Reduction of commutation torque ripple in a brushless DC motor drive
基于二阶滑模观测器的无刷直流电机转子位置估计
基于二阶滑模观测器的无刷直流电机转子位置估计史婷娜;马银银;王迎发;夏长亮【摘要】针对一阶滑模观测器(F-SMO)存在的抖振和相位延迟问题,提出了基于二阶滑模观测器(S-SMO)的线反电势(LBEMF)估计策略,将不连续控制作用在滑模变量的高阶微分上,采用超螺旋算法设计控制率,能较好地削弱抖振,得到连续光滑且无滞后的反电势估计值.针对相反电势法存在的相移问题,采用线反电势过零点直接作为换相点的换相策略.仿真和实验结果表明,所提策略能够准确估计无刷直流电机线反电势,获得准确的转子位置换相点,实现无刷直流电机的无位置传感器控制.【期刊名称】《天津大学学报》【年(卷),期】2014(047)008【总页数】6页(P697-702)【关键词】无刷直流电机;二阶滑模观测器;线反电势;换相策略【作者】史婷娜;马银银;王迎发;夏长亮【作者单位】天津大学电气与自动化工程学院,天津300072;天津大学电气与自动化工程学院,天津300072;天津大学电气与自动化工程学院,天津300072;天津大学电气与自动化工程学院,天津300072【正文语种】中文【中图分类】TM383无刷直流电机由于具有效率高、输出转矩大、响应快、惯性低等诸多的优点，在航空、汽车和家庭应用等方面得到广泛应用[1-3]．传统无刷直流电机的闭环控制需要采用位置传感器来获得转子位置，但位置传感器的存在不仅导致系统成本的提高，而且还影响系统的可靠性和鲁棒性，因此无刷直流电机无位置传感器技术成为目前的一个重要研究方向．近年来，国内外文献介绍的无位置传感器检测方法主要包括相反电势法、磁链法、电感法、续流二极管法等．其中，相反电势法因其简单、实用等特点，成为目前研究的热点[4-6]．相反电势法通过检测无刷直流电机三相端电压，计算得到电机相反电动势过零点，再相移/6π 电角度得到无刷直流电机换相位置，其原理简单，实现方便，应用广泛．但在相移角计算过程中，通常依赖于电机速度，尤其是在调速过程中，相移角不准确易造成电机运行性能变差．如何避免相移角计算并直接获得换相点，成为一个新的研究思路．文献[7]提出了一种利用三次谐波检测转子位置的新方法，可检测速度更宽，不需要相移滤波，但在低速下三次谐波严重畸变，导致不能估算转子位置．文献[8]通过对电机模型分析，构造G函数直接确定无刷直流电机的换相点，扩展了无位置传感器控制调速范围，但系统的计算量增大．基于滑模观测器的反电势估计策略能准确估算出反电势信号．然而由于其控制作用的不连续性所引起的抖振现象，会导致被控系统出现危险的高频振荡．文献[9]将sigmoid函数代替开关函数，在一定程度上削弱了抖振，但也不可避免地降低了响应速度，使系统的鲁棒性变差．而低通滤波器的使用会导致相位滞后，难以精确补偿．文献[10]设计了反电势观测器，省去了低通滤波器和相位补偿环节，但估算的反电势存在抖振和噪声，影响准确性．二阶滑模是解决抖振问题和相位延迟的一种有效的方法，在此方法中，不连续控制并不作用在滑模变量的一阶微分上，而是作用在其高阶微分上，这样不仅保留了一阶滑模控制的所有优点，还可以削弱抖振和相位滞后现象[11-15]．因此本文采用二阶滑模观测器估算电机线反电动势．本文先采用超螺旋算法设计控制率，再设计二阶滑模微分估计器对电流微分进行估计．此二阶滑模观测器能较好地削弱抖振、得到连续光滑且无滞后的线反电势估计值，提高了无刷直流电机无位置传感器控制的换相精度．通过分析线反电动势过零点与换相时刻的对应关系，提出了采用线反电势过零点直接作为换相点的换相策略，根据虚拟霍耳信号建立无刷直流电机换相逻辑，避免了传统相反电势存在的相移角计算问题．无刷直流电机三相绕组电压、电流方程表示[16]为式中：ua0、ub0、uc0分别为三相定子绕组电压；un为电机中性点电压；ia、ib、ic分别为定子相电流；ea、eb、ec为定子相反电势；R和 Ls分别为定子相电阻和等效电感．由于无刷直流电机中性点电压难以直接检测，将式(1)和式(2)简化为 2个并联的线性无关的一阶电流模型，整理成线电压的状态空间形式为式中：和 ebc为绕组线反电势，eab=ea-，uab和ubc为绕组线电压同时，线反电势之间存在关系由式(3)可知，直接计算能够得到线反电势，但开环计算方式及计算中的电流微分项会导致计算过程中存在一定误差，而采用闭环形式的观测器则可进一步提高线反电势估计精度．根据式(3)，构建无刷直流电机的二阶滑模观测器式中：Z为二阶滑模观测器控制量，将式(6)与式(3)相减，得到无刷直流电机的状态误差方程为式中当滑模面存在且在有限时间内收敛时，即可得下面对无刷直流电机的二阶滑模观测器进行分析．2.1 滑模面选择将无刷直流电机线电流差作为误差标准，其表示为选择二阶滑模观测器的滑模面为式中σ为无刷直流电机线电流误差构成的滑模面，增加常数 c可以任意地加快收敛速率．