Studying on the Synchronization of a Mechanical Centrifugal Flywheel Governor System

Abstract:

In this paper, the dynamical behaviors of the centrifugal flywheel governor with external disturbance are discussed, and the system exhibits exceedingly complicated dynamic behaviors. The influence of system parameter on the chaotic system is discussed through Lyapunov-exponents spectrum and global bifurcation diagram, which accurately portray the partial dynamic behavior of the system. It is chaotic with proper system parameter, and we utilize Poincaré sections to study the Hopf bifurcation and chaos forming of the centrifugal flywheel governor system. Then, we utilize coupled-feedback control and adaptive control to realize the chaotic synchronization and obtain the conditions of chaos synchronization. Finally, we carry on the theory proof using the Lyapunov stability theory to the obtained conditions, the theoretical proof and number simulation shows the effectiveness of these methods.

• Periodical: Key Engineering Materials (Volumes 385-387)
• Pages: 309-312
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.385-387.309
• Online since: July 2008
• Authors: Yan Dong Chu, Jian Gang Zhang, Xian Feng Li, Ying Xiang Chang
• Keywords: Chaos Synchronization, Flywheel Governor, Hopf Bifurcation, Poincaré Map

References

[1] Pecora LM, Carroll TL: Phys Rev Lett Vol. 64 (1990), p.821.

[2] Terry JR, Thornburg KS: Phys Rev E Vol. 359 (1999), p.4036.

[3] Yang, T, Chua, LO: Int. J. Bifurcation and Chaos Vol. 7 (1997), p.645.

[4] Yang, T, Chua, LO: Int. J. Bifurcation and Chaos Vol. 8 (1998), p.1657.

[5] Tao Chao-hai, Lu Jun-an, Lü Jin-hu: Acta Physica Sinica Vol. 51 (2002), p.1497.

[6] Z.M. Ge, J.K. Lee: Applied Mathematics and Computation Vol. 163 (2005), p.667.

[7] Z.M. Ge, J.K. Lee: Journal of Sound and Vibration Vol. 282 (2005), p.635.