低分辨率位置传感器永磁同步电机精确位置估计方法综述
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摘要
伺服电机在装备制造、新能源和家电等领域有着广阔的应用,为得到高精度转子位置信息,通常采用旋转变压器或光电编码器等高分辨率位置码盘,但其价格普遍较高,增加了系统设计成本。而无传感器技术当前还很难全面满足工业及家电等领域的应用要求。低分辨率位置传感器永磁同步电机驱动技术是一种能够保证电机运行性能,同时能有效控制系统成本、提高系统可靠性的转子位置检测技术,受到国内外产业界的广泛关注。介绍开关型霍尔位置传感器的使用方法与工作原理,总结原始霍尔位置信息误差的来源与校正方法;重点讨论基于插值法、同步坐标系滤波器法和观测器法的转子位置/转速估算策略,从提高低分辨率位置传感器电机系统低速性能等方面分析和比较不同估算策略的原理、优缺点、适用范围及应用情况;最后,总结现有研究成果及有待解决的问题。
Servo motor has been widely used in household appliances, new energy utilization and equipment manufacture. To obtain high precise rotor position information, the rotary transformers or photoelectric encoders are often adopted, but their prices are relatively high in general thus may add the system design cost. The sensorless technology can barely meet the application standards of industry utilization and household appliances. However, the low-resolution position sensor technology can guarantee the motor operation performance, which will effectively reduce the system cost and enhance the system reliability. In this paper, the application method and operation principle of switching hall position sensor are introduced, the coming source and correction method of the original hall positional information error are summarized. The rotor position/speed estimation strategies, such as interpolation method, synchronous frame filter method and observer method, are discussed in detail. The analysis and comparison of principles, advantages, disadvantages, application scopes and application conditions of different estimation methods were conducted from the aspects of the enhancement of motor system performance under low speed with low resolution position sensor. Lastly, existing research achievements and issues to be solved are summarized.
Servo motor has been widely used in household appliances, new energy utilization and equipment manufacture. To obtain high precise rotor position information, the rotary transformers or photoelectric encoders are often adopted, but their prices are relatively high in general thus may add the system design cost. The sensorless technology can barely meet the application standards of industry utilization and household appliances. However, the low-resolution position sensor technology can guarantee the motor operation performance, which will effectively reduce the system cost and enhance the system reliability. In this paper, the application method and operation principle of switching hall position sensor are introduced, the coming source and correction method of the original hall positional information error are summarized. The rotor position/speed estimation strategies, such as interpolation method, synchronous frame filter method and observer method, are discussed in detail. The analysis and comparison of principles, advantages, disadvantages, application scopes and application conditions of different estimation methods were conducted from the aspects of the enhancement of motor system performance under low speed with low resolution position sensor. Lastly, existing research achievements and issues to be solved are summarized.
引文
[1]Holtz J.Sensorless control of induction machines—With or without signal injection[J].IEEE Transactions on Industrial Electronics,2006,53(1):7-30.
[2]Qiao Z,Shi T,Wang Y,et al.New sliding-mode observer for position sensorless control of permanent-magnet synchronous motor[J].IEEE Transactions on Industrial Electronics,2013,60(2):710-719.
[3]Villet W T,Kamper M J.Variable-gear EV reluctance synchronous motor drives—an evaluation of rotor structures for position-sensorless control[J].IEEE Transactions on Industrial Electronics,2014,61(10):5732-5740.
[4]Fan Y,Zhang L,Cheng M,et al.Sensorless SVPWM-FADTC of a new flux-modulated permanentmagnet wheel motor based on a wide-speed sliding mode observer[J].IEEE Transactions on Industrial Electronics,2015,62(5):3143-3151.
[5]Gabriel F,De Belie F,Neyt X,et al.High-frequency issues using rotating voltage injections intended for position self-sensing[J].IEEE Transactions on Industrial Electronics,2013,60(12):5447-5457.
[6]Lee K W,Park S,Jeong S.A seamless transition control of sensorless PMSM compressor drives for improving efficiency based on a dual-mode operation[J].IEEE Transactions on Power Electronics,2015,30(3):1446-1456.
[7]Bernardes T,Foletto Montagner V,Grundling H A,et al.Discrete-time sliding mode observer for sensorless vector control of permanent magnet synchronous machine[J].IEEE Transactions on Industrial Electronics,2014,61(4):1679-1691.