根据滑模控制的设计要求，控制必须能保证滑模变量1σ和2σ收敛到零点．令有合理地选择常数c可使误差在有限时间内趋于0．滑模变量的微分表示为式中：其中A1、A2、A3、A4、A5是由电机参数确定的常数．2.2 控制率设计本文采用超螺旋算法作为二阶滑模观测器中的控制率．超螺旋算法是指在 -σ σ˙平面内，状态轨迹在有限时间内围绕原点螺旋式地收敛到原点．该算法不需要滑模变量的一阶导数和符号信息，离散项出现在控制量的一阶微分上，滑模变量的相关度为 1，能够有效地削弱抖振现象．采用超螺旋算法的二阶滑模观测器控制率为控制率中的参数V1和V2按照约束规则选取，约束规则为式中为正常数，满足条件当控制率参数满足以上条件时，超螺旋算法可保证滑模变量在有限时间 tf内收敛到滑模面，即时，保证存在．当滑模变量达到收敛状态时，可准确估算出线反电势信号，估计值为根据式(5)，可得线反电势eca的估计值为了便于编程应用，考虑式(11)的 Euler离散化形式，得到式中：，τ 为采样时间； 0,1,2j= ．2.3 二阶滑模微分估计器式(9)需要对电流误差e(t)求取微分信号，但实际中微分器通常采用一阶差分信号，容易引入噪声干扰．因此，本文采用二阶滑模算法构成微分估计器，估计电流误差微分信号．设定微分估计器输入为电流误差信号 e(t)，电流误差信号微分量为滑模量及其微分量为采用超螺旋算法建立电流误差信号微分估计器式(16)收敛的充分条件为在超螺旋算法控制率作用下，微分估计器经过有限时间后达到收敛，存在因此，二阶滑模微分器能够较好地得到无刷直流电机线电流误差微分信号．根据以上分析，设计的无刷直流电机二阶滑模线反电势观测器结构如图1所示．无刷直流电机的换相需要确定 6个离散的位置信号，在位置传感器控制中通常由霍耳信号提供6个换相点．而霍耳信号对应的换相点滞后相应相反电势过零点30°电角度，因此相反电势法存在相移角计算问题，造成计算复杂．本文从线反电势的角度出发，分析霍耳信号与线反电势之间的关系．图 2所示为线反电势过零点与实际霍耳换相信号示意．由图2中可以看出，线反电势过零点直接与霍耳信号的换相点对应．若线反电势为正时表示为 1，为负时表示为 0，可得 eab、ebc、eca分别对应H2、H3和(“”表示信号取反)，用虚拟霍耳信号和表示．建立霍耳信号换相逻辑表，如表1所示．4.1 仿真结果及分析利用 Matlab/Simulink建立一阶和二阶滑模观测器仿真模型，电机参数如表2所示．电机运行在n=2,000,r/min、TL=0.2,N·m条件下，采用一阶滑模观测器对无刷直流电机线反电势估计，反电势估计结果如图3所示．图3中，实线和虚线分别代表实际线反电势和估算线反电势．一阶滑模观测器由于低通滤波器的使用，反电势估计值存在相位延迟，该延迟会加大电机换相误差，降低电机运行性能．图4为无刷直流电机分别运行在n=200,r/min、n=1,000,r/min、n=2,000,r/min，TL=0.2,N·m条件下，采用二阶滑模观测器得到的线反电势估计值．实线和虚线分别代表实际线反电势和估算线反电势．由图 4中可以看出，二阶滑模观测器在高、中、低速范围内均能较好地跟踪实际线反电势，能得到连续光滑且无滞后的线反电势估计值，实现无刷直流电机正确换相．图 5为无刷直流电机在 n=1,000,r/min、TL= 0.2,N·m、电阻Ra增大20%的条件下，线反电势实际值和估计值的仿真结果．由图5中可以看出，电阻Ra增大20%时，二阶滑模观测器仍能较好地估计出线反电势，表明二阶滑模观测器对电机参数的扰动具有较好的抑制能力．图 6为TL=0.2,N·m条件下，电机从 n= 200,r/min变速运行到n=2,000,r/min 时，线反电势估计值和功率管换相信号．图 6(a)表明在变速条件下，二阶滑模观测器仍能准确估算出线反电势，表明二阶滑模观测器具有较好的鲁棒性．图 6(b)中，PT1为根据实际霍耳信号得到的换相信号，为根据本文分析的虚拟霍耳信号得到的换相信号，通过两者对比可以看出，根据线反电动势过零点得到的新的换相策略能准确确定换相位置，实现无刷直流电机无位置传感器控制．4.2 实验结果及分析为了进一步验证策略的有效性，以TI公司DSP芯片 TMS320F28335为核心控制器建立无刷直流电机实验系统．为了得到较好的实验效果，电压、电流检测均采用霍耳电压、电流传感器，同时设计了 4阶巴特沃斯低通滤波器滤除数据采集中的干扰信号．图7为n=800,r/min时线电压和换相信号的实验结果．由图 7中可以看出，换相信号和估计值基本重合，因此基于二阶滑模观测器的线反电势换相策略能够准确地换相，较好地实现无刷直流电机无位置传感器控制．图 8为线反电势实际值和通过二阶滑模观测器估计得到的线反电势估计值．可以看出，二阶滑模观测器能够较好地估计出无刷直流电机线反电势，且抖振较小，不存在相位滞后．(1) 二阶滑模观测器不仅保留了一阶滑模观测器的所有优点，且能够较好地削弱抖振，得到连续光滑且无滞后的线反电势估计值．