本研究主要在探討應用改良型順滑模態電流觀測器於無轉軸角度偵測元件永磁同步電動機驅動器之轉子角度估測。
一般而言，順滑模態觀測器是採用傳統正負號切換函數或是線性飽和切換函數。在此設計下，都必須採用低通濾波器以解決切跳的問題。本研究使用S型之切換函數來做設計，將可降低切跳之現象，增加轉子角度估測之精確度，也可免除因低通濾波器設計之需要所造成角度估測延遲。
模擬結果顯示出本研究設計之優點。更進一步，應用此理論於低成本16位元微控制器之實作，驗證了本方法之優越性與可行性。

The main objective of this research is to explore the estimation for the
rotor angle of a sensorless permanent magnet synchronous motor (PMSM) drive by applying an improved sliding mode observer (SMO) to the PMSM drive.
In general, a sign function or a saturation function is conventionally used in the SMO design. Under this case, an additional design of a low-pass filter is necessary to solve the chattering problem. In this research, we use an S-curve, i.e. a sigmoid switching function, to replace the conventional switching function. Based on this design, it will reduce chattering phenomena and improve the accuracy of the rotor angle of a PMSM. Moreover, it can prevent the estimation delay due to the design of a low-pass filter.
Simulation results show the advantages of the proposed design.
Furthermore, the implementation in a low-cost 16-bit micro controller unit
(MCU) proves the superiority and feasibility of the applied method.

[1] S.-N. Kumar and W.-M. Beevi, “Quasi sinusoid commutation for BLDC motor–a simplified approach on 16 bit microcontroller platform,” IEEE International Conference on Power Electronics, Drives and Energy Systems, Bengaluru, India, pp. 1-9, Dec. 16-19, 2012.
[2] C. Pollock and M. Brackley, “Comparison of the acoustic noise of a flux-switching and a switched reluctance drive,” IEEE Transactions on Industry Applications, vol. 39, no. 3, pp. 826-834, 2003.
[3] S. Chi and J. Sun, “A novel sliding mode observer with multilevel discontinuous control for position sensorless PMSM drives,” IEEE Conference and Exposition on Applied Power Electronics, Austin, TX, pp. 127-131, Feb. 24-28, 2008.
[4] S. Shinnaka and Y. Amano, “Sensorless control of brushless dc motors with torque constant estimation for home appliances,” IEEE Transactions on Industrial Applications, vol. 48, no. 2, pp. 677-684, 2012.
[5] M. Bertoluzzo and G. Buja, “Development of electric propulsion systems for light electric vehicles,” IEEE Transactions on Industrial Informatics, vol.7, no. 3, 2011.
[6] R. Nalepa and T. Orlowska-Kowalska, “Optimum trajectory control of the current vector of a nonsalient-pole PMSM in the field-weakening region,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 2867-2876, 2012.
[7] A. Akrad, M. Hilairet, and D. Diallo, “Design of a fault-tolerant controller based on observers for a PMSM drive,” IEEE Transactions on Industrial Electronics, vol. 58, no. 4, pp. 1416-1427, 2011.
[8] G. Pellegrino, A. Vagati, P. Guglielmi, and B. Boazzo, “Performance comparison between surface-mounted and interior pm motor drives for electric vehicle application,” IEEE Transactions on Industrial Electronics, vol. 59, no. 2, pp. 803-811, 2012.
[9] W. Su, H. Rahimi-Eichi, W. Zeng, and M.-Y. Chow, “A survey on the electrification of transportation in a smart grid environment,” IEEE Transactions on Industrial Informatics, vol. 8, no. 1, pp. 1-10, 2012.
[10] J. Sopanen, V. Ruuskanen, J. Nerg, and J. Pyrhönen, “Dynamic torque analysis of a wind turbine drive train including a direct-driven permanent-magnet generator,” IEEE Transactions on Industrial Electronics, vol. 58, no. 9, pp. 3859-3867, 2011.
[11] P. Sergeant, F.-D. Belie, and J. Melkebeek, “Rotor geometry design of interior PMSMs with and without flux barriers for more accurate sensorless control,” IEEE Transactions on Industrial Electronics, vol. 59, no. 6, pp. 2457-2465, 2012.
[12] K. Gulez, A.-A. Adam, and H. Pastaci, “Torque ripple and EMI noise minimization in PMSM using active filter topology and field-oriented control,” IEEE Transactions on Industrial Electronics, vol. 55, no. 1, pp. 251-257, 2008.
