无位置传感器无刷直流电机调速系统控制策略研究
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摘要
本文介绍了无刷直流电机的应用状况、常见的技术问题以及它的工作原理,建立了无刷直流电机的数学模型和MATLAB仿真模型,重点对无刷直流电机的无位置传感器技术以及转矩脉动抑制技术的相关问题进行了研究。
无位置传感器无刷直流电机位置信号相位误差严重影响了电机的运行性能,为此本文对校正位置信号相位进行了深入的研究。详细分析了无位置传感器无刷直流电机位置信号相位与非导通相续流电流的关系,指出了非导通相续流电流偏差能够准确地反应无位置传感器无刷直流电机位置信号相位误差。根据分析所得结论,提出了一种校正位置信号相位的新型控制方法。该闭环控制方法以控制非导通相续流电流对称为目标,以非导通相续流电流偏差为反馈量,通过PI调节器调节,及时调整过零点延时角度,从而达到自动校正位置信号相位的目的。
换相转矩脉动亦为影响电机运行性能的一大重要因素,本文介绍了无刷直流电机换相转矩脉动产生的原因,提出了一种保持非换向相绕组换相前后施加电压不变的方法,抑制无刷直流电机换相转矩脉动。为减小换相前非导通相续流引起的电压补偿量计算误差,将该方法与PWM_ON_PWM调制方式相结合,进一步改善了转矩脉动抑制效果,同时也抑制了正常导通期间转矩脉动;并在此基础上推导出适合宽转速范围抑制换相转矩脉动的电压补偿方法。
最后,为验证本文所提的控制方法,搭建了基于DSP、CPLD的无刷直流电机控制平台。详细介绍了系统的硬件构成,并说明了各组成部分的功能,给出了软件程序流程图。
ii The paper introduces the application situation , the technique problems and the working principle of Brushless DC Motor(BLDCM), establishes the mathematic model and the simulation model of BLDCM, the simulation model is established based on simulation software matlab.And this paper pays more attention to the position sensorless techniques and torque ripple suppression techniques of BLDCM.
The position phase error can seriously affect the operation performance of Sensorless BLDCM (SBLDCM), thus the method to correct position phase error is studied in this paper. The relationship between position phase error and freewheel current of silent phase is detailedly analyzed. It is noted that freewheel current error can exactly reflect position phase error. Based on the aforementioned analysis, a novel closed control method to correct position phase is proposed. Freewheel current error is inputted to PI controller in order to keep freewheel current of the silent phase symmetrical, and delaying angel after zero-crossing is adjusted in time through PI controller. Thus the phase error is corrected immediately.
Commutation torque ripple is another important factor affecting the operation performance of BLDCM. In order to suppress the commutation torque ripple for BLDCM, this paper analyzes the reasons of the commutation torque ripple and proposes a novel control method, which keeps the un-commutated phase voltage during commutation the same with the one before commutation. Furthermore, this method combined with the PWM scheme’PWM_ON_PWM’can reduce the voltage compensation error caused by freewheel of silent phase during conduction. And the commutation torque ripple is suppressed further, conduction torque ripple is suppressed at the same time. Based on the aforementioned method, a strategy suited for wide speed range is given to suppress commutation torque ripple.
Moreover, a control system based on DSP and CPLD is built to verify the validity of the proposed methods.Finally, this paper detailedly introduces the hardware composing of BLDCM speed regulation system,and explains the function of every component. And program flowcharts are also given.
无位置传感器无刷直流电机位置信号相位误差严重影响了电机的运行性能,为此本文对校正位置信号相位进行了深入的研究。详细分析了无位置传感器无刷直流电机位置信号相位与非导通相续流电流的关系,指出了非导通相续流电流偏差能够准确地反应无位置传感器无刷直流电机位置信号相位误差。根据分析所得结论,提出了一种校正位置信号相位的新型控制方法。该闭环控制方法以控制非导通相续流电流对称为目标,以非导通相续流电流偏差为反馈量,通过PI调节器调节,及时调整过零点延时角度,从而达到自动校正位置信号相位的目的。
换相转矩脉动亦为影响电机运行性能的一大重要因素,本文介绍了无刷直流电机换相转矩脉动产生的原因,提出了一种保持非换向相绕组换相前后施加电压不变的方法,抑制无刷直流电机换相转矩脉动。为减小换相前非导通相续流引起的电压补偿量计算误差,将该方法与PWM_ON_PWM调制方式相结合,进一步改善了转矩脉动抑制效果,同时也抑制了正常导通期间转矩脉动;并在此基础上推导出适合宽转速范围抑制换相转矩脉动的电压补偿方法。
最后,为验证本文所提的控制方法,搭建了基于DSP、CPLD的无刷直流电机控制平台。详细介绍了系统的硬件构成,并说明了各组成部分的功能,给出了软件程序流程图。
ii The paper introduces the application situation , the technique problems and the working principle of Brushless DC Motor(BLDCM), establishes the mathematic model and the simulation model of BLDCM, the simulation model is established based on simulation software matlab.And this paper pays more attention to the position sensorless techniques and torque ripple suppression techniques of BLDCM.
