本論文主要在分析滾球型自動平衡器置裝在轉子系統中之系統動態行為，並針對自動平衡器內的滾珠，因滾動摩擦而產生定位位置不一致，造成系統殘餘振動量過大的問題，設計主動控制器，重新定位滾珠位置，以提升自動平衡器的性能。
論文中經由適當的假設，建立數學模型方程式，利用複合時間比例法找出系統所有的穩態解並作穩定度分析、以模擬及實驗的方式討論各項參數（如軌道的偏心、滾珠的滾動阻力、流體拖引力、馬達轉速、扭轉自由度…）對滾珠定位及系統性能的影響，從而提供滾珠型自動平衡器設計的參考方針。
經由分析所得到適當的參數設計，可以找出提升平衡器的性能的方法，但是在現實系統中，因滾動阻力所產生的滾珠定位不一致問題不易解決，本論文提出兩種主動控制計畫，以進一步改善：一是利用滑動模式控制理論，加外一控制力，使滾珠再定位；一是利用模糊控制理論，設計馬達轉速調節器，使滾珠精確定位在所要的位置，以抵消轉子的不平衡量，此種設計，需要一觀測器來提供系統狀態的估測，因此本研究中亦設計了一個滑動模式觀測器來協助控制器的運作，最後並以實驗及模擬的方式，證明此兩種控制器是可行的。

This study is dedicated to analyze the dynamic behaviors of a ball-type balancer system installed on a rotor system and to synthesize intelligent control schemes to reposition the balancing balls inside the automatic ball balancer (ABB) for overcoming the performance inconsistence caused by inevitable rolling friction moment of the rolling balls in contact with its race, which may lead to large, undesired radial vibrations. A mathematical model is first established based on some proper assumptions to describe the dynamics of the balls and rotor system. The method of multiple scales is then applied to formulate a scaled model for finding all possible steady-state solutions and analyzing corresponding stabilities. Through experiments and simulations, the influence of concerned parameters, e.g. runway eccentricity and rolling resistance, drag force, rotor speed, factor of torsional freedom, and etc. on system performance and balls positioning was analyzed and discussed. And then design guidelines for the implementation of ABB are distilled.
Although the design guidelines could be proposed through the process of analysis and discussion, the aforementioned performance inconsistence due to rolling friction moment of balancing balls cannot be easily remedied in practical systems. Two intelligent control schemes are proposed in this study for further enhancing performance. One is a semi-active sliding-mode force control scheme acted on the supporting structure of motor. It applies external control forces to settle the ball as near as possible to the desired position. The other is to design a fuzzy speed-regulating mechanism on rotor rotation in order to reposition the rolling balls at the exactly desired location as the rotor spindle reaches the target operation speed. For the proper operation of the fuzzy regulator, a sliding-mode observer is also needed designing in this study to provide the estimated on-line positions of the rolling balls. Finally, both the simulations and experiments prove feasibility and performance of the semi-active sliding-mode control scheme and the fuzzy speed-regulator.

[1] Bae, S., Lee, J. M., Kang, Y. J., Kang, J. S., and Yun, J. R., 2002, “Dynamic Analysis of an Automatic Washing Machine with a Hydraulic Balancer,” Journal of Sound and Vibration, 257, pp. 3–18.
[2] Rajalingham, C. and Rakheja, S., 1998, “Whirl Suppression in Hand-held Power Tool Rotors Using Guided Rolling Balancers,” Journal of Sound and Vibration, 217, pp. 453-466.
[3] Takashi, K., Yoshihiro, S., Yoshiaki, Y., Shozo, S., and Shigeki, M., 1998, “Disk Type Storage Device,” Japanese Patent 10,092,094.
[4] Kiyoshi, M., Kazuhiro, M., Shuichi, Y., Michio, F., Tokuaki, U., and Masaaki, K., 1997, “Disk Drive Device,” Japanese Patent 10,083,622.
