本篇論文探討一帶振動離心調速器之旋轉機械受到簡諧激力所產生的動態行為。由李亞普諾夫直接法可求得系統運動的穩定條件。此外藉相位圖、功率譜法、龐加萊映射法及李亞普諾夫指數可觀察到週期性及渾沌運動。並且參數變化對系統的影響可以由分歧圖即參數圖表現出來。及全局分析中，系統每個吸引子之吸引區即運動的全貌由改進式內插包映射法(modified interpolated cell mapping)求得。最後，利用外加定值的力矩、週期力矩、輸入週期脈衝、延遲迴授控制、最佳控制、bang-bang控制、適應控制及輸入一顫振訊號法則來有效地抑制渾沌行為。

The dynamic behaviors of the rotational machine with vibrating fly-ball governor that is subjected by two different forms of external disturbances are studied in the thesis. The Lyapunov direct method is applied to obtain conditions of stability of the motions of system. By applying numerical result, phase diagrams, power spectrum, Poincare maps, and Lyapunov exponents are presented to observer periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractors of the system are located by employing the modified interpolated cell mapping (MICM) method. Finally, various methods, such as the addition of periodic torque, using periodic impulse input as control torque, the delayed feedback control, optimal control, bang-bang control, adaptive control algorithm and the injection of a dither signal method are used to control chaos effectively.

ABSTRACTi
CONTENTSii
LIST OF TABLE AND FIGURESiv
NOMENCLATURESix
Chapter 1INTRODUCTION1
Chapter 2THE ANALYTICAL ANALYSES OF THE SYSTEM4
2.1A Dynamical Model4
2.2Stability Analysis by Lyapunov Direct Method6
Chapter 3COMPUTATIONAL ANALYSES OF NONAUTONOMOUS SYSTEM12
3.1Phase Portraits and Poincare Map12
3.1Time History and Power Spectrum13
3.3Poincare Map and Bifurcation Diagram14
3.4Lyapunov Exponent and Lyapunov Dimension15
3.5Global Analysis by Modified Interpolated Cell Mapping Method17
Chapter 4CONTROLLING CHAOS20
4.1Controlling Chaos by the Addition of Constant Torque20
4.2Controlling Chaos by the Addition of Periodic Torque21
4.3Controlling Chaos by the Addition of Periodic Impulse Input22
4.4Control of Chaos by Delayed Feedback22
4.5Optimal Control of Chaos23
4.6Using Bang-Bang Control Chaos25
4.7Control of Chaos by Adaptive Control Algorithm26
4.8Controlling Chaos by Injecting Dither Signal27
Chapter 5CONCLUSIONS29
REFERENCES69