The position phase error can seriously affect the operation performance of Sensorless BLDCM (SBLDCM), thus the method to correct position phase error is studied in this paper. The relationship between position phase error and freewheel current of silent phase is detailedly analyzed. It is noted that freewheel current error can exactly reflect position phase error. Based on the aforementioned analysis, a novel closed control method to correct position phase is proposed. Freewheel current error is inputted to PI controller in order to keep freewheel current of the silent phase symmetrical, and delaying angel after zero-crossing is adjusted in time through PI controller. Thus the phase error is corrected immediately.
Commutation torque ripple is another important factor affecting the operation performance of BLDCM. In order to suppress the commutation torque ripple for BLDCM, this paper analyzes the reasons of the commutation torque ripple and proposes a novel control method, which keeps the un-commutated phase voltage during commutation the same with the one before commutation. Furthermore, this method combined with the PWM scheme’PWM_ON_PWM’can reduce the voltage compensation error caused by freewheel of silent phase during conduction. And the commutation torque ripple is suppressed further, conduction torque ripple is suppressed at the same time. Based on the aforementioned method, a strategy suited for wide speed range is given to suppress commutation torque ripple.
Moreover, a control system based on DSP and CPLD is built to verify the validity of the proposed methods.Finally, this paper detailedly introduces the hardware composing of BLDCM speed regulation system,and explains the function of every component. And program flowcharts are also given.
引文
[1]贡俊,陆国林,无刷直流电机在工业中的应用和发展,微特电机,2000(5):15-1.
[2]李朝东,微电机研究的最新动态与应用展望,微特电机,1999(5):23-25.
[3]季小尹,符向荣,王安丽,混合动力电动汽车用永磁无刷直流电机的设计与实现,微特电机,2004(2):5-7.
[4] Wook-Jin Lee, Seung-Ki Sul,A New Starting Method of BLDC Motors Without Position sensor,IEEE transactions on industry application,2006,42(6):1532-1538.
[5] Byoung-Gun Park, Tae-Sung Kim, Ji-Su Ryu , Fuzzy back-EMF observer for improving performance of sensorless brushless DC motor drive,APEC’06,Seoul,South Korea,2006,on pages:674-678.
[6] J.X.Shen, S.Iwasaki,Sensorless Control of Ultrahigh-Speed PM Brushless Motor Using PLL and Third Harmonic Back EMF,IEEE transactions on power electronics, 2006, 53(2):421-428.
[7] Quan Jiang, Ruoyu Huang,A NEW Phase-Delay-Free Method to Detect Back EMF Zero-Crossing Points for Sensorless Control of Spindle Motors,IEEE transactions on magetics,2005, 41(7):2287-2294.
[8] Chang-Liang Xia,Wei Chen,Sensorless Control of Brushless DC Motors at Low Speed Using Neural Networks,Proceedings of the fourth International Conference on Machine Learning and Cybernetics, Guangzhou,18-21 August 2005,pages:1099-1103.
[9] Zhigan Wu,Genfu Zhou,Jian-ping Ying. High dynamic sensorless BLDCM drive with very wide speed range,The 30th annual conference of the IEEE industrial Electronics Society,2-6 November,2004,busan,Korea,pages:981-986.
[10] Yong-Ho Yoon,Mu-Seon Woo, Tae-Won Lee,PLL control Algorithm for Precise Speed Control of the Slotless PM Brushless DC Motor Using 2Hall-ICs. 2004 35th Annual IEEE Power Electronics Specialists Conference,Aachen, Germany,2004,pages: 1315-1321.
[11]韦坤,任军军,张仲超,一种新的直流无刷电机的无传感器控制方法,电力电子技术,2004,38(3): 70-72.