(2) 通过分析无刷直流电机线反电动势与换相时刻的对应关系，得出线反电动势过零时刻即为换相时刻的结论，建立了虚拟霍耳信号换相逻辑．(3) 仿真与实验表明，本文策略能够准确估计出无刷直流电机线反电势，获得准确的转子位置换相点，实现了无刷直流电机无位置传感器控制的准确换相，提高了换相精度．【相关文献】［1］张志刚，王毅，黄守道，等. 无刷双馈电机在变速恒频风力发电系统中的应用[J]. 电气传动，2005，35(4)：61-64.Zhang Zhigang，Wang Yi，Huang Shoudao，et al. The application study for brushless doubly-fed machine in the variable speed constant frequency generation system[J]. Electric Drive，2005，35(4)：61-64(in Chinese).［2］ Shi Tingna，Guo Yuntao，Song Peng，et al. A new approach of minimizing commutation torque ripple for brushless DC motor based on DC-DC converter[J]. IEEE Transactions on Industrial Electronics，2010，57(10)：3483-3490.［3］ Chen Yie-Tone，Chiu Chun-Lung，Tang Zong-Hong，et al. Optimizing efficiency driver comprising phaselocked loop for the single-phase brushless DC fan motor[J]. IEEE Transactions on Magnetics，2012，48(5)：1937-1942.［4］ Shao Jianwen. An improved microcontroller-based sensorless brushless DC motor drive for automotive applications[J]. IEEE Transactions on Industry Applications，2006，42(5)：1216-1221.［5］ Imoru O，Tsado J. Modelling of an electronically commutated(brushless DC)motor drives with back-emf sensing[C] //16,th IEEE Mediterranean ElectrotechnicalConference(MELECON). 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TI TIDA-00916民用无人机电子速度控制(ESC)参考设计
TI公司的TIDA-00916是用于无人驾驶飞机电子速度控制(ESC)的无传感器高速磁场定向控制(FOC)参考设计,提供最好的FOC算法,以达到更长的飞行时间,更好的动态范围,更高的集成度,更小的板尺寸和更少的BOM元件.采用3颗LiPo电池速度高达12000RPM.主要用在无人驾驶飞机和UAV,高速马达和电池动力的电动工具.本文介绍了参考设计TIDA-00916主要特性,框图,无人驾驶飞机系统主要指标以及电路图和材料清单.ESC modules are important subsystems for non-military drones andusers demanding more efficient models that provide longer flight timesand higher dynamic behavior with smoother and more stable performance. This design implements an Electronic Speed Controller (ESC) commonlyused for unmanned aerial vehicles (UAV) or drones.The speed control is done sensorless, and the motor has been tested up to 1.2 kHz electrical frequency (12kRPM with a 6 pole pair motor), using FOC speed control. Our high-speed sensorless-FOC reference design for Drone ESCs provides best-in-class FOC algorithm implementation toachieve longer flight time, better dynamic performance and higherintegration, resulting smaller board size and fewer BOM components.Sensorless high speed FOC control using TI’s FAST™ software observerleveraging InstaSPIN-Motion™ C2000™ LaunchPad and DRV8305BoosterPack.