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研究生:楊吉雯
研究生(外文):chi-wen Yang
論文名稱:速率陀螺儀之渾沌同步與反控制
論文名稱(外文):Chaos Synchronization and Chaos Anticontrol of a Rate Gyroscope
指導教授:戈正銘戈正銘引用關係
指導教授(外文):Zheng-Ming Ge
學位類別:碩士
校院名稱:國立交通大學
系所名稱:機械工程系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:76
中文關鍵詞:速率陀螺儀渾沌同步渾沌反控制李亞普諾夫指數法耦合項臨界耦合強度
外文關鍵詞:Rate gyroscopeChaos synchronizationChaos anticontrolLyapunov exponentCoupling termCritical coupling strength
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本篇論文研究速率陀螺儀非線性系統的渾沌同步,不同相位對同步之影響與反控制。藉由一個相同於原系統但初始值不同的系統,利用六種不同的耦合項去使兩系統產生渾沌同步。並且以李亞普諾夫指數法,時間響應以及系統同步時間去驗證系統同步時的臨界耦合強度值。接著引進歐幾里得距離以研究單向耦合時同步的暫態時間,並作出一耦合強度與距離的關係圖。然後討論如果兩個相同系統初始相位值不同,會對同步發生的影響。
繼之,以外加控制項使原來之週期解改變為渾沌以達成反控制的要求。使用的反控制方法為:外加定力矩、外加週期力矩、外加週期脈衝、時間延遲控制、適應性反控制。

Chaos synchronization and anticontrol of a rate gyroscope are studied in this thesis. By generating two identical systems with different initial conditions, six different coupling terms are used to synchronize the chaotic systems. Lyapunov exponent, time response and synchronous time are used to confirm the critical coupling strength. Then Euclidean distance is used to unidirectional synchronization and plot a figure with coupling strength vs the distance. Next, it is discovered that two identical systems with different initial phase may give different effect to synchronization.
Finally anticontrolling term is added to change state from regular to chaos. The anticontrolling methods such as adding of a constant torque, a periodic torque, a periodic impulse torque, time delay control, and adaptive anticontrol are used.

CHINESE ABSTRACT i
ENGLISH ABSTRACT ii
ACKNOWLEDGMENTS iii
CONTENTS iv
LIST OF FIGURES vi
Chapter 1 Introduction 1
Chapter 2 Simulation Analysis of Chaos Synchronization
of Coupled Systems 3
2.1 Description of the System Model and
Differential Equation of Motion 3
2.2 Synchronization of Coupled Chaotic Systems
by Adding Linear Coupling Term 5
2.3 Synchronization of Coupled Chaotic Systems
by Adding Periodic Coupling Term 7
2.4 Synchronization of Coupled Chaotic Systems
by Adding a Product of Cosine and Sine Coupling
Term 8
2.5 Transient Time in Chaotic Synchronization 9
Chapter 3 Effect of the Phase Difference of Harmonic
Excitations for Two Coupled Systems 11
Chapter 4 Anticontrol of Chaos 14
4.1 Anticontrol of Chaos by Adding of a Constant
Torque 14
4.2 Anticontrol of Chaos by Adding of a Periodic
Torque 15
4.3 Anticontrol of Chaos by Adding of a Periodic
Impulse Torque 15
4.4 Anticontrol of Chaos by Using Time-Delay
Feedback Systems 16
4.5 Anticontrol of Chaos by Using Adaptive Control
16
Chapter 5 Conclusions 18
References 75

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9. Giovanni Santobont, Steven R. Bishop and Alberto Varone, “Transient Time in Unidirectional Synchronization”, International Journal of Bifurcation and Chaos, Vol. 9, No. 12, pp.2345-2352, 1999.
10. H. J. Zhang, “Phase Effect of Two Coupled Periodically Driven Duffing Oscillators”, Physics Review E, Vol. 58, No. 5, pp.5683-5688, 1998.
11. Z. Qu, G. Hu, G. Yang, and G. Qin, “Phase Effect in Taming Nonautonomous Chaos by Weak Harmonic Perturbations”, Physics Review Letter 74,1736, 1995.
12. M. G. Rosenblum, A. S. Pikovsky, and J. Kurths, “From Phase to Lag Synchronization in Coupled Chaotic Oscillators”, Physical Review Letters, pp.4193-4196, 1996.
13. Guanrong Chen “Control and Anticontrol of Chaos”, IEEE, pp.181-186, 1997.
14. Xiao Fan Wang, Guanrong Chen, Xinghuo Yu “Anticontrol of Chaos in Continuous-Time Systems via Time-Delay Feedback”, Chaos, Vol. 10, No. 4, pp.771-779, 2000.
15. G. Chen ”Chaos: Control and anticontrol”, IEEE Circuits Syst. Soc. Newslett., Vol.9, pp.1-5, 1998.
16. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto “Controlling chaos in the brain”, Nature, Vol. 370, pp.615-620,1994.
17. W. Yang, M. Ding, A. J. Mandell, and E. Ott “Preserving Chaos: Control Strategies to Preserve Complex Dynamics with Potential Relevance to Biological Disorders”, Physics Letters E, Vol. 51, pp.102-110, 1995.

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