suppression of Fractional order Willamowski–Rössler Chemical system and its synchronization using Sliding Mode Control

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
2192-8010
eISSN
2192-8029
DOI
10.1515/nleng-2016-0027
Publisher site
See Article on Publisher Site

Abstract

Abstract Most of the Real systems shows chaotic behavior when they approach complex states. Especially in physical and chemical systems these behaviors define the character of the system. The control of these chaotic behaviors is of very high practical importance and hence mathematical models of these chaotic systems proves vital in deciding the control structures. One such model of chemical reactors is the Willamowski–Rössler system (WR). In this paper we derive a fractional order sliding mode control scheme where the states of the WR system are driven back to the defined equilibrium points. We have also synchronized master and slave fractional order WR system using sliding mode control. As the entire control law is defined in fractional order, we derived a new methodology to prove the stability of the controller. The numerical simulation and analysis are achieved with LabVIEW.

Journal

Nonlinear Engineering – de Gruyter

Published: Sep 1, 2016

References

  • Entropy Production of the Willamowski–Rössler Oscillator
  • A note on the stability of fractional order systems
  • Fractional order systems without equilibria: The firstexample of hyperchaos and its application to synchronization
  • Sliding mode controller design for the global chaos synchronization of Coullet systems, Lecture Notes of the Institute for Computer Sciences