[8]Xie G,Lu K,Kumar D S,et al.High bandwidth zero voltage injection method for sensorless control of PMSM[C]//The 17th International Conference on Electrical Machines and Systems(ICEMS),Hangzhou,China,2014:3546-3552.
[9]樊英,张丽,程明.基于宽速滑模观测器的新型自减速永磁轮毂电机无传感器直接转矩控制[J].电工技术学报,2014,29(5):141-148.Pan Ying,Zhang Li,Cheng Ming.A wide-speed mode obsever for sensorless direct torque control of a new self-decelerating permanent magnet in-wheel motor[J].Transactions of China Electrotechnical Society,2014,29(5):141-148.
[10]Pahlevaninezhad M,Das P,Moschopoulos G,et al.Sensorless control of a Boost PFC AC/DC converter with a very fast transient response[C]//Applied Power Electronics Conference and Exposition(APEC),Long Beach,CA,USA,2013:356-360.
[11]鲁家栋,刘景林,卫丽超.永磁同步电机转子初始位置检测方法[J].电工技术学报,2015,30(7):105-111.Lu Jiadong,Liu Jinglin,Wei Lichao.Estiamtion of the initial rotor position for permanent magnet synchronous motors[J].Transactions of China Electrotechnical Society,2015,30(7):105-111.
[12]王高林,杨荣峰,李刚,等.基于高频信号注入的IPMSM无位置传感器控制策略[J].电工技术学报,2012,27(11):62-68.Wang Gaolin,Yang Rongfeng,Li Gang,et al.Position sensorless control strategy of IPMSM based on high frequency signal injection[J].Transactions of China Electrotechnical Society,2012,27(11):62-68.
[13]Kim S,Ha J I,Sul S K.PWM switching frequency signal injection sensorless method in IPMSM[J].IEEE Transactions on Industry Applications,2012,48(5):1576-1587.
[14]Jung S,Ha J I.Analog filtering method for sensorless AC machine control with carrier-frequency signal injection[J].IEEE Transactions on Industrial Electronics,2015,62(9):5348-5358.
[15]刘颖,周波,冯瑛,等.永磁同步电机低速无传感器控制及位置估计误差补偿[J].电工技术学报,2012,27(11):38-45.Liu Ying,Zhou Bo,Feng Ying.A novel sensorless control method of SPMSM at low speed and estimated rotor position error compensation[J].Transactions of China Electrotechnical Society,2012,27(11):38-45.
[16]Yang S C,Suzuki T,Lorenz R D,et al.Surfacepermanent-magnet synchronous machine design for saliency-tracking self-sensing position estimation at zero and low speeds[J].IEEE Transactions on Industry Applications,2011,47(5):2103-2116.
[17]Burger F,Besse P A,Popovic R S.New single chip Hall sensor for three phases brushless motor control[J].Sensors and Actuators A:Physical,2000,81(1):320-323.
[18]Beccue P B,Pekarek S D,Deken B J,et al.Compensation for asymmetries and misalignment in a Hall-effect position observer used in PMSM torqueripple control[J].IEEE Transactions on Industry Applications,2007,43(2):560-570.
[19]Calzo L.Sinusoidal current shaping in variable-speed distributed generating units with low-resolution position sensors[C]//IEEE Energy Conversion Congress and Exposition(ECCE),Raleigh,NC,USA,2012:2646-2653.
[20]Raute R,Caruana C,Staines C S,et al.Analysis and compensation of inverter nonlinearity effect on a sensorless PMSM drive at very low and zero speed operation[J].IEEE Transactions on Industrial Electronics,2010,57(12):4065-4074.
[21]Yang Y P,Ting Y Y.Improved angular displacement estimation based on hall-effect sensors for driving a brushless permanent-magnet motor[J].IEEE Transactions on Industrial Electronics,2014,61(1):504-511.
[22]Morimoto S,Sanada M,Takeda Y.Sinusoidal current drive system of permanent magnet synchronous motor with low resolution position sensor[C]//The31st IAS Annual Meeting,Industry Applications Conference,San Diego,CA,USA,1996:9-14.
[23]Bu J,Xu L,Sebastian T,et al.Near-zero speed performance enhancement of PM synchronous machines assisted by low-cost Hall effect sensors[C]//Applied Power Electronics Conference and Exposition,Anaheim,CA,USA,1998:64-68.
[24]Gu J,Ouyang M,Li J,et al.Driving and braking control of PM synchronous motor based on lowresolution hall sensor for battery electric vehicle[J].Chinese Journal of Mechanical Engineering,2013,26(1):1-10.