[12]黄玉,王剑,陈瑜,无刷直流电机的新型位置检测方法,山东大学学报(工学版),2003,33(3): 297-291.
[13] Joong-Ho Song,and Ick Choy,Commutation Torque Ripple Reduction in Brushless DC Motor Drives Using a Single DC Current Sensor,IEEE Transactions on power electronics,2004,19(2):312 -319.
[14]韦昆,胡长生,张仲超,一种新的消除无刷直流电机非导通相续的PWM调制方式,中国电机工程学报,2005,25(7):104-108.
[15] H.Zeroug,B.Boukais,and H.Sahraoui,Analysis of Torque Ripple in a BLDCM,IEEE Transactions on Magnetics,2002,38(2): 1293- 1296.
[16] Yong Liu,Z.Q.Zhu,David Howe,Direct Torque Control of Brushless DC Drives With Reduced Torque Ripple,IEEE Transactions on industry applactions,2005,41(2): 599-608.
[17] Zhang Xiaofeng,Lu Zhengyu,A New BLDC Motor Drives Method Based on BUCK Converter for Torque Ripple Reduction,Power Electronics and Motion Control Conference,2006,5th International,Shanghai China,Aug 2006, Volume 3: 1-4.
[18] N’diaye.A,Espanet.C,Miraoui.A,Reduction of the torque ripples in brushless PM motors by optimization of the supply - theoretical method and experimental implementation,Industrial Electronics,2004 IEEE International Symposium, France,2004,Volume 2: 1345-1350.
[19] Yong Liu,Zi Qiang Zhu, David Howe,Instantaneous Torque Estimation in Sensorless Direct-Totque-Contrulled Brushless DC Motors,IEEE transactions on industry applications,2006,42(5):1275-1283.
[20] Byoung-Hee Kang,Choel-Ju Kim,Hyung-Su Mok. Analysis of torque ripple in BLDC motor with commutation time,ISIE 2001,IEEE International symposium,2001,voltume 2, pages: 1044-1048.
[21]韦坤,林平,张仲超,无刷直流电机换相转矩脉动的电流预测控制,浙江大学学报(工学版),2006,40(1):171-175.
[22] Tae-Hyung Kim, Mehrdad Ehsani.Sensorless Control of the BLDC Motors From Near-Zero to High Speeds,IEEE transactions on power elsctronics,2004,19(6): 1635-1645.
[23] C.-G.Kim,J.-H.Lee,H.-Waked, M.-J.Youn,Study on maximum torque generation for sensorless controlled brushless DC mortor with trapezoidal back EMF,IEE Proc.-Electr. Power Appl, 2005, 152(2): 277-291.
[24]张磊,瞿文龙,陆海峰,肖伟,一种新颖的无刷直流电机无位置传感器控制系统,电工技术学报,2006,21(10): 26-30.
[25] G. H. Jang, M. G. Kim,Optimal Commutation of a BLDC Motor by Utilizing the Symmetric Terminal Voltage,IEEE transactions on magnetics 2006, 42(10): 3473-3475.
[26] Cheng-Tsung Lin,Chung-Wen Hung,Chih-Wen Liu,Sensorless Control for Four-Switch Three-Phase Brushless DC Motor Drives,Industry Applications Conference,2006. 8-12Oct,2006,Volume4: 2048-2053.
[27] Wei Chen, Changliang Xia,Sensorless Control of Brushless DC Motor Based on Fuzzy Logic,WCICA 2006,21-23June 2006,Volume2: 6298-6032.
[28] Cheng-Hu Chen, Ming-Yang Cheng,A New Sensorless Commutation Drive for Brushless DC Motors and Alternators,IEEE ISIE 2006, July9-12, 2006 , volume3: 2116-2121.
[29] Cheng-Hu Chen,Ming-Yang Cheng,New Cost Effective Sensorless Commutation Method for Brushless DC Motors Without Phase Shift Circuit and Neutral Voltage,IEEE Transactions on power electronics,2007,22(2): 644-652.
[30] Tae-Hyung Kim,Ehsani. M,An error analysis of the sensorless position estimation for BLDC motors,Industry Applications Conference,2003,vol.1: 611-617.
[31] Lin Mingyao,Li Qiang.,Gu Weigang,Effect of rotor position error on commutation in sensorless BLDC motor drives,ICEMS 2005,Vol.1: 497-499.
[32]韦鲲,任军军,张仲超,三次谐波检测无刷直流电机转子位置的研究,中国电机工程学报. 2004,24(5): 163-167.