[13] O. Wallmark, S. Lundberg, and M. Bongiorno, “Input admittance expressions for field-oriented controlled salient PMSM drives,” IEEE Transactions on Power Electronics, vol. 27, no. 3, pp.1514-1520 , 2012.
[14] M. Rashed, P.-F.-A. MacConnell, A.-F. Stronach, and P. Acarnley, “Sensorless indirect-rotor-field-orientation speed control of a permanent-magnet synchronous motor with stator-resistance estimation,” IEEE Transactions on Industrial Electronics, vol. 54, no. 3, pp. 1664-1675, 2007.
[15] F. Genduso, R. Miceli, C. Rando, and G.-R. Galluzzo, “Back EMF sensorless-control algorithm for high-dynamic performance PMSM,” IEEE Transactions on Industrial Electronics, vol. 57, no. 6, pp. 2092-2100, 2010.
[16] S. Ichikawa, M. Tomita, and S. Doki, “Sensorless control of permanent-magnet synchronous motors using online parameter identification based on system identification theory,” IEEE Transactions on Industrial Electronics, vol. 53, no. 2, pp. 363-372, 2006.
[17] S. Diao, D. Diallo, Z. Makni, C. Marchand, and J.-F. Bisson, “A differential algebraic estimator for sensorless permanent-magnet synchronous machine drive,” IEEE Transactions on Energy Conversion, vol. 30, no. 1, pp. 82-89, 2015.
[18] S. Zaim, B. Nahid-Mobarakeh, and F. Meibody-Tabar, “Robust position sensorless control of nonsalient PMSM at standstill and low speeds,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 2, no. 3, pp. 640-650, 2014.
[19] M. Hinkkanen, T. Tuovinen, L. Harnefors, and J. Luomi, “A combined position and stator-resistance observer for salient PMSM drives: design and stability analysis,” IEEE Transactions on Power Electronics, vol. 27, no. 2, pp. 601-609, 2012.
[20] M.-A. Hamida, J.-D Leon, A. Glumineau, and R. Boisliveau, “An adaptive interconnected observer for sensorless control of PM synchronous motors with online parameter identification,” IEEE Transactions on Industrial Electronics, vol. 60, no. 2, pp. 739-748, 2013.
[21] O.-A. Mohammed, A.-A. Khan, A.-M. El-Tallawy, A. Nejadpak, and M.-J. Roberts, “A wavelet filtering scheme for noise and vibration reduction in high-frequency signal injection-based sensorless control of PMSM at low speed,” IEEE Transactions on Energy Conversion, vol. 27, no. 2, pp. 250-260, 2012.

[22] F.-M.-L.-D. Belie, P. Sergeant, and J.-A. Melkebeek, “A sensorless drive by applying test pulses without affecting the average-current samples,” IEEE Transactions on Power Electronics, vol. 25, no. 4, pp. 875-888, 2010.
[23] N. Ertugrul and P. Acamley, “A new algorithm for sensorless operation of permanent magnet motors,” IEEE Transactions on Industry Applications, vol. 30, no. 1, pp. 126-133, 1994.
[24] X. Yu, B. Wang, and X. Li, “Computer-controlled variable structure systems: the state-of-the-art,” IEEE Transactions on Industrial Informatics, vol. 8, no. 2, pp. 197-205, 2012.
[25] X. Zhang, L. Sun, K. Zhao, and L. Sun, “Nonlinear speed control for PMSM system using sliding-mode control and disturbance compensation techniques,” IEEE Transactions on Power Electronics, vol. 28, no. 3, pp. 1358-1365, 2013.
[26] M.-A. Hamida, J.-D. Leon, A. Glumineau, and R. Boisliveau, “An adaptive interconnected observer for sensorless control of PM synchronous motors with online parameter identification,” IEEE Transactions on Industrial Electronics, vol. 60, No. 2, pp. 739-748, 2013.
[27] S. Chi, Z. Zhang, and L. Xu, “Sliding-mode sensorless control of direct-drive PM synchronous motors for washing machine applications,” IEEE Transactions on Industry Applications, vol. 45, no. 2, pp. 582-590, 2009.
[28] G. H. Beng-Foo and M. F. Rahman, “Direct torque control of an IPM-synchronous motor drive at very low speed using a sliding-mode stator flux observer,” IEEE Transactions on Power Electronics, vol. 25, no. 4, pp. 933-942, 2010.
