Bifurcation Analysis of Horizontal Platform System
Horizontal platform system (HPS) is popularly applied
in offshore and earthquake technology, but it is difficult and
time-consuming for regulation. In order to understand the nonlinear
dynamic behavior of HPS and reduce the cost when using it, this paper
employs differential transformation method to study the bifurcation
behavior of HPS. The numerical results reveal a complex dynamic
behavior comprising periodic, sub-harmonic, and chaotic responses.
Furthermore, the results reveal the changes which take place in the
dynamic behavior of the HPS as the external torque is increased.
Therefore, the proposed method provides an effective means of
gaining insights into the nonlinear dynamics of horizontal platform
system.
[1] A. N. Miliou ´╣É I. P. Antoniades ´╣É S. G. Stavrinides ´╣É and A. N.
Anagnostopoulos´╣É"Secure communication by chaotic synchronization:
robustness under noisy conditions," Nonlinear Analysis-Real World
Applications´╣É vol. 8, pp. 1003-1012´╣ÉJuly 2007.
[2] M. Chen´╣É and W. Min´╣É"Unknown input observer based chaotic secure
communication," Physics Letters A´╣É vol. 372, pp. 1595-1600´╣É March 2008.
[3] C. K. Huang´╣É S. C. Tsay´╣É and Y. R. Wu´╣É"Implementation of chaotic secure
communication systems based on OPA circuits," Chaos Solitons &
Fractals´╣É vol. 23, pp. 589-600´╣ÉJan 2005.
[4] S. C. Tsay´╣É C. K. Huang´╣É D. L. Qiu´╣É and W. T. Chen´╣É"Implementation of
bidirectional chaotic communication systems based on Lorenz circuits,"
Chaos Solitons & Fractals´╣É vol. 20, pp. 567-579´╣É May 2004.
[5] M. Itoh ´╣É "Synthesis of electronic circuits for simulating nonlinear
dynamics," International Journal of Bifurcation and Chaos´╣É vol. 11, pp.
605-653´╣ÉMar 2001.
[6] H. H. Chen´╣É"Stability and chaotic dynamics of a perturbed rate gyro,"
Chaos Solitons & Fractals´╣É vol. 30, pp. 822-835´╣ÉNov 2006.
[7] Z. Wang´╣É and K. T. Chau´╣É"Anti-control of chaos of a permanent magnet
DC motor system for vibratory compactors," Chaos Solitons & Fractals´╣É
vol. 36, pp. 694-708´╣É May 2008.
[8] C. L. Huang´╣É"Nonlinear Dynamics of the Horizontal Platform," Master of
Science in Mechanical Engineering Thesis´╣ÉNCTU´╣É1996.
[9] Z. M. Ge´╣É T. C. Yu´╣É and Y. S. Chen´╣É"Chaos synchronization of a horizontal
platform system," Journal of Sound and Vibration´╣É vol. 268, pp. 731-749´╣É
Dec 2003.
[10] X. F. Wu´╣É J. P. Cai´╣É and M. H. Wang´╣É"Master-slave chaos synchronization
criteria for the horizontal platform systems via linear state error feedback
control," Journal of Sound and Vibration´╣É vol. 295, pp. 378-387´╣ÉAug
2006.
[11] X. F. Wu´╣É J. P. Cai´╣É and M. H. Wang´╣É"Robust synchronization of chaotic
horizontal platform systems with phase difference," Journal of Sound and
Vibration´╣É vol. 305, pp. 481-491´╣ÉAug 2007.
[12] J. Y. Lee´╣É"The corresponding phenomena of mechanical and electronic
impact oscillator," Journal of Sound and Vibration´╣É vol. 311, pp. 579-587
´╣ÉMar 2008.
[13] C. C. Wang, and H. T. Yau, "Analysis of nonlinear dynamic behavior of
atomic force microscope using differential transformation method,"
ACTA Mechanica, vol. 198, pp. 87-98, 2008.
[14] C. C. Wang, "Application of a hybrid method to the nonlinear dynamic
analysis of a spherical gas journal bearing system," Nonlinear
Analysis-Theory Methods & Applications, vol.70, pp. 2035-2053, 2009.
[15] C. C. Wang, "Chaotic analysis and control of microcandilevers with PD
feedback using differential transformation method," International
Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, pp.
425-444, April 2009.
[1] A. N. Miliou ´╣É I. P. Antoniades ´╣É S. G. Stavrinides ´╣É and A. N.