[5] Takatoshi, Y., 1998, “Disk Drive Device,” Japanese Patent 10,188,465.
[6] Masaaki, K., 1998, “Disk Device,” Japanese Patent 10,208,374.
[7] Huang, W. Y., Chao, C. P., Kang, J. R. and Sung, C. K., 2002, “The Application of Ball-Type Balancers on Radial Vibration Reduction of High-Speed Optic Disk Drives,” Journal of Sound and Vibration, 250, pp 415-430.
[8] Yang, Quangang, Ong, Eng-Hong, Sun, Jisong, Guo, Guoxiao, Lim, Siak-Piang, 2004, “Study on the Influence of Friction in an Automatic Ball Balancing System,” Journal of Sound and Vibration, 285, pp. 73-99.
[9] Majewski, T., 1988, “Position Errors Occurrence in Self Balancers Used on Rigid Rotors of Rotating Machinery,” Mechanism and Machine Theory, 23, pp. 71-78.
[10] Gosiewski, Z., 1985, “Automatic Balancing of Flexible Rotors, Part I: Theoretical Background,” Journal of Sound and Vibration, 100, pp. 551–567.
[11] Gosiewski, Z., 1987, “Automatic Balancing of Flexible Rotors, Part II: Synthesis of System,” Journal of Sound and Vibration, 114, pp. 103–119.
[12] J. van de Vegte, 1981, “Balancing of Flexible Rotors during Operation,” Journal of Mechanical Engineering Science, 23, pp. 257-261.
[13] Bishop, R. E. D., 1982, “On the Possibility of Balancing Rotating Flexible Rotor,” Journal of Mechanical Engineering Science, 24, pp. 215-220.
[14] Thearle, E. L., 1950, “Automatic Dynamic Balancers (Part 1 Leblanc Balancer),” Machine Design, 22, Sept., pp. 119-124.
[15] Thearle, E. L., 1950, “Automatic Dynamic Balancers (Part 2 – Ring, Pendulum, Ball Balancers),” Machine Design, 22, pp. 103-106.
[16] Inoue, J., Jinnouchi, Y., and Kubo S., 1979, “Automatic Balancers,” Transactions of the JSME, Part C, 49, pp. 2142-2148.
[17] B□vik, P. and H□gfors, C., 1986, “Autobalancing of Rotors,” Journal of Sound and Vibration, 111, pp. 429-440.
[18] Jinnouchi, Y., Araki, Y., Inoue, J., Ohtsuka, Y., and Tan, C., 1993, “Automatic Balancer (Static Balancing and Transient Response of a Multi-Ball Balancer),” Transactions of the JSME, Part C, 59, pp. 79-84.
[19] Rajalingham, C., Bhat, R. B., and Rakheja, S., 1998, ‘‘Automatic Balancing of Flexible Vertical Rotors Using a Guided Ball,’’ International Journal of Mechanical Sciences, 40(9), pp. 825–834.
[20] Lee, J. and Moorhem, V., 1996, “Analytical and Experimental Analysis of a Self-compensating Dynamic Balancer in a Rotating Mechanism,” ASME Journal of Dynamic Systems, Measurement, and Control, 118, pp. 468–475.
[21] Adolfsson, J., 1997, A study of stability using multiple correction masses, Master thesis, Department of mechanics, Royal institute of technology, Stockholm.
[22] Chung, J., and Ro, D. S., 1999, ‘‘Dynamic Analysis of an Automatic Dynamic Balancer for Rotating Mechanism,’’ Journal of Sound and Vibration, 228, pp. 1035–1056.
[23] Hwang, C.H. and Chung, J., 1999, “Dynamic Analysis of an Automatic Ball Balancer with Double Races,” JSME International Journal, Series C, 42 (2), pp. 265–272.
[24] Kang, J. R., Chao, C. P., Huang, C. L. and Sung, C. K., 2001, “The Dynamics of a Ball-type Balancer System Equipped with a Pair of Free-moving Balancing Masses,” ASME Journal of Vibration and Acoustics, 123 (4), pp. 456 - 465.
