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Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay

Author

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  • Ge, Zheng-Ming
  • Lee, Ching-I

Abstract

Chaos, control, anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor and spring for which time-delay effect is considered are studied in the paper. By applying numerical results, phase diagram and power spectrum are presented to observe periodic and chaotic motions. Linear feedback control and adaptive control algorithm are used to control chaos effectively. Linear and nonlinear feedback synchronization and phase synchronization for the coupled systems are presented. Finally, anticontrol of chaos for this system is also studied.

Suggested Citation

  • Ge, Zheng-Ming & Lee, Ching-I, 2005. "Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1855-1864.
    • Handle: RePEc:eee:chsofr:v:23:y:2005:i:5:p:1855-1864
    DOI: 10.1016/j.chaos.2004.07.023
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    Citations

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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. Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    3. Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
    4. Ge, Zheng-Ming & Lin, Guo-Hua, 2007. "The complete, lag and anticipated synchronization of a BLDCM chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 740-764.
    5. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    6. Yang, Yanling & Wang, Qiubao, 2023. "Capture of stochastic P-bifurcation in a delayed mechanical centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Yan, Jun-Juh & Lin, Jui-Sheng & Liao, Teh-Lu, 2007. "Robust dynamic compensator for a class of time delay systems containing saturating control input," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1223-1231.
    8. Tam, Lap Mou & Si Tou, Wai Meng, 2008. "Parametric study of the fractional-order Chen–Lee system," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 817-826.
    9. Ge, Zheng-Ming & Chang, Ching-Ming, 2009. "Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1959-1974.
    10. Chen, Juhn-Horng, 2008. "Controlling chaos and chaotification in the Chen–Lee system by multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 843-852.
    11. 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.
    12. Yeh, Jiin-Po, 2007. "Identifying chaotic systems using a fuzzy model coupled with a linear plant," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1178-1187.
    13. Du, Shengzhi & van Wyk, Barend J. & Qi, Guoyuan & Tu, Chunling, 2009. "Chaotic system synchronization with an unknown master model using a hybrid HOD active control approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1900-1913.
    14. 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.
    15. Alidousti, J. & Eskandari, Z., 2021. "Dynamical behavior and Poincare section of fractional-order centrifugal governor system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 791-806.
    16. Ge, Zheng-Ming & Zhang, An-Ray, 2007. "Chaos in a modified van der Pol system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1791-1822.
    17. Ge, Zheng-Ming & Hsu, Mao-Yuan, 2007. "Chaos in a generalized van der Pol system and in its fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1711-1745.

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