1. Moon, F. C., "Chaotic Vibrations: An Introduction for Applied for Scientists and Engineers", Wiley, Now York, 1987.
2. Khalil, H. K., "Nonlinear Systems", Prentice Hall, New Jersey, 1996.
3. Vidyasagar, M., "Nonlinear Systems Analysis", Prentice Hall, New Jersey, 1990.
4. Thompson, J. M. T., and H. B. Stewart, "Nonlinear Dynamics and Chaos", Wiley, Chichester, 1986.
5. Brockett, T. W., "On Conditions Leading to Chaos in Feedback Systems", Proc. IEEE 21st Conf. Decision and Control, 1982, pp. 932-936.
6. Holmes, P., "Bifurcation and Chaos in a Simple Feedback Control System", Proc. IEEE 22nd Conf. Decision and Control, 1983, pp. 365-370.
7. Sanders, J. A., and F. Verhulst, "Averaging Methods in Nonlinear Dynamics", Spinger-Verlag, New York, 1985.
8. Nayfeh, A. H., "Perturbation Methods", Wiley, New York, 1973.
9. Sekar, P., and S. Narayanan, "Periodic and Chaotic Motions of a Square Prism in Cross-Flow", Journal of Sound and Vibration, Vol. 170, No. 1, pp. 1-24, 1994.
10. Gottlieb, O., "Bifurcations and Routes to Chaos in Wave-Structure Interaction Systems", Journal of Guidance Control and Dynamics, Vol.15, No.4, pp. 832-839, 1992.
11. Lau, S. L., and Y. K. Cheung, "Amplitude Incremental Variational Principle for Nonlinear Vibration of Elastic Systems", ASME Journal of Applied Mechanics, Vol. 48, pp. 959-964, 1981.
12. Cheung, Y. K., and S. H. Chen, "Application of the Incremental Harmonic Balance Method to Cubic Nonlinear Systems", Journal of Sound and Vibration, Vol. 140, No.2, pp. 273-286, 1990.
13. Friedmann, P., C. E. Hammond, and T. H. Woo, "Efficient Numerical Treatment of Periodic Systems with Application to Stability Problems", International Journal of Numerical Methods in Engineering, Vol. 11, pp. 1117-1136, 1977.
14. Ge, Z. M., and S. C. Lee, "A Modified Interpolated Cell Mapping", Journal of Sound of Vibration, Vol. 199, pp. 189-206, 1997.
15. Ge, Z. M., and F. N. Ku and H. K. Chen, "Stability and Instability of an Earth Satellite with a Cylindrical Shield in the Newtonian Central Force Field for Accuracy", JSME International Journal Series C, Vol. 40, No. 30, 1997.
16. Pyragas, K., "Continuous Control of Chaos by Self-Controlling Feedback", Physics Letters A, Vol. 170, pp. 421-428, 1992.
17. Sinha, S., R. Ramaswamy, and J. S. Rao, "Adaptive Control in Nonlinear Dynamics", Physica D Vol. 43, pp. 118-128, 1991.
18. Pontryagin, L. S., "Ordinary Differential Equations", Addison-Wesley, Reading, Massachusetts, 1962, pp. 213-220.
19. Hassard, B. D., N. D. Kazarinoff, and Y. H. Wan, "Theory and Applications of Hopf Bifurcation", Cambridge University Press, Cambridge, England, pp. 149-156, 1981.
20. Chetayev, N. G., "The Stability of Motion", Pergamon Press, Now York, 1961.
21. Wiggins, S., "Introduction to Applied Nonlinear Dynamical Systems and Chaos", Springer-Verlag, Berlin, 1990.
22. Carr, J., "Applications of Center Manifold Theory", Applied Mathematical Sciences, No. 35, Springer-Verlag, New York, 1981.
23. Poincare, H., "Les Methodes Nouvelles de la Mecanique Celeste", Gauthier-Villars, Paris, Vol. 3, 1899.
24. Ge, Z. M., and H. K. Chen, "Stability and Chaotic Motions of a Symmetric Heavy Gyroscope, Japan Journal of Applied Physics, Part 1, Vol. 35, No. 3, 1996.
25. Ge Z. M. and H. H. Chen, "Stability and Chaotic of a Rate Gyro with Feedback Control", Japan Journal of Applied Physics, Part 1, Vol. 36, No. 8, 1997.
26. Wolf, A., J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov Exponents from a Time Series", Physica, 16D, pp.285-317, 1985.
27. Wright, J., "Method for Calculating a Lyapunov Exponent", Physical Review A, Vol. 29, No. 5, pp. 2924-2927, 1984.
28. Frederickson, P., J. L. Kaplan, E. D. Yorke, and J. A. Yorke, "The Liapunov Dimension of Stranger Attractors", Journal of Differential Equations, Vol. 49, pp. 185-207, 1983.
29. Tongue, B. H., "On the Global Analysis of Nonlinear System through Interpolated Cell Mapping", Physica D, Vol. 28, pp. 401-408, 1987.
30. Tongue, B. H., K. Gu, "Interpolated Cell Mapping of Dynamical Systems", ASME Journal of Applied Mechanics, Vol. 55, pp. 461-466, 1988.
31. Guckenheimer, J., and P. J. Holmes, "Nonlinear Oscillations of Dynamical Systems and Bifurcations of Vector Fields", Springer-Verlag, Berlin, 1983.
32. Chen, G., and X. Dong, "From Chaos to Order: Methodologies, Perspectives and Applications", World Scientific, New Jersey, 1998.
33. Gollub, J. P., and S. V. Benson, "Many Routes to Turbulent Convection", Journal of Fluid Mechanics, Vol. 100, pp. 449-470, 1980.
34. Ianstiti, M., Q. Hu, R. M. Westervelt, and M. Tinkham, "Noise and Chaos in a Fractal Basin Boundary Regime in a Josephson Junction", Physical Review Letter, Vol. 55, pp. 746-749, 1985.
35. Fenstermacher, P. R., H. L. Swinney, and J. P. Gollub, "Dynamical Instabilities and the Transition to Chaotic Taylor Vortex Flow", Journal of Fluid Mechanics, Vol. 94, pp. 104-128, 1979.
36. Fuh, C. C., and P. C. Tung, "Experimental and Analytical Study of Dither Signals in a Class of Chaotic Systems", Physics Letters A, Vol. 229, pp. 228-234, 1997.