图1:无人驾驭飞机示意图参考设计TIDA-00916主要特性:InstaSPIN-FOC™ sensorless FOC achieves highest dynamic performance. Tested up to 12,000 RPM with 3 LiPo cellsHigh dynamic performance: 1 kRPM to 10 kRPM (electrical frequency 100 Hz to 1 kHz) speed in <0.2 s to provide high performance yaw and pitch movementFast speed reversal capability for roll movementLonger flight time due to improved efficiency of FOC over blockcommutationHigher PWM switching frequency, tested up to 60 kHz to reducecurrent/torque ripple with low inductance / high-speed motors, and to avoid interference with ultrasonic sensorsTI TIDA－00916民用无人机电子速度控制(ESC)参考设计Fast time-to market due to InstaSPIN-FOC’s automatic motor parameter identification: auto-tuning sensorless FOC solutionMotor temperature estimation from winding resistance changes to protect motor from damage during temporary overload conditions参考设计TIDA-00916应用:Drones and UAVs High-Speed MotorsBattery-Operated Power Tools图2:参考设计TIDA-00916完整系统外形图(顶视图)图3:LaunchPad 板外形图(顶视图)图4:无人驾驶飞机电子速度控制(ESC)框图图5:无人驾驶飞机系统模块图无人驾驶飞机系统主要指标:图7:LAUNCHXL-F28069M电路图(2)图8:LAUNCHXL-F28069M电路图(3)图9:LAUNCHXL-F28069M电路图(4)图UNCHXL-F28069M电路图(5))图UNCHXL-F28069M电路图(6)图12:LAUNCHXL-F28069M电路图(7)图13:MDBU003A电路图。
无刷直流电机助力式EPS控制系统研究
无刷直流电机助力式ＥＰＳ控制系统研究
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（１）忽略电机铁心饱和，不计涡流损耗和磁滞损耗；
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基于递推最小二乘法的永磁同步电动机参数辨识_张洪东
i q （ k） － i q （ k － 1 ） pi q = Ts
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设计分析 esign and analysis 由于逆变器的开关周期选用的是 10 kHz， 取 Ts = 1 × 10 － 4 s。 在状态变量处理过程中引入了三阶 巴特沃思滤波器截止频率 800 Hz 进行修正。 3 仿真结果及分析 Matlab 7． 0 Simulink 在 的 环境下搭建基于 SVPWM 的双闭环永磁同步电动机参数辨识系统的 仿真模型。根据模块化仿真建模的思想， 如图 2 所 可以将整个永磁同步电动机控制系统分割为各 示， 个功能独立的子模块， 包括： 永磁同步电动机模块， 电机矢量控制（ SVPWM） 模块， 最小二乘法参数辨识 模块。 通过这些功能模块的有机整合， 在 Simulink q 轴电枢电感 中仿真实现电机的定子电阻 R s 和 d、 Ld 、 L q 在线辨识。 图 2 基于 SVPWM 的双闭环永磁同步电动机 参数辨识系统的仿真模型 仿真系统中永磁同步电动机参数如表 1 所示。 