[33] Nobuyuki Kasa,Hiroshi Watanabe,A Mechanical Sensorless Control System for Salient-Pole Brushless DC Motor with Autocalibration of Estimated Position Anglew,IEEE transactions on industrial electronics,2000,47(2): 389-395.
[34] J.X.Shen, K.J.Tseng,Analysis and Compensation of Rotor Position Detection Error in Sensorless PM Brushelss DC Motor Drives,IEEE Transactions on energy conversion,2003,18(1): 87-93.
[35] Joong-Ho Song,Ick Choy,A rotor Position sensorless control based on neutral voltage compensation of brushless dc motors,PESC 04,South Korea,20-25 June 2004,Volume2: 1431-1437.
[36] Genfu Zhou,Zhigan Wu,Jianping Ying,Improved Sensorless Brushless DC Motor Drive,PESC '05. IEEE 36th,2005,pages: 1353– 1357.
[37] H.Tan, S.L.Ho,A novel single current sensor technique suitable for bldcm drivers,PEDS’99,July 1999,Hong Kong,volume 1,pages:133-138.
[38] FRENCH C, ACARNLEY P,Control of permanent magnet motor drives using a new position estimation technique,IEEE Trans on Ind Appl, 1996,32(5): 1089-1097.
[39] Jang. G. H.,Park. J. H.,Chang. J. H,Position detection and start-up algorithm of a rotor in a sensorless BLDC motor utilizing inductance variation,Electric Power Applications,2002,Volume 149,pages: 137-142.
[40] Jung-Sik Yim,Seung-Ki Sul,Hyeong-Joon Ahn, Dong-Chul Han,Sensorless position control of active magnetic bearings based on high frequency signal injection with digital signal processing,AEPC’04,Nineteenth annual IEEE,Volume 2,2004:1351-1354.
[41] Tae-Hyung, Byung-Kuk Lee,Mehrdad Ehsani,sensorless control of the BLDC motors from near zero to high speed,APEC’03,Eighteenth Annual IEEE,Volume 1,2003: 306-312.
[42] H.-S. Yan,Y.-C. Wu,A Novel Design of a Brushless DC Motor Integrated with an Embedded Planetary Gear Train,Mechatronics,IEEE/ASME Transactions,2006,11(5): 551-557.
[43] Mohammad S. Islam,Sayeed Mir,Tomy Sebastian,Issues in Reducing the Cogging Torque of Mass-Procuced Permanent-Magnet Brushless DC Motor , IEEE Transactions on industry applications,2004,40(3):813-820.
[44] Pan Seok Shin, Han-Deul Kim,Gyo-Bum Chung,Shape Optimization of a Large-Scale BLDC Motor Using an Adaptive RSM Utilizing Design Sensitivity Analysis,IEEE Transactions on magnetics,2007,43(4): 1653-1656.
[45] Z. Q. Zhu,D. Howe,Influence of design parameters on cogging torque in permanent magnet machines,IEEE Transactions on conversion,2000,43(4):407-411.
[46] Ge Xin, Han Guangxian,Cheng Zhi,Research of cogging torque in the brushless DC motor with fractional ratio of slots and poles,12th Biennial IEEE Conference,2006,pages: 241-241.
[47] Upadhyay.p, Rajaqopal.K.R,Torque Ripple Minimization of Interior Permanent Magnet Brushless DC Motor Using Rotor Pole Shaping,PEDES’06, International Conference,2006,pages:1-3.
[48] Han-Woong Park,Sung-Jun Park,Yang-Woo Lee,Reference frame approach for torque ripple minimization of BLDCM over wide range including cogging torque,ISIE2001.Pusan,KOREA, 2001,volume,pages:637-642.
[49]揭贵生,马伟明,考虑换相时无刷直流电机脉宽调制方法研究,电工技术学报,2006,20(9): 66-71.
[50]张相军,陈伯时,无刷直流电机控制系统中PWM调制方式对换相转矩脉动的影响,电机与控制学报,2003,7(2): 87-91.
[51]林平,韦昆,张仲超,新型无刷直流电机换相转矩脉动的抑制控制方法,中国电机工程学报,2005,26(3): 153-158.
[52] Xi Xiao,Yongdong Li,Meng Zhang,A novel control strategy for brushless DC motor drive with low torque ripples,IECON 2005.32nd annual Conference of IEEE,2005,pages:1660-1664.