Anagnostopoulos´╣É"Secure communication by chaotic synchronization:
robustness under noisy conditions," Nonlinear Analysis-Real World
Applications´╣É vol. 8, pp. 1003-1012´╣ÉJuly 2007.
[2] M. Chen´╣É and W. Min´╣É"Unknown input observer based chaotic secure
communication," Physics Letters A´╣É vol. 372, pp. 1595-1600´╣É March 2008.
[3] C. K. Huang´╣É S. C. Tsay´╣É and Y. R. Wu´╣É"Implementation of chaotic secure
communication systems based on OPA circuits," Chaos Solitons &
Fractals´╣É vol. 23, pp. 589-600´╣ÉJan 2005.
[4] S. C. Tsay´╣É C. K. Huang´╣É D. L. Qiu´╣É and W. T. Chen´╣É"Implementation of
bidirectional chaotic communication systems based on Lorenz circuits,"
Chaos Solitons & Fractals´╣É vol. 20, pp. 567-579´╣É May 2004.
[5] M. Itoh ´╣É "Synthesis of electronic circuits for simulating nonlinear
dynamics," International Journal of Bifurcation and Chaos´╣É vol. 11, pp.
605-653´╣ÉMar 2001.
[6] H. H. Chen´╣É"Stability and chaotic dynamics of a perturbed rate gyro,"
Chaos Solitons & Fractals´╣É vol. 30, pp. 822-835´╣ÉNov 2006.
[7] Z. Wang´╣É and K. T. Chau´╣É"Anti-control of chaos of a permanent magnet
DC motor system for vibratory compactors," Chaos Solitons & Fractals´╣É
vol. 36, pp. 694-708´╣É May 2008.
[8] C. L. Huang´╣É"Nonlinear Dynamics of the Horizontal Platform," Master of
Science in Mechanical Engineering Thesis´╣ÉNCTU´╣É1996.
[9] Z. M. Ge´╣É T. C. Yu´╣É and Y. S. Chen´╣É"Chaos synchronization of a horizontal
platform system," Journal of Sound and Vibration´╣É vol. 268, pp. 731-749´╣É
Dec 2003.
[10] X. F. Wu´╣É J. P. Cai´╣É and M. H. Wang´╣É"Master-slave chaos synchronization
criteria for the horizontal platform systems via linear state error feedback
control," Journal of Sound and Vibration´╣É vol. 295, pp. 378-387´╣ÉAug
2006.
[11] X. F. Wu´╣É J. P. Cai´╣É and M. H. Wang´╣É"Robust synchronization of chaotic
horizontal platform systems with phase difference," Journal of Sound and
Vibration´╣É vol. 305, pp. 481-491´╣ÉAug 2007.
[12] J. Y. Lee´╣É"The corresponding phenomena of mechanical and electronic
impact oscillator," Journal of Sound and Vibration´╣É vol. 311, pp. 579-587
´╣ÉMar 2008.
[13] C. C. Wang, and H. T. Yau, "Analysis of nonlinear dynamic behavior of
atomic force microscope using differential transformation method,"
ACTA Mechanica, vol. 198, pp. 87-98, 2008.
[14] C. C. Wang, "Application of a hybrid method to the nonlinear dynamic
analysis of a spherical gas journal bearing system," Nonlinear
Analysis-Theory Methods & Applications, vol.70, pp. 2035-2053, 2009.
[15] C. C. Wang, "Chaotic analysis and control of microcandilevers with PD
feedback using differential transformation method," International
Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, pp.
425-444, April 2009.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:61800", author = "C. C. Wang and N. S. Pai and H. T. Yau and T. T. Liao and M. J. Jang and C. W. Lee and W. M. Hong", title = "Bifurcation Analysis of Horizontal Platform System", abstract = "Horizontal platform system (HPS) is popularly applied
in offshore and earthquake technology, but it is difficult and
time-consuming for regulation. In order to understand the nonlinear
dynamic behavior of HPS and reduce the cost when using it, this paper
employs differential transformation method to study the bifurcation
behavior of HPS. The numerical results reveal a complex dynamic
behavior comprising periodic, sub-harmonic, and chaotic responses.
Furthermore, the results reveal the changes which take place in the
dynamic behavior of the HPS as the external torque is increased.
Therefore, the proposed method provides an effective means of
gaining insights into the nonlinear dynamics of horizontal platform
system.", keywords = "horizontal platform system, differentialtransformation method, chaotic.", volume = "4", number = "5", pages = "618-4", }