[25]Kim H,Yi S,Kim N,et al.Using low resolution position sensors in bumpless position/speed estimation methods for low cost PMSM drives[C]//The 40th IAS Annual Meeting,Industry Applications Conference,Kowloon,Hong Kong,China,2005:2518-2525.
[26]Capponi F G,De Donato G,Del Ferraro L.Brushless AC drive using an axial flux synchronous PM motor with low resolution position sensors[C]//Power Electronics Specialists Conference,Aachen,Germany,2004:2287-2292.
[27]曾风平,郑成勇,章跃进.基于开关型霍尔位置传感器的永磁同步电动机正弦波驱动[J].微特电机,2010,38(8):56-58.Zeng Fengping,Zheng Chengyong,Zhang Yuejin.Sin wave driver with switched Hall position sensor for permanent magnet sychronnous motor[J].Small&Special Electrical Machines.2010,38(8):56-58.
[28]Scelba G,De Donato G,Scarcella G,et al.Fault-tolerant rotor position and velocity estimation using binary Hall-effect sensors for low-cost vector control drives[J].IEEE Transactions on Industry Applications,2014,50(5):3403-3413.
[29]Brown R H,Schneider S C,Mulligan M G.Analysis of algorithms for velocity estimation from discrete position versus time data[J].IEEE Transactions on Industrial Electronics,1992,39(1):11-19.
[30]Zhang X,Zhang W.An improved rotor position estimation in PMSM with low-resolution Hall-effect sensors[C]//The 17th International Conference on Electrical Machines and Systems(ICEMS),Hangzhou,China,2014:2722-2727.
[31]Tesch T R,Lorenz R D.Disturbance torque and motion state estimation using low resolution position interfaces[C]//The 41st IAS Annual Meeting,Industry Applications Conference,Tamil Nadu,India,2006:917-924.
[32]Dalala Z M,Cho Y,Lai J S.Enhanced vector tracking observer for rotor position estimation for PMSM drives with low resolution Hall-effect position sensors[C]//IEEE International Electric Machines&Drives Conference(IEMDC),Chicago,IL,USA,2013,DOI:10.1109/IEMDC.2013.6556140.
[33]Lenine D,Reddy B R,Kumar S V.Estimation of speed and rotor position of BLDC motor using extended Kalman filter[C]//IET-UK International Conference on Information and Communication Technology in Electrical Sciences(ICTES),Tamil Nadu,India,2007:433-440.
[34]Song Y,Dougal R,Gao L,et al.A novel brushless DC motor speed estimator based on space-frequency localized wavelet neural networks(WNNs)[C]//IEEE Applied Power Electronics Conference(APEC),Austin,TX,USA,2005:927-932.
[35]Davis R I.A nonlinear observer for instantaneous internal combustion engine crankshaft torque and active torque smoothing control using a crankshaft mounted electric motor[D].Madison:University of Wisconsin-Madison,1999.
[36]Capponi F G,De Donato G,Del Ferraro L,et al.AC brushless drive with low-resolution Hall-effect sensors for surface-mounted PM machines[J].IEEE Transactions on Industry Applications,2006,42(2):526-535.
[37]Harke M C,De Donato G,Capponi F G,et al.Implementation issues and performance evaluation of sinusoidal,surface-mounted PM machine drives with Hall-effect position sensors and a vector-tracking observer[J].IEEE Transactions on Industry Applications,2008,44(1):161-173.
[38]García P,Briz F,Degner M W,et al.Accuracy,bandwidth,and stability limits of carrier-signalinjection-based sensorless control methods[J].IEEE Transactions on Industry Applications,2007,43(4):990-1000.
[39]Dalala Z M,Cho Y,Lai J S.Enhanced vector tracking observer for rotor position estimation for PMSM drives with low resolution Hall-effect position sensors[C]//IEEE International Electric Machines&Drives Conference(IEMDC),Chicago,IL,USA,2013:484-491.
[40]Yoo A,Sul S K,Lee D C,et al.Novel speed and rotor position estimation strategy using a dual observer for low-resolution position sensors[J].IEEE Transactions on Power Electronics,2009,24(12):2897-2906.
[41]Bojoi R,He B,Rosa F,et al.Sensorless direct flux and torque control for direct drive washing machine applications[C]//IEEE Energy Conversion Congress and Exposition(ECCE),Phoenix,AZ,USA,2011,DOI:10.1109/ECCE.2011.6063790.
