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Synchronization of Fractional-Order Chaotic System via Adaptive PID Controller

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New Trends in Nanotechnology and Fractional Calculus Applications

Abstract

Chaos in hard spring ϕ6-Van der Pol Oscillator, and its modelling and control with fractional-Order Calculus (FOC) is studied in this research. An adaptive PID controller with fractional order adaptation mechanism is proposed to synchronize fractional-order chaotic system. PID coefficients are updated using the gradient method when a proper sliding surface is chosen. Fractional-order ϕ6-Van der Pol Oscillator is used as case study to verify the proposed method.

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Author information

Authors and Affiliations

  1. Intelligent system research group, Faculty of Electrical and Computer Engineering, Noushirvani University of Technology, Babol, 47135-484, Iran

    Mohammad Mahmoudian, Reza Ghaderi, Abolfazl Ranjbar, Jalil Sadati & Seyed Hassan Hosseinnia

  2. Department of Mathematics, Faculty of Science, University of Jordan, Amman, 11942, Jordan

    Shaher Momani

Authors
  1. Mohammad Mahmoudian
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  2. Reza Ghaderi
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  3. Abolfazl Ranjbar
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  4. Jalil Sadati
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  5. Seyed Hassan Hosseinnia
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  6. Shaher Momani
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Corresponding author

Correspondence to Abolfazl Ranjbar .

Editor information

Editors and Affiliations

  1. Fac. Engineering & Architecture, Cankaya University, Ogretmenler Cad. 14, Ankara, 06530, Turkey

    Dumitru Baleanu

  2. Fac. Engineering & Architecture, Cankaya University, Ogretmenler Cad. 14, Ankara, 06530, Turkey

    Ziya B. Guvenc

  3. Polytechnic Institute of Porto, Institute of Engineering of the, Rua Dr. Antonio Bernardino de Almeida, Porto, 4200-072, Portugal

    J. A. Tenreiro Machado

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Mahmoudian, M., Ghaderi, R., Ranjbar, A., Sadati, J., Hosseinnia, S.H., Momani, S. (2010). Synchronization of Fractional-Order Chaotic System via Adaptive PID Controller. In: Baleanu, D., Guvenc, Z., Machado, J. (eds) New Trends in Nanotechnology and Fractional Calculus Applications. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3293-5_38

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  • DOI: https://doi.org/10.1007/978-90-481-3293-5_38

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-3292-8

  • Online ISBN: 978-90-481-3293-5

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