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Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems

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  • Ge, Zheng-Ming
  • Chang, Ching-Ming
  • Chen, Yen-Sheng

Abstract

Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented.

Suggested Citation

  • Ge, Zheng-Ming & Chang, Ching-Ming & Chen, Yen-Sheng, 2006. "Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1298-1315.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1298-1315
    DOI: 10.1016/j.chaos.2005.04.095
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    1. Sarasola, C. & Torrealdea, F.J. & d’Anjou, A. & Graña, M., 2002. "Cost of synchronizing different chaotic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(4), pages 309-327.
    2. Bernd Blasius & Amit Huppert & Lewi Stone, 1999. "Complex dynamics and phase synchronization in spatially extended ecological systems," Nature, Nature, vol. 399(6734), pages 354-359, May.
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    Cited by:

    1. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2008. "Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 592-604.
    2. Zribi, Mohamed & Oteafy, Ahmed & Smaoui, Nejib, 2009. "Controlling chaos in the permanent magnet synchronous motor," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1266-1276.
    3. Chen, Juhn-Horng & Chen, Hsien-Keng & Lin, Yu-Kai, 2009. "Synchronization and anti-synchronization coexist in Chen–Lee chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 707-716.
    4. Tsai, Hsun-Heng & Fuh, Chyun-Chau, 2007. "Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 886-895.
    5. Wang, Zheng & Chau, K.T., 2008. "Anti-control of chaos of a permanent magnet DC motor system for vibratory compactors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 694-708.

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