表 1 永磁同步电机仿真参数 定子电阻 R s / Ω 0． 24 0． 48 × 10 － 3 转动惯量 J / （ kg·m2 ） 永磁磁链 ψ f / Wb 0． 12 4 极对数 p d 轴电感 L d / H 2 × 10 － 3 额定转速 / （ r·min － 1 ） 2 000 q 轴电感 L q / H 2 × 10 － 3 负载转矩 T L / （ N·m） 7． 14 最小二乘法参数辨识模块由于需要大量数据进 基 于 行矩阵运算， 编写函数 S － function 作为一个模块嵌 递 推 入整个永磁同步电动机控制系统仿真环境中 ， 将电 最 iq 、 ud 、 u q 5 组数据作为函数的输 小 ω、 机模型输出的 i d 、 二 入。仿真过程中电机的初始电磁参数都为零， 仿真 乘 法 －4 最大步长设置为 100 μs， 采样时间 T s = 1 × 10 s，的 永 利用递推最小二乘算法修正前一时刻辨识出的电机 磁 同 参数， 获得新的电机辨识参数。如图 3 所示。 步 图 4 是永磁同步电动机控制过程中电阻和电感 电 动 的辨识的仿真结果。实线表示应用递推算法的估计 机 参 值， 虚线表示实际电机的电磁参数。 可以看出永磁 数 q 轴电枢电感 L d 、 L q 辨 同步电动机的定子电阻 R s 及 d、 识 从初始值零单调向电机相应参数的实际值进行收 敛， 并无限地接近相应电机参数的实际值 。 15
BLDCM换相转矩脉动的优化策略
BLDCM换相转矩脉动的优化策略王晓锋;林伟【摘要】First of all, this article creates the mathematical model of blushless DC Motor.Secondly, analyze the reduction theory of commutation torque ripple. Finally, put forward a strategy to reduce the commutation torque ripple from the low-speed level and high-speed level.This method guarantee equal between current decline rate of shutdown phase and current rising rate of opening phase during commutation, thus keep the current of un-commutation stable.Build a real brushless DC motor control platform for experimental verification,the proposed strategy of brushless DC motor commutation torque ripple is suppressed effectively.%首先建立了无刷直流电机(Brushless direct current motor, BLDCM)的数学模型，然后分析了换相转矩脉动的抑制原理，最后提出了低速阶段和高速阶段抑制换相转矩脉动的策略。
此方法保证在换相期间，关断相的电流下降率和开通相的电流上升率绝对值相等，继而保证在换相期间非换相相电流保持恒定。
搭建了实际直流无刷电机控制平台并进行实验验证，所提出的策略有效地抑制了直流无刷电机换相转矩脉动。
基于双H桥变换器的无刷直流电机转矩脉动抑制方法
控制与应用技术I EMCA違权控刹名阄2018,45 (7)基于双H桥变换器的无刷直流电机转矩脉动抑制方法#李东"2，冯金磊1，孔全存1，刘桂礼"2，赵双琦"(1.北京信息科技大学仪器科学与光电工程学院，北京100192;2.北京信息科技大学现代测控技术教育部重点实验室，北京100192)摘要：针对无刷直流电机(BLDCM)的换相转矩脉动问题，提出了一种基于双H桥变换器的BLDCM转矩 脉动抑制方法。
H桥变换器电生电流，减小非换相相电流的波动，从而达BLDCM转矩脉动的目的。
在MATLAB/Simulink下构建了 BLDCM转矩脉动仿真模型并进行对比仿真，与传统PID控制方法相比，该方非换相相电流波动在高、了70%: 40%, 的转矩波动了约80%。
:所提方法对于BLDCM在高高精的重。