[29] T. Bernardes, V.-F. Montagner, H.-A. Gründling, and H. Pinheiro, “Discrete-time sliding mode observer for sensorless vector control of permanent magnet synchronous machine,” IEEE Transactions on Industrial Electronics, vol. 61, no. 4, pp. 1679-1691, 2014.
[30] Y. Feng, X. Yu, and F. Han, “High-order terminal sliding-mode observer for parameter estimation of a permanent-magnet synchronous motor,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4271-4280, 2013.
[31] Y. Feng, J. Zheng, X. Yu, and N.-V. Truong, “Hybrid terminal sliding-mode observer design method for a permanent-magnet synchronous motor control system,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3424-3431, 2009.
[32] Y. Zhao, W. Qiao, and L. Wu, “An adaptive quasi-sliding-mode rotor position observer-based sensorless control for interior permanent magnet synchronous machines,” IEEE Transactions on Power Electronics, vol. 28, no. 12, pp. 5618-5629, 2013.
[33] G. Foo and M. F. Rahman, “Sensorless sliding-mode MTPA control of an IPM synchronous motor drive using a sliding-mode observer and HF signal injection,” IEEE Transactions on Industrial Electronics, vol. 57, no. 4, pp. 1270-1278, 2010.
[34] K.-Y. Cheng and Y.-Y. Tzou, “Design of a sensorless commutation IC for BLDC motors,” IEEE Transactions on Power Electronics, vol. 18, no. 6, pp.1365-1375, 2003.
[35] N. Samoylenko, Q. Han, and J. Jatskevich, “Dynamic performance of brushless DC motors with unbalanced hall sensors,” IEEE Transactions on Energy Conversion, vol. 23, no. 3, pp. 752-763, 2008.
[36] S. Ogasawara and H. Akagi, “An approach to position sensorless drive for brushless DC motors,” IEEE Transactions on Industry Applications, vol. 27, no. 5, pp. 928-933, 1991.
[37] Y. Wu, Z. Deng, X. Wang, X. Ling, and X. Cao, “Position sensorless control based on coordinate transformation for brushless DC motor drives,” IEEE Transactions on Power Electronics, vol. 25, no. 9, pp. 2365-2371, 2010.
[38] J.-W. Park, S.-H. Hwang, and J.-M. Kim, “Sensorless control of brushless DC motors with torque constant estimation for home appliances,” IEEE Transactions on Industry Applications, vol. 48, no. 2, pp. 677-684, 2012.
[39] K. Iizuka, H. Uzuhashi, M. Kano, T. Endo, and K. Mohri, “Microcomputer control for sensorless brushless motor,” IEEE Transactions on Industry Applications, vol. IA-21, no. 4, pp. 595-601, 1985.
[40] P. Damodharan and K. Vasudevan, “Sensorless brushless DC motor drive based on the zero-crossing detection of back electromotive force (EMF) From the line voltage difference,” IEEE Transactions on Energy Conversion, vol. 25, no. 3, pp. 661-668, 2010.
[41] H.-C. Chen and C.-M. Liaw, “Current-mode control for sensorless BDCM drive with intelligent commutation tuning,” IEEE Transactions on Power Electronics, vol. 17, no. 5, pp. 747-756, 2002.
[42] J.-H. Song and I. Choy, “A rotor position sensorless control based on neutral voltage compensation of brushless DC motors,” 35th Annul IEEE Power Elecrronics Speciulisrs Conference, vol. 2, Aachen, Germany, pp. 1431-1437, Jun. 20-25, 2004.
[43] G.-H. Jang and M.-G. Kim., “Optimal commutation of a BLDC motor by utilizing the symmetric terminal voltage,” IEEE Transactions on Magnetics, vol. 42, no. 10, pp. 3473-3475, 2006.
[44] G.-H. Jang, J.-H. Park, and J.-H. Chang, “Position detection and start-up algorithm of a rotor in a sensorless BLDC motor utilising inductance variation,” IET Journal on Electric Power Applications, vol. 149, no. 2, pp.137-142, 2002.
[45] M. Masmoudi, B.-E. Badsi, and A. Masmoudi, “Direct torque control of brushless DC motor drives with improved reliability,” IEEE Transactions on Industry Applications, vol. 50, no. 6, pp. 3744-3753, 2014.
[46] C.-T. Lin, C.-W. Hung, and C.-W. Liu, “Position sensorless control for four-switch three-phase brushless DC motor drives,” IEEE Transactions on Power Electronics, vol. 23, no. 1, pp. 438-444, 2008.