[42]Song Xinda,Fang Jiancheng,Han Bangcheng.High-precise rotor position detection for high-speed surface PMSM drive based on linear Hall-effect sensors[J].IEEE Transactions on Power Electronics,2016,31(7):4720-4731.
[43]Batzel T D,Lee K Y.Commutation torque ripple minimization for permanent magnet synchronous machines with Hall effect position feedback[J].IEEE Transactions on Energy Conversion,1998,13(3):257-262.
[44]Kim S Y,Choi C,Lee K,et al.An improved rotor position estimation with vector-tracking observer in PMSM drives with low-resolution Hall-effect sensors[J].IEEE Transactions on Industrial Electronics,2011,58(9):4078-4086.
[45]Zaim S,Martin J P,Nahid-Mobarakeh B,et al.High performance low cost control of a permanent magnet wheel motor using a Hall effect position sensor[C]//Vehicle Power and Propulsion Conference(VPPC),Chicago,IL,USA,2011:1-6.
[46]Liu Y,Zhao J,Xia M,et al.Model reference adaptive control-based speed control of brushless DC motors with low-resolution Hall-effect sensors[J].IEEE Transactions on Power Electronics,2014,29(3):1514-1522.
[47]Yang Y P,Ting Y Y.Improved angular displacement estimation based on Hall-effect sensors for driving a brushless permanent-magnet motor[J].IEEE Transactions on Industrial Electronics,2014,61(1):504-511.
[2]Qiao Z,Shi T,Wang Y,et al.New sliding-mode observer for position sensorless control of permanent-magnet synchronous motor[J].IEEE Transactions on Industrial Electronics,2013,60(2):710-719.
[3]Villet W T,Kamper M J.Variable-gear EV reluctance synchronous motor drives—an evaluation of rotor structures for position-sensorless control[J].IEEE Transactions on Industrial Electronics,2014,61(10):5732-5740.
[4]Fan Y,Zhang L,Cheng M,et al.Sensorless SVPWM-FADTC of a new flux-modulated permanentmagnet wheel motor based on a wide-speed sliding mode observer[J].IEEE Transactions on Industrial Electronics,2015,62(5):3143-3151.
[5]Gabriel F,De Belie F,Neyt X,et al.High-frequency issues using rotating voltage injections intended for position self-sensing[J].IEEE Transactions on Industrial Electronics,2013,60(12):5447-5457.
[6]Lee K W,Park S,Jeong S.A seamless transition control of sensorless PMSM compressor drives for improving efficiency based on a dual-mode operation[J].IEEE Transactions on Power Electronics,2015,30(3):1446-1456.
[7]Bernardes T,Foletto Montagner V,Grundling H A,et al.Discrete-time sliding mode observer for sensorless vector control of permanent magnet synchronous machine[J].IEEE Transactions on Industrial Electronics,2014,61(4):1679-1691.
[8]Xie G,Lu K,Kumar D S,et al.High bandwidth zero voltage injection method for sensorless control of PMSM[C]//The 17th International Conference on Electrical Machines and Systems(ICEMS),Hangzhou,China,2014:3546-3552.
[9]樊英,张丽,程明.基于宽速滑模观测器的新型自减速永磁轮毂电机无传感器直接转矩控制[J].电工技术学报,2014,29(5):141-148.Pan Ying,Zhang Li,Cheng Ming.A wide-speed mode obsever for sensorless direct torque control of a new self-decelerating permanent magnet in-wheel motor[J].Transactions of China Electrotechnical Society,2014,29(5):141-148.
[10]Pahlevaninezhad M,Das P,Moschopoulos G,et al.Sensorless control of a Boost PFC AC/DC converter with a very fast transient response[C]//Applied Power Electronics Conference and Exposition(APEC),Long Beach,CA,USA,2013:356-360.
[11]鲁家栋,刘景林,卫丽超.永磁同步电机转子初始位置检测方法[J].电工技术学报,2015,30(7):105-111.Lu Jiadong,Liu Jinglin,Wei Lichao.Estiamtion of the initial rotor position for permanent magnet synchronous motors[J].Transactions of China Electrotechnical Society,2015,30(7):105-111.
[12]王高林,杨荣峰,李刚,等.基于高频信号注入的IPMSM无位置传感器控制策略[J].电工技术学报,2012,27(11):62-68.Wang Gaolin,Yang Rongfeng,Li Gang,et al.Position sensorless control strategy of IPMSM based on high frequency signal injection[J].Transactions of China Electrotechnical Society,2012,27(11):62-68.