关键词：无刷直流电机"转矩脉动；抑制方法；非换相相电流"双H桥变换器中图分类号：TM 301.2 文献标志码：A 文章编号：1673-6540(2018)07-0030-08AMethodto Inhibit Torque Ripple of Brushless DCMotorBased on Double H-Bridge Converter #LI Dong12，FENGJinlei1，KONG Quancun1，LIUGuili1，2，ZHAOShuangqi1(1.School of Instrumentation Science and Opto-Electronics Engineering，Beijing Information Science andTechnology University，Beijing 100192，China；2.Modern Measurement and Control Technology of Ministry of Education Key Laboratory，Beijing InformationScience and Technology University，Beijing 100192，China)Abstract: Aiming at the problem of commutation torque ripple in brushless DCmotor (BLDCM)，a method to inhibit torque ripple of BLDCM based on double H-bridge converter was proposed. Through the compensating orreducing current generated by the double H-bridge converter circuit，the fluctuation of the non-commutation phasecurrent could be reduced so as to inhibit the torque ripple of the BLDCM. The simulation model of BLDCM wasconstructed in MATLAB/Simulink and was conducted comparative experiment，compared with the traditional PIDcontrol method，the new method) s current ripple of non-commutation phase decreased about 70% at high speed and40% at low speed，respectively. Meanwhile，the balanced torque ripple decreased about 80%. The results showed tha the new method has some practical value.Key words: brushless DC motor (BLDCM); torque ripple; inhibiting method; non-commutation phase current; double H-bridge converter#基金项目：国家自然科学基金项目（51675054);北京市自然科学基金项目（3172013);北京市教委科技发展计划面上项目(KM201711232005);北京市重点实验室（机电系统测控）开放项目（5221735107)作者简介：李东（1959—），男，硕士，教授，硕导，研究方向为电子测量技术。
直流无刷电机启动算法
直流无刷电机启动算法英文回答：Brushless DC (BLDC) motors are widely used in various industrial and consumer applications due to their high efficiency, reliability, and long lifespan. However, starting a BLDC motor can be challenging, especially inlow-speed and high-torque applications.Challenges in Starting BLDC Motors:1. Back-Electromotive Force (BEMF): BLDC motors generate BEMF when the rotor rotates, which opposes the applied voltage. This can make it difficult for the motor to start, especially when the rotor is stationary.2. Cogging Torque: Cogging torque is a torque variation caused by the interaction between the stator and rotor magnets. It can cause the motor to oscillate or stall during startup.3. High Inertia: In