[53] Zhang Lei,Qu Wenglong,Commutation Torque Ripple Restraint in BLDC Motor over Whole Speed Range,ICEMS 2005, Proceeding of the Eighth International Conference,2005,Volume 2,pages: 1501-1506.
[2]李朝东,微电机研究的最新动态与应用展望,微特电机,1999(5):23-25.
[3]季小尹,符向荣,王安丽,混合动力电动汽车用永磁无刷直流电机的设计与实现,微特电机,2004(2):5-7.
[4] Wook-Jin Lee, Seung-Ki Sul,A New Starting Method of BLDC Motors Without Position sensor,IEEE transactions on industry application,2006,42(6):1532-1538.
[5] Byoung-Gun Park, Tae-Sung Kim, Ji-Su Ryu , Fuzzy back-EMF observer for improving performance of sensorless brushless DC motor drive,APEC’06,Seoul,South Korea,2006,on pages:674-678.
[6] J.X.Shen, S.Iwasaki,Sensorless Control of Ultrahigh-Speed PM Brushless Motor Using PLL and Third Harmonic Back EMF,IEEE transactions on power electronics, 2006, 53(2):421-428.
[7] Quan Jiang, Ruoyu Huang,A NEW Phase-Delay-Free Method to Detect Back EMF Zero-Crossing Points for Sensorless Control of Spindle Motors,IEEE transactions on magetics,2005, 41(7):2287-2294.
[8] Chang-Liang Xia,Wei Chen,Sensorless Control of Brushless DC Motors at Low Speed Using Neural Networks,Proceedings of the fourth International Conference on Machine Learning and Cybernetics, Guangzhou,18-21 August 2005,pages:1099-1103.
[9] Zhigan Wu,Genfu Zhou,Jian-ping Ying. High dynamic sensorless BLDCM drive with very wide speed range,The 30th annual conference of the IEEE industrial Electronics Society,2-6 November,2004,busan,Korea,pages:981-986.
[10] Yong-Ho Yoon,Mu-Seon Woo, Tae-Won Lee,PLL control Algorithm for Precise Speed Control of the Slotless PM Brushless DC Motor Using 2Hall-ICs. 2004 35th Annual IEEE Power Electronics Specialists Conference,Aachen, Germany,2004,pages: 1315-1321.
[11]韦坤,任军军,张仲超,一种新的直流无刷电机的无传感器控制方法,电力电子技术,2004,38(3): 70-72.
[12]黄玉,王剑,陈瑜,无刷直流电机的新型位置检测方法,山东大学学报(工学版),2003,33(3): 297-291.
[13] Joong-Ho Song,and Ick Choy,Commutation Torque Ripple Reduction in Brushless DC Motor Drives Using a Single DC Current Sensor,IEEE Transactions on power electronics,2004,19(2):312 -319.
[14]韦昆,胡长生,张仲超,一种新的消除无刷直流电机非导通相续的PWM调制方式,中国电机工程学报,2005,25(7):104-108.
[15] H.Zeroug,B.Boukais,and H.Sahraoui,Analysis of Torque Ripple in a BLDCM,IEEE Transactions on Magnetics,2002,38(2): 1293- 1296.
[16] Yong Liu,Z.Q.Zhu,David Howe,Direct Torque Control of Brushless DC Drives With Reduced Torque Ripple,IEEE Transactions on industry applactions,2005,41(2): 599-608.
[17] Zhang Xiaofeng,Lu Zhengyu,A New BLDC Motor Drives Method Based on BUCK Converter for Torque Ripple Reduction,Power Electronics and Motion Control Conference,2006,5th International,Shanghai China,Aug 2006, Volume 3: 1-4.
[18] N’diaye.A,Espanet.C,Miraoui.A,Reduction of the torque ripples in brushless PM motors by optimization of the supply - theoretical method and experimental implementation,Industrial Electronics,2004 IEEE International Symposium, France,2004,Volume 2: 1345-1350.
[19] Yong Liu,Zi Qiang Zhu, David Howe,Instantaneous Torque Estimation in Sensorless Direct-Totque-Contrulled Brushless DC Motors,IEEE transactions on industry applications,2006,42(5):1275-1283.
[20] Byoung-Hee Kang,Choel-Ju Kim,Hyung-Su Mok. Analysis of torque ripple in BLDC motor with commutation time,ISIE 2001,IEEE International symposium,2001,voltume 2, pages: 1044-1048.
[21]韦坤,林平,张仲超,无刷直流电机换相转矩脉动的电流预测控制,浙江大学学报(工学版),2006,40(1):171-175.
