超音波馬達為藉由轉子與振動子間的摩擦力所驅動，此驅動方式造成馬達輸出轉速存在著與轉子位置相關的波動現象，或稱作為速度漣波。本論文以傅立葉級數數學表示式描述此速度漣波現象，並在馬達速度控制系統引入外掛型的重覆控制器，達到更好的速度控制效能。外掛型的重覆控制器型式，能在不影響原控制系統的穩定性，獨立設計控制器，本論文並提出兩種實現重覆控制器的方法作為比較。考量實際系統中，速度漣波的不確定性，以位置訊號為依據的重覆控制器實現架構較能有效的抑制馬達輸出轉速的漣波現象。由實驗結果也可證實本論文所提出之超音波馬達模型的正確性，及所採用之速度控制系統能有效地降低馬達的速度漣波現象。

Ultrasonic motors are driven by the friction force between the rotor and the vibrator, which often induces speed fluctuations synchronizing with the rotor position periodically, namely, speed ripple. In this thesis, the mathematical description of the ultrasonic motor for speed ripple is introduced using Fourier series, after which the speed control is designed with a plug-in type repetitive controller to enhance speed control accuracy. Such a design allows the plug-in type repetitive controller to be separated from the conventional speed controller, enabling it to be added subsequently without disturbing the existing stability of the control system. Moreover, two different implementations to estimate the period of speed ripple are discussed. Considering the uncertainty of the speed ripple, the position-dependent repetitive controller is also proposed to improve control efficiency in speed ripple reduction. Experiments also confirm the validity of the proposed ultrasonic motor model and speed control system, which significantly reduces speed ripple.

[1] K. Uchino, “Piezoelectric Actuators/Ultrasonic Motors: Their Development and Markets,” IEEE Int. Symposium on Applications of Ferroelectrics ISAF’94, pp. 319-324, 1994
[2] T. Maeno, “Recent Progress of Ultrasonic Motors in Japan,” Int. Workshop Motors and Actuators, pp. 15-17, 2005
[3] I. Yamano, and T. Maeno, “Five-fingered Robot Hand using Ultrasonic Motors and Elastic Elements,” IEEE Proc. Int. Conf. Robotics and Automation, pp. 2673-2678, 2005
[4] VO. Del Cura, FL. Cunha, ML. Aguiar, and A. Cliquet, “Study of the Different Types of Actuators and Mechanisms for Upper Limb Prostheses,” Int. Society for Artificial Organs, vol. 27, no. 6, pp. 507-516, 2003
[5] J.L. Pons, H. Rodríguez, I. Luyckx, D. Reynaerts, R. Ceres, and H. Van Brussel, “High Torque Ultrasonic Motors for Hand Prosthetics: Current Status and Trends,” Technology and Health Care, vol. 10, no. 2, pp. 121-133, 2002
[6] S. Toyama, and J. Yonetake, “Development of the Ultrasonic Motor-Powered Assisted Suit System,” IEEE Int. Conf. Complex Medical Engineering, pp. 1361-1366, 2007
[7] N.W. Hagood IV, and A.J. McFarland, “Modeling of a Piezoelectric Rotary Ultrasonic Motor,” IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control, vol. 42, no. 2, pp. 210-224, 1995
[8] M. Aoyagi, Y. Tomikawa, and T. Takano, “Simplified Equivalent Circuit of an Ultrasonic Motor and its Applications,” Ultrasonics, vol. 34, no. 2-5, pp. 275-278, 1996