[47] S. Tsotoulidis and A.-N. Safacas, “Deployment of an adaptable sensorless commutation technique on BLDC motor drives exploiting zero sequence voltage,” IEEE Transactions on Industrial Electronics, vol. 62, no. 2, pp. 877-886, 2015.
[48] D.-K. Kim, K.-W. Lee, and B.-I. Kwon, “Commutation torque ripple reduction in a position sensorless brushless DC motor drive,” IEEE Transactions on Power Electronics, vol. 21, no. 6, pp. 1762-1768, 2006.
[49] K.-Y. Nam, W.-T. Lee, C.-M. Lee, and J.-P. Hong, “Reducing torque ripple of brushless DC motor by varying input voltage,” IEEE Transactions on Magnetics, vol. 42, no. 4, pp. 1307-1310, 2006.
[50] A. Darba, F.-D. Belie, and Jan A. Melkebeek, “A back-EMF threshold self-sensing method to detect the commutation instants in BLDC drives,” IEEE Transactions on Industrial Electronics, vol. 62, no. 10, pp. 6064-6075, 2015.
[51] Z. Zhang and J. Shu, “Matlab-based permanent magnet synchronous motor vector control simulation,” IEEE International Conference on Computer Science and Information Technology, vol. 9, Chengdu, pp. 539-542, Jul. 9-11, 2010.
[52] D. Vindel and M. Design, Simulation and Implementation of a PMSM Drive System, Division of Electric Power Engineering Department of Energy and Environment Chalmers University of Technology Göteborg, Sweden 2011.
[53] A. K. Parvathy and R. Devanathan, Linearization of Permanent Magnet Synchronous Motor Using MATLAB and Simulink, Hindustan Institute of Technology and Science, Chennai India, 2011.
[54] K. Boby1, A.-M Kottalil, and N.-P. Ananthamoorthy, “Mathematical modelling of PMSM vector control system based on SVPWM with PI controller using MATLAB,” International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, No. 1, 2013.
[55] H. Akita, Y. Nakahara, N. Miyake, and T. Oikawa, “New core structure and manufacturing method for high efficiency of permanent magnet motors,” IEEE on Industry Applications Conference, vol. 1, SLC, USA, pp. 367-372, Oct. 12-16, 2003.
[56] 陳瑞霖，「永磁同步電動機轉軸角度估測及驅動系統的研製」，碩士論文，國立台灣科技大學電機工程學系，2006年5月。
[57] P. Pillay, and R. Krishnan, “Modeling, simulation, and analysis of permanent-magnet motor drives, part I: the permanent-magnet synchronous motor drive,” IEEE Transactions on Industry Applications, vol. 25, no. 2, pp. 265-273, 1989.
[58] T. Sebastian, G.-R. Slemon, and M.-A. Rahman, “Modelling of permanent magnet synchronous motors,” IEEE Transactions on Magnetics, vol. mag-22, no. 5, pp. 1069-1071, 1986.
[59] M. Ertugrul, O. Kaynak, A. Sabanovhc, and K. Ohnishi, “A generalized approach for Lyapunov design of sliding mode controllers for motion control applications,” IEEE International Workshop on Advanced Motion Control, vol. 1, Mie University, Tsu-City, Mie-Pref., Japan, pp. 18-21, Mar. 18-21, 1996.

[60] D. Ingenieurs and W. Utschick, Sliding Mode Control of Electromechanical Systems, 2009.
[61] 趙欣彥，「以順滑模態觀測器實現永磁式同步馬達之無感測器速度控制」， 碩士論文，國立成功大學，2004年6月。
[62] S. Chi and L. Xu, “Position sensorless control of pmsm based on a novel sliding mode observer over wide speed range,” Power Electronics and Motion Control Conference, vol. 3, Shanghi, China, pp. 1-7, Aug. 14-16, 2006.
[63] Microchip Technology Inc., 16-Bit Microcontrollers and Digital Signal Controllers with High-Speed PWM, Op Amps and Advanced Analog, Microchip dsPIC33EP256MC204 Datasheet, 2011.
[64] D. Wilson, Taxas Instruments Motor Control Training, Taxas Instruments Inc. Motor Solutions Group, 2012.
[65] Microchip Technology Inc., MCLV-2 Development Board User's Guide, http://ww1.microchip.com/downloads/en/DeviceDoc/DS-52080a.pdf, 2012.