[13]Kim S,Ha J I,Sul S K.PWM switching frequency signal injection sensorless method in IPMSM[J].IEEE Transactions on Industry Applications,2012,48(5):1576-1587.
[14]Jung S,Ha J I.Analog filtering method for sensorless AC machine control with carrier-frequency signal injection[J].IEEE Transactions on Industrial Electronics,2015,62(9):5348-5358.
[15]刘颖,周波,冯瑛,等.永磁同步电机低速无传感器控制及位置估计误差补偿[J].电工技术学报,2012,27(11):38-45.Liu Ying,Zhou Bo,Feng Ying.A novel sensorless control method of SPMSM at low speed and estimated rotor position error compensation[J].Transactions of China Electrotechnical Society,2012,27(11):38-45.
[16]Yang S C,Suzuki T,Lorenz R D,et al.Surfacepermanent-magnet synchronous machine design for saliency-tracking self-sensing position estimation at zero and low speeds[J].IEEE Transactions on Industry Applications,2011,47(5):2103-2116.
[17]Burger F,Besse P A,Popovic R S.New single chip Hall sensor for three phases brushless motor control[J].Sensors and Actuators A:Physical,2000,81(1):320-323.
[18]Beccue P B,Pekarek S D,Deken B J,et al.Compensation for asymmetries and misalignment in a Hall-effect position observer used in PMSM torqueripple control[J].IEEE Transactions on Industry Applications,2007,43(2):560-570.
[19]Calzo L.Sinusoidal current shaping in variable-speed distributed generating units with low-resolution position sensors[C]//IEEE Energy Conversion Congress and Exposition(ECCE),Raleigh,NC,USA,2012:2646-2653.
[20]Raute R,Caruana C,Staines C S,et al.Analysis and compensation of inverter nonlinearity effect on a sensorless PMSM drive at very low and zero speed operation[J].IEEE Transactions on Industrial Electronics,2010,57(12):4065-4074.
[21]Yang Y P,Ting Y Y.Improved angular displacement estimation based on hall-effect sensors for driving a brushless permanent-magnet motor[J].IEEE Transactions on Industrial Electronics,2014,61(1):504-511.
[22]Morimoto S,Sanada M,Takeda Y.Sinusoidal current drive system of permanent magnet synchronous motor with low resolution position sensor[C]//The31st IAS Annual Meeting,Industry Applications Conference,San Diego,CA,USA,1996:9-14.
[23]Bu J,Xu L,Sebastian T,et al.Near-zero speed performance enhancement of PM synchronous machines assisted by low-cost Hall effect sensors[C]//Applied Power Electronics Conference and Exposition,Anaheim,CA,USA,1998:64-68.
[24]Gu J,Ouyang M,Li J,et al.Driving and braking control of PM synchronous motor based on lowresolution hall sensor for battery electric vehicle[J].Chinese Journal of Mechanical Engineering,2013,26(1):1-10.
[25]Kim H,Yi S,Kim N,et al.Using low resolution position sensors in bumpless position/speed estimation methods for low cost PMSM drives[C]//The 40th IAS Annual Meeting,Industry Applications Conference,Kowloon,Hong Kong,China,2005:2518-2525.
[26]Capponi F G,De Donato G,Del Ferraro L.Brushless AC drive using an axial flux synchronous PM motor with low resolution position sensors[C]//Power Electronics Specialists Conference,Aachen,Germany,2004:2287-2292.
[27]曾风平,郑成勇,章跃进.基于开关型霍尔位置传感器的永磁同步电动机正弦波驱动[J].微特电机,2010,38(8):56-58.Zeng Fengping,Zheng Chengyong,Zhang Yuejin.Sin wave driver with switched Hall position sensor for permanent magnet sychronnous motor[J].Small&Special Electrical Machines.2010,38(8):56-58.
[28]Scelba G,De Donato G,Scarcella G,et al.Fault-tolerant rotor position and velocity estimation using binary Hall-effect sensors for low-cost vector control drives[J].IEEE Transactions on Industry Applications,2014,50(5):3403-3413.
[29]Brown R H,Schneider S C,Mulligan M G.Analysis of algorithms for velocity estimation from discrete position versus time data[J].IEEE Transactions on Industrial Electronics,1992,39(1):11-19.