[9] N. Elghouti, and J. Helbo, “Equivalent Circuit Modeling of a Rotary Piezoelectric Motor,” Int. Conf. Modeling and Simulation, 2000
[10] P.A. Juang, and D.W. Gu, “Speed Control of a New Disc-Type Ultrasonic Motor by using Current Controller,” IEEE Trans. Power Electronics, vol. 21, no. 1, pp. 219-224, 2006
[11] G. Bal, and E. Bekiroğlu, “Characteristics Estimation of Travelling-Wave Ultrasonic Motor using Equivalent Circuit Model,” Int. Conf. Electrical and Electronics Engineering, pp. 62-66, 2001
[12] K. Nakamura, M. Kurosawa, H. Kurebayashi, and S. Ueha, “An Estimation of Load Characteristics of an Ultrasonic Motor by Measuring Transient Responses,” IEEE Trans. Ultrasonics, Ferroelectrics and Frequency Control, vol. 38, no. 5, pp. 481-485, 1991
[13] Y. Izuno, and M. Nakaoka, “Speed Tracking Servocontrol System with Speed Ripple Reduction Scheme for Traveling-Wave-Type Ultrasonic Motor,” Electronics and Communications in Japan, Part 3, vol. 81, no. 9, pp. 1-9, Sep. 1998
[14] T. Senjyu, H. Miyazato, and K. Uezato, “Perofrmance Comparison of PI and Adaptive Controller for Adjustable Speed Drives of Ultrasonic Motors,” Proc. Int. Conf. Industrial Technology, pp. 519-523, 1994
[15] T. Senjyu, S. Yokada, H. Miyazato, and K. Uezato, “Speed Control of Ultrasonic Motors by Adaptive Control with a Simplified Mathematical Model,” IEEE. Proc. Electric Power Applications, vol. 145, no. 3, pp. 180-184, 1998
[16] X. Xu, Y.C. Liang, H.P. Lee, W.Z. Lin, S.P. Lim, and X.H. Shi, “A Stable Adaptive Neural-Network-based Scheme for Dynamical System Control,” Journal of Sound and Vibration, vol. 285, no. 3, pp. 653-667, 2005

[17] Z. Sun, R. Xing, C. Zhao, and W. Huang, “Fuzzy Auto-Tuning PID Control of Multiple Joint Robot Driven by Ultrasonic Motors,” Ultrasonics, vol. 46, no. 4, pp. 303-312, 2007
[18] T. Senjyu, H. Miyazato, and K. Uezato, “Precise Speed Control of Ultrasonic Motors with Repetitive Control,” IEEE Proc. Int. Conf. Industrial Automation and Control, pp. 165-169, 1995
[19] Y. Kobayashi, T. Kimura, and S. Yanabe, “Robust Speed Control of Ultrasonic Motor Based on H∞ Control with Repetitive Compensator,” Japan Society of Mechanical Engineers, Series C, vol. 42, no. 4, pp. 884-890, 1999
[20] H. Rodriguez, J.L. Pons, and R. Ceres, “A ZPET-Repetitive Speed Controller for Ultrasonic Motors, Proc”. IEEE Int. Conf. Robotics and Automation, pp. 3654-3659, 2000
[21] K. Uchino, “Piezoelectric Ultrasonic Motors: Overview,” Smart Materials and Structures, vol. 7, no. 3, pp. 279-285, 1998
[22] E. Bekiroglu, “Ultrasonic motors: Their models, drives, controls and applications,” Electroceramics, vol. 20, no. 3-4, 277-286, 2008
[23] T. Sashida, and T. Kenjo, An Introduction to Ultrasonic Motor, New York: Clarendon Press, 1993
[24] S.W. Hsiao, and M.C. Tsai, “Single-Phase Drive Linear Ultrasonic Motor with Perpendicular Electrode Vibrator,” Japanese Journal of Applied Physics, vol. 49, no. 2, pp. 024201-024201-7, 2010
[25] L. Peti, N. Rizet, R. Briot, and P. Gonnard, “Frequency behaviour and speed control of piezomotors,” Sensors and Actuators A: Physical, vol. 80, no. 1, pp. 45-52, 2000
[26] S. Hara, Y. Yamanoto, T. Omata, and M. Nakano, “Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals,” IEEE Trans. Automatic Control, vol. 33, no. 7, pp. 659-668, 1988
[27] B.A. Francis, and W.M. Wonham, “The Internal Model Principle for Linear Multivariable Regulators,” Applied Mathematics and Optimization, vol. 2, no. 4, pp. 170-194, 1975
[28] M.C. Tsai, and W.S. Yao, “Design of a Plug-In Type Repetitive Controller for Periodic Inputs,” IEEE Trans. Control Systems Technology, vol. 10, no. 4, pp. 547-555, 2002
[29] B.A. Francis, A Course in H∞ Control Theory, Springer Verlag Berlin, 1987
[30] K. Srinivasan, and F.R. Shaw, “Analysis and Design of Repetitive Control Systems using the Regeneration Spectrum,” ASME Trans. Dynamical System Measure and Control, vol. 113, pp. 216-222, 1991