[25] Kim, W., Leeb, D.-J., Chung, J., and Chung, J., 2005, “Three-dimensional Modeling and Dynamic Analysis of an Automatic Ball Balancer in an Optical Disk Drive,” Journal of Sound and Vibration, 285, pp. 547-569.
[26] Zadeh, L., 1965, “Fuzzy Sets,” Information and Control, 8, pp. 338-353.
[27] Mamdani, E. H, 1974, “Application of Fuzzy Algorithm of Simple Dynamic Plant,” Proc. IEE, 121, pp. 1585-1588.
[28] Lee, C. 1990, “Fuzzy Logic in Control Systems: Fuzzy Logic-part I & II,” IEEE Transactions On System, Man and Cybernetics, vol. 20, pp. 404–435.
[29] Driankov, D., Hellendoorn, H. and Reinfrank, M., 1993, An Introduction to Fuzzy Control, Springer-Verlag, Berlin.
[30] He, S. Z., Tan, S. and Xu, F. L., 1993, “Fuzzy Self-tuning of PID Controllers,” Fuzzy Sets System, 56, pp. 37–4.
[31] Takagi, T. and Sugeno, M., 1985, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Transactions On System, Man and Cybernetics, 15, pp. 116-132.
[32] Sugeno, M. and Kang, G. T., 1988, “Structure identification of fuzzy model,” Fuzzy Sets and Systems, 28, pp. 15-33.
[33] Jang, S.R., Sun, C.T. and Mizutani, E., 1997, Neuro-Fuzzy and Soft Computing, Pretice-Hall, Inc.
[34] Utkin, V. I., 1977, “Variable Structure Systems with Sliding Modes: A Survey,” IEEE Transactions Automatmatic Control, AC-22, pp. 212–222.
[35] Young, K. D., Utkin, V.I., and Ozguner, U, 1999, “A Control Engineer's Guide to Sliding Mode Control,” IEEE Transactions Control Systems Technology, 7, pp. 328-342.
[36] Slotine, J.-J. E., 1984, “Sliding Control Design for Nonlinear Systems,” International Journal of Control, 40 (2), pp. 421-434.
[37] Slotine, J.-J. E. and Li, W., 1991, Applied Nonlinear Control, Englewood Cliffs.
[38] Edwards, C. and Spurgeon, S., 1994, “On the development of discontinuous observers,” International Journal of Control, 59, pp. 1211-1229.
[39] Utkin, V., 1992, Sliding Mode in Control Optimization, Springer Verlag.
[40] Walcott, B. L., Corless, M. J. and Zak, S. H., 1987, “Comparative Study of Nonlinear State-observation techniques,” International Journal of Control, 45, pp. 2109-2132.
[41] Husain, I., Sodhi, S., and Ehsani, M., 1994, “A Sliding Mode Observer Based Controller for Switched Reluctance Motor Drives,” in Conference Record of the IEEE-IAS Annual Meeting, Denver, CO, pp. 635-643.
[42] Misawa, E. A. and Hedrik, J. K., 1979, “Nonlinear Observers: A State-of-the-Art Survey,” ASME Journal Dynamic Systems, Measurement, and Control, 111, no. 3, pp. 344-352.
[43] Slotine, J. J., Lyons, J. P. and Misawa, E. A., 1987, “On Sliding Observers for Nonlinear Systems,” ASME Journal of Dynamic Systems, Measurement, and Control, 109, pp. 245-252.
[44] Rabinowicz, E., 1965, Friction and Wear of Materials, New York: John Wiley and Sons, Inc.
[45] Drutowski, R., 1959, “Energy Losses of Ball Rolling on Plates,” Friction and Wear, Elsevier Publishing Company, New York: Elsevier Publishing Company.
[46] Munson, B. R., Young, D. F., and Okiishi, T, H., 1990, Fundamentals of Fluid Mechanics, New York: John Wiley and Sons, Inc.