[30]Zhang X,Zhang W.An improved rotor position estimation in PMSM with low-resolution Hall-effect sensors[C]//The 17th International Conference on Electrical Machines and Systems(ICEMS),Hangzhou,China,2014:2722-2727.
[31]Tesch T R,Lorenz R D.Disturbance torque and motion state estimation using low resolution position interfaces[C]//The 41st IAS Annual Meeting,Industry Applications Conference,Tamil Nadu,India,2006:917-924.
[32]Dalala Z M,Cho Y,Lai J S.Enhanced vector tracking observer for rotor position estimation for PMSM drives with low resolution Hall-effect position sensors[C]//IEEE International Electric Machines&Drives Conference(IEMDC),Chicago,IL,USA,2013,DOI:10.1109/IEMDC.2013.6556140.
[33]Lenine D,Reddy B R,Kumar S V.Estimation of speed and rotor position of BLDC motor using extended Kalman filter[C]//IET-UK International Conference on Information and Communication Technology in Electrical Sciences(ICTES),Tamil Nadu,India,2007:433-440.
[34]Song Y,Dougal R,Gao L,et al.A novel brushless DC motor speed estimator based on space-frequency localized wavelet neural networks(WNNs)[C]//IEEE Applied Power Electronics Conference(APEC),Austin,TX,USA,2005:927-932.
[35]Davis R I.A nonlinear observer for instantaneous internal combustion engine crankshaft torque and active torque smoothing control using a crankshaft mounted electric motor[D].Madison:University of Wisconsin-Madison,1999.
[36]Capponi F G,De Donato G,Del Ferraro L,et al.AC brushless drive with low-resolution Hall-effect sensors for surface-mounted PM machines[J].IEEE Transactions on Industry Applications,2006,42(2):526-535.
[37]Harke M C,De Donato G,Capponi F G,et al.Implementation issues and performance evaluation of sinusoidal,surface-mounted PM machine drives with Hall-effect position sensors and a vector-tracking observer[J].IEEE Transactions on Industry Applications,2008,44(1):161-173.
[38]García P,Briz F,Degner M W,et al.Accuracy,bandwidth,and stability limits of carrier-signalinjection-based sensorless control methods[J].IEEE Transactions on Industry Applications,2007,43(4):990-1000.
[39]Dalala Z M,Cho Y,Lai J S.Enhanced vector tracking observer for rotor position estimation for PMSM drives with low resolution Hall-effect position sensors[C]//IEEE International Electric Machines&Drives Conference(IEMDC),Chicago,IL,USA,2013:484-491.
[40]Yoo A,Sul S K,Lee D C,et al.Novel speed and rotor position estimation strategy using a dual observer for low-resolution position sensors[J].IEEE Transactions on Power Electronics,2009,24(12):2897-2906.
[41]Bojoi R,He B,Rosa F,et al.Sensorless direct flux and torque control for direct drive washing machine applications[C]//IEEE Energy Conversion Congress and Exposition(ECCE),Phoenix,AZ,USA,2011,DOI:10.1109/ECCE.2011.6063790.
[42]Song Xinda,Fang Jiancheng,Han Bangcheng.High-precise rotor position detection for high-speed surface PMSM drive based on linear Hall-effect sensors[J].IEEE Transactions on Power Electronics,2016,31(7):4720-4731.
[43]Batzel T D,Lee K Y.Commutation torque ripple minimization for permanent magnet synchronous machines with Hall effect position feedback[J].IEEE Transactions on Energy Conversion,1998,13(3):257-262.
[44]Kim S Y,Choi C,Lee K,et al.An improved rotor position estimation with vector-tracking observer in PMSM drives with low-resolution Hall-effect sensors[J].IEEE Transactions on Industrial Electronics,2011,58(9):4078-4086.
[45]Zaim S,Martin J P,Nahid-Mobarakeh B,et al.High performance low cost control of a permanent magnet wheel motor using a Hall effect position sensor[C]//Vehicle Power and Propulsion Conference(VPPC),Chicago,IL,USA,2011:1-6.
[46]Liu Y,Zhao J,Xia M,et al.Model reference adaptive control-based speed control of brushless DC motors with low-resolution Hall-effect sensors[J].IEEE Transactions on Power Electronics,2014,29(3):1514-1522.
[47]Yang Y P,Ting Y Y.Improved angular displacement estimation based on Hall-effect sensors for driving a brushless permanent-magnet motor[J].IEEE Transactions on Industrial Electronics,2014,61(1):504-511.