[22] Tae-Hyung Kim, Mehrdad Ehsani.Sensorless Control of the BLDC Motors From Near-Zero to High Speeds,IEEE transactions on power elsctronics,2004,19(6): 1635-1645.
[23] C.-G.Kim,J.-H.Lee,H.-Waked, M.-J.Youn,Study on maximum torque generation for sensorless controlled brushless DC mortor with trapezoidal back EMF,IEE Proc.-Electr. Power Appl, 2005, 152(2): 277-291.
[24]张磊,瞿文龙,陆海峰,肖伟,一种新颖的无刷直流电机无位置传感器控制系统,电工技术学报,2006,21(10): 26-30.
[25] G. H. Jang, M. G. Kim,Optimal Commutation of a BLDC Motor by Utilizing the Symmetric Terminal Voltage,IEEE transactions on magnetics 2006, 42(10): 3473-3475.
[26] Cheng-Tsung Lin,Chung-Wen Hung,Chih-Wen Liu,Sensorless Control for Four-Switch Three-Phase Brushless DC Motor Drives,Industry Applications Conference,2006. 8-12Oct,2006,Volume4: 2048-2053.
[27] Wei Chen, Changliang Xia,Sensorless Control of Brushless DC Motor Based on Fuzzy Logic,WCICA 2006,21-23June 2006,Volume2: 6298-6032.
[28] Cheng-Hu Chen, Ming-Yang Cheng,A New Sensorless Commutation Drive for Brushless DC Motors and Alternators,IEEE ISIE 2006, July9-12, 2006 , volume3: 2116-2121.
[29] Cheng-Hu Chen,Ming-Yang Cheng,New Cost Effective Sensorless Commutation Method for Brushless DC Motors Without Phase Shift Circuit and Neutral Voltage,IEEE Transactions on power electronics,2007,22(2): 644-652.
[30] Tae-Hyung Kim,Ehsani. M,An error analysis of the sensorless position estimation for BLDC motors,Industry Applications Conference,2003,vol.1: 611-617.
[31] Lin Mingyao,Li Qiang.,Gu Weigang,Effect of rotor position error on commutation in sensorless BLDC motor drives,ICEMS 2005,Vol.1: 497-499.
[32]韦鲲,任军军,张仲超,三次谐波检测无刷直流电机转子位置的研究,中国电机工程学报. 2004,24(5): 163-167.
[33] Nobuyuki Kasa,Hiroshi Watanabe,A Mechanical Sensorless Control System for Salient-Pole Brushless DC Motor with Autocalibration of Estimated Position Anglew,IEEE transactions on industrial electronics,2000,47(2): 389-395.
[34] J.X.Shen, K.J.Tseng,Analysis and Compensation of Rotor Position Detection Error in Sensorless PM Brushelss DC Motor Drives,IEEE Transactions on energy conversion,2003,18(1): 87-93.
[35] Joong-Ho Song,Ick Choy,A rotor Position sensorless control based on neutral voltage compensation of brushless dc motors,PESC 04,South Korea,20-25 June 2004,Volume2: 1431-1437.
[36] Genfu Zhou,Zhigan Wu,Jianping Ying,Improved Sensorless Brushless DC Motor Drive,PESC '05. IEEE 36th,2005,pages: 1353– 1357.
[37] H.Tan, S.L.Ho,A novel single current sensor technique suitable for bldcm drivers,PEDS’99,July 1999,Hong Kong,volume 1,pages:133-138.
[38] FRENCH C, ACARNLEY P,Control of permanent magnet motor drives using a new position estimation technique,IEEE Trans on Ind Appl, 1996,32(5): 1089-1097.
[39] Jang. G. H.,Park. J. H.,Chang. J. H,Position detection and start-up algorithm of a rotor in a sensorless BLDC motor utilizing inductance variation,Electric Power Applications,2002,Volume 149,pages: 137-142.
[40] Jung-Sik Yim,Seung-Ki Sul,Hyeong-Joon Ahn, Dong-Chul Han,Sensorless position control of active magnetic bearings based on high frequency signal injection with digital signal processing,AEPC’04,Nineteenth annual IEEE,Volume 2,2004:1351-1354.
[41] Tae-Hyung, Byung-Kuk Lee,Mehrdad Ehsani,sensorless control of the BLDC motors from near zero to high speed,APEC’03,Eighteenth Annual IEEE,Volume 1,2003: 306-312.
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