本論文提出一創新方法以實現自我感測位置(Self-Position-Sensing)與長行程(Long-Stroke)之壓電致動器(Piezoelectric actuator)。由於壓電致動器之可驅動範圍被定義為驅動邊的x與y方向位移為同相位的範圍，因此，本研究透過改變壓電致動器之驅動電極的長度，以有限元素法來分析壓電致動器之相位分佈情形及振幅大小，來決定驅動電極的尺寸，進而延長壓電致動器之長驅動行程。有限元素法分析結果顯示，由被選定之驅動電極尺寸所組成的長行程壓電致動器之尺寸為44.2×8×1.5 mm^3，而理論的行程約為37.5 mm，透過等比例放大或縮小，亦可獲得理想之致動區域。本研究以網印技術來製作壓電致動器之驅動電極，而扣件則以自有彈簧力夾持在壓電塊材之驅動邊，並以循序驅動來實現長行程致動。為了驅動壓電致動器在共振頻率，本研究基於鎖相迴路(Phase-locked loop)開發出適用於壓電致動器之驅動電路(Driving circuit)，並透過自動追頻的特性，確保每對以循序驅動的電極維持在共振模態。本研究將兩梳狀的感測電極結合進壓電致動器，採用電容感測原裡實現位置偵測，並以電容讀取之集成電路(Integrated circuit, IC)來讀取電容訊號，運用積體電路匯流排(Inter-integrated circuit, I2C)做為此IC與微處理器(Microcontroller unit, MCU)之溝通介面。為了抑制電容感測器之雜訊，本研究基於自適性卡爾曼濾波器(Adaptive Kalman filter)，且根據本系統之電容變化之趨勢，將正弦曲線方程式整合於濾波迭代演算法，以精準地預測感測器之實際變動趨勢，設計出適用於本系統之數位濾波器，並將此濾波迭代演算法寫進微處理器，實現電容訊號之即時處理。實驗結果顯示，本研究所提出之濾波迭代演算法，有效地將原始電容訊號之標準差由200降低至30，同時也有效地抑制原始電容訊號之雜訊比約30%。

In this paper, a novel piezoelectric actuator with long-stroke and self-position-sensing is proposed. The driving range (DR) of the piezoelectric actuator has been defined as the in-phase range for driving edge in x- and y-components. To extend the stroke of a piezoelectric actuator, the in-phase range and amplitude of the driving edge were analyzed by utilizing finite element method under various dimensions of driving electrodes. Simulation results indicate that the dimensions of the long-stroke piezoelectric actuator, which is comprised of the selected driving electrode, is 44.2×8×1.5 mm^3 and its theoretical stroke is approximately 37.5 mm. Furthermore, the driving range is also acceptable by the varied dimensions of the long-stroke piezoelectric actuators half and twice of the originals. The driving electrodes were screen printed on a piezoelectric plate, and a clip fastener was clamped to the plate by its spring force, which was driven by sequential excitation. To drive the piezoelectric actuator at its resonance frequency, a driving circuit based on a phase-locked loop (PLL) was used and the piezoelectric actuator could be therefore maintained on its resonant mode at each sequential excitation states. To achieve the self-position-sensing function, a pair of comb-shaped electrodes were designed and integrated into the piezoelectric actuator as a capacitive position sensor. A capacitance readout integrated circuit (IC) was connected to a microcontroller unit (MCU) by using an inter-integrated circuit (I2C). A digital filter based on the Kalman filter was developed to process the capacitance signal in real time and implanted in a MCU, thereby suppressing the noise of the capacitance signal. According to the variations in the capacitance signal of comb-shaped capacitive sensor, a sinusoidal-prediction equation was used to modify the adaptive Kalman filter as the specifically adaptive Kalman filter (SAKF) for this system. In the experimental results, the SAKF reduced the standard deviation from 200 to 30, and suppressed the noise ratio of the capacitance signal approximately 30%.

國立中山大學研究生學位論文審定書 i
致謝 ii
摘要 iii
ABSTRACT iv
CONTENTS vi
LIST OF FIGURES ix
LIST OF TABLES xvi
LIST OF SYMBOLS xvii
CHAPTER 1 INTRODUCTION 1
1.1 Motivation 1
1.2 Literature Survey 2
1.2.1 Piezoelectric Actuators 2
1.2.2 Driving Circuit of Piezoelectric Actuators 9
1.2.3 Self-Position-Sensing piezoelectric actuators and In-Plane Capacitive Sensor 11
1.2.4 Kalman Filter 17
CHAPTER 2 LONG-STROKE PIEZOELECTRIC ACTUATOR 21
2.1 Piezoelectric Materials 21
2.2 Design of the Width of the Direction-Controlled Electrodes 24
2.3 Design of the Long-stroke Piezoelectric Actuators 31
CHAPTER 3 CONSTRUCTION OF THE SELF-POSITION-SENSING AND LONG-STROKE PIEZOELECTRIC ACTUATOR 57
3.1 Comb-Shaped Capacitance Sensor 57
3.2 Design of the Clip Fastener 60
3.3 Pedestal of the Self-Position-Sensing and Long-stroke Piezoelectric Actuator 62
CHAPTER 4 CIRCUITS FOR SELF-POSITION-SENSING AND LONG-STROKE PIEZOELECTRIC ACTUATOR AND KALMAN FILTER 64
4.1 Driving Circuit of Piezoelectric Actuator 64
4.1.1 Function of Automatically Tracing Resonance Frequency for Piezoelectric Actuators 65
4.1.2 Velocity Modulation 69
4.2 Capacitance Readout Circuit and Kalman Filter 70
CHAPTER 5 EXPERIMENTAL RESULTS 80
5.1 Experimental Setting and Prototype 80
5.2 Performance of the Driving Circuit and Piezoelectric Actuator 82
5.3 Performance of the Comb-Shaped Capacitive Sensor and the SAKF 83
CHAPTER 6 CONCLUSIONS AND FUTURE WORKS 93
6.1 Conclusions 93
6.2 Future Works 94
6.2.1 Long-stroke Piezoelectric Actuator 94
6.2.2 Comb-Shaped Capacitive Sensor 95
6.2.3 Micro-Controlled Unit 96
REFERENCES 97

[1] T. Bein, E.J. Breitbach, and K. Uchino, “A linear ultrasonic motor using the first longitudinal and the fourth bending mode,” Smart Materials and Structures, vol. 6, no. 5, pp. 619-627, 1997.
[2] J. Li, X. Zhou, H. Zhao, M. Shao, P. Hou, and X. Xu, “Design and experimental performances of a linear piezoelectric actuator by means of lateral motion,” Smart Materials and Structures, vol. 24, no. 6, 065007, 2015.
[3] K. Uchino, “Piezoelectric ultrasonic motors: overview,” Smart Materials and Structures, vol. 7, no. 3, pp. 273-285, 1998.
[4] T. Sashida, “Trial construction and operation of an ultrasonic vibration driven motor-theoretical and experimental investigation of its performances,” A Monthly Publication of the Japan Society of Applied Physics, vol. 51, no. 6, pp. 713-720, 1982.
[5] D. Mazeika, G. Kulvietis, I. Tumasoniene, and R. Bansevicius, “New cylindrical piezoelectric actuator based on traveling wave,” Mechanical Systems and Signal Processing, vol. 36, no. 1, pp. 127-135, 2013.
[6] L. Wang, C. Shu, Q. Zhang, and J. Jin, “A novel sandwich-type traveling wave piezoelectric tracked mobile system,” Ultrasonics, vol. 75, pp. 28-35, 2017.
[7] I. A. Renteria Marquez, and V. Bolborici, “A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method,” Ultrasonics, vol. 77, pp. 69-78, 2017.
[8] K. Spanner, O. Vyshnevskyy, and W. Wischnewskiy, “New linear ultrasonic micromotor for precision mechatronic systems,” In Proceedings of the 10th International Conference on New Actuators, Bremen, Germany, pp. 439-443, 2006.
[9] O. Vyshnevskyy, S. Kovalev, and W. Wischnewskiy, “A novel, single-mode piezoceramic plate actuator for ultrasonic linear motors,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 52, no. 11, pp. 2047-2053, 2005.
[10] Y.J. Wang, Y.C. Chen, and S.C. Shen, “Design and analysis of a standing-wave trapezoidal ultrasonic linear motor,” Journal of Intelligent Material Systems and Structures, vol. 26, no. 6, pp. 2295-2303, 2015.
[11] Y.J. Wang, C. Li, Y.B. Jiang, and K.C. Fu, “Design and dynamic analysis of a piezoelectric linear stage for pipetting liquid samples,” Smart Materials and Structures, vol. 26, no. 6, 065004, 2017.
[12] J.L. Pons, P. Ochoa, and M. Villegas, J.F. Fern´andez, E. Rocon and J. Moreno, “Self-tuned driving of piezoelectric actuators: The case of ultrasonic motors,” Journal of the European Ceramic Society, vol. 27, no. 13-15, pp. 4163-4167, 2007.
[13] P. Ge, and M. Jouaneh, “Tracking control of a piezoceramic actuator,” IEEE Transactions on Control Systems Technology, vol. 4, no. 3, pp. 209-216, 1996.
[14] S. B. Yaakov, and S. Lineykin, “Frequency tracking to maximum power of piezoelectric transformer HV converters under load variations,” IEEE Power Electronics Specialists Conference, Cairns, Qld., Australia, vol. 2, pp. 657-662, 2002.
[15] M. Flueckiger, J. M. Fernandez, and Y. Perriard, “Adaptive control of ultrasonic motors using the maximum power point tracking method,” IEEE International Ultrasonics Symposium Proceeding, Beijing, China, pp. 1823-1826, 2008.
[16] B.Y. Li, and Z. Ding, “Research on the frequency automatic tracking in ultrasonic power supply based on Fuzzy-DDS,” IEEE International Conference on Automation and Logistics, Zhengzhou, China, pp. 448-451, 2012.
[17] A. Kawamata , Y. Kadota , H. Hosaka, and T. Morita, “Self-sensing piezoelectric actuator using permittivity detection,” Ferroelectrics, vol. 368, no. 1, pp. 194-201, 2008.
[18] H. Ikeda, and T. Morita, “High-precision positioning using a self-sensing piezoelectric actuator control with a differential detection method,” Sensors and Actuators A: Physical, vol. 170, no. 1-2, pp. 147-155, 2011.
[19] M. Rakotondrabe, I. A. Ivan, S. Khadraoui, P. Lutz, and N. Chaillet, “Simultaneous displacement/force self-sensing in piezoelectric actuators and applications to robust control,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 2, pp. 519-531, 2015.
[20] P. B. Kosel, G. S. Munro, and R.Vaughan, “Capacitive transducer for accurate displacement control,” IEEE Transactions on Instrumentation and Measurement, vol. IM-30, no. 2, pp. 114-123, 1981.
[21] M. Hirasawa, M. Nakamura, and M. Kanno, “Optimum form of capacitive transducer for displacement measurement,” IEEE Transactions on Instrumentation and Measurement, vol. IM-33, no. 4, pp. 276-280, 1984.
[22] M. H. W. Bonse, F. Zhu, and H. F. Ven Beek, “A long-range capacitive displacement sensor having micrometer resolution,” Measurement Science and Technology, vol. 4, no. 8, pp. 801-807, 1993.
[23] D. Kang, and W. Moon, “Electrode configuration method with surface profile effect in a contact-type area-varying capacitive sensor,” Sensors and Actuators: A Physical, vol. 189, DOI: 10.1016/j.sna.2012.09.011, pp. 33-44, 2013.
[24] M. Kim, W. Moon, E. Yoon, and K. R. Lee, “A new capacitive displacement sensor with high accuracy and long-range,” Sensors and Actuators: A Physical, vol. 130, no. SI, pp. 135-141, 2006.
[25] M. Kim, and W. Moon, “A new linear encoder-like capacitive displacement sensor,” Measurement, vol. 39, no. 6, pp. 481-489, 2006.
[26] H. Yu, L. Zhang, and M. Shen, “Novel capacitive displacement sensor based on interlocking stator electrodes with sequential commutating excitation,” Sensors and Actuators: A Physical, vol. 230, DOI: 10.1016/j.sna.2015.04.024, pp. 94-101, 2015.
[27] X. Liu, K. Peng, Z. Chen, H. Pu, and Z. Yu, “A new capacitive displacement sensor with nanometer accuracy and long range,” IEEE Sensors Journal, vol. 16, no.8, pp. 2306-2316, 2016.
[28] F. M. L. Van Der Goes, and G.C.M. Meijer, “A novel low-cost capacitive-sensor interface,” IEEE Transactions on Instrumentation and Measurement, vol. 45, no. 2, pp. 536-540, 1996.
[29] X. Li, and G. C. M. Meijer, “An accurate interface for capacitive sensors,” IEEE Transactions on Instrumentation and Measurement, vol. 51, no. 5, pp. 935-939, 2002.
[30] R. Nojdelov, and S. Nihtianov, “Capacitive-sensor interface with high accuracy and stability,” IEEE Transactions on Instrumentation and Measurement, vol. 58, no. 5, pp. 1633-1639, 2009.
[31] R. E. Kalman, “A new approach to linear filtering and predication problems,” Journal of Basic Engineering, vol. 82, no. 1, pp. 35-45, 1960.
[32] R. E. Kalman, and R. S. Bucy, “New results in linear filtering and prediction theory,” Journal of Basic Engineering, vol. 83, no. 1, pp. 95-108, 1961.
[33] R. Mehra, “On the identification of variances and adaptive Kalman filtering,” IEEE Transactions on Automatic Control, vol. 15, no. 2, pp. 175-184, 1970.
[34] K. Myers, and B. Tapley, “Adaptive sequential estimation with unknown noise statistics,” IEEE Transactions on Automatic Control, vol. 21, no. 4, pp. 520-523, 1976.
[35] H. G. Yeh, “Real-time implementation of a narrow-band Kalman filter with floating-point processor DSP32,” IEEE Transactions on Industrial Electronics, vol. 37, no. 1, pp. 13-18, 1990.
[36] Y. Yang, and W. Gao, “An optimal adaptive Kalman filter,” Journal of Geodesy, vol. 80, no. 4, pp. 177-183, 2006.
[37] B. Feng, M. Fu, H. Ma, Y. Xia, and B. Wang, “Kalman filter with recursive covariance estimation-sequentially estimating process noise covariance,” IEEE Transactions on Industrial Electronics, vol. 61, no. 11, pp. 6253-6263, 2014.
[38] C. L. Lin, T. C. Chu, C. E. Wu, Y. M. Chang, T. C. Lin, J. F. Chen, C. Y. Chuang, and W. C. Chiu, “Tracking touched trajectory on capacitive touch panels using an adjustable weighted prediction covariance matrix,” IEEE Transactions on Industrial Electronics, vol. 64, no. 6, pp. 4910-4916, 2017.
[39] D. Z. Xia, Y. W. Hu, and L. Kong, “Adaptive Kalman filtering based on higher-order statistical analysis for digitalized silicon microgyroscope,” Measurement, vol. 75, DOI: 10.1016/j.measurement.2015.07.039, pp. 244-254, 2015.
[40] J. M. Jou, Piezoelectricity mechanics. Taipei, R.O.C: Chuan Hwa Book Co., LTD., 2003.
[41] Texas Instruments, “CMOS Micropower Phase-Locked Loop,” CD4046B TYPES datasheet, 2003 [Revised Jul. 2003].
[42] Micrel, “Dual 1.5A-Peak Low-Side MOSFET Drive,” MIC4426/4427/4428 datasheet, Apr. 2008.
[43] Texas Instruments, “Differential Comparator with Strobes,” LM111/ LM211/ LM311 datasheet, Sep. 1973 [Revised Mar. 2017].
[44] Texas Instruments, “Mixed Signal Microcontroller,” MSP430G2x53/ MSP430G2x13 datasheet, Apr. 2011 [Revised Aug. 2012].
[45] Analog Devices, “Ultra-Low Power, 2-Channel, Capacitance Converter for Proximity Sensing,” AD7150 datasheet, 2007 [Last content update Feb. 2017].
[46] P. Zarchan, and H. Musoff, Fundamentals of Kalman filtering: A practical approach second edition. American Institute of Aeronautics and Astronautics Inc., 2005.
[47] W. X. Su, “Application of Sage-Husa adaptive filtering algorithm for high precision SINS initial alignment,” International Computer Conference on Wavelet Active Media Technology and Information Processing, Chengdu, China, pp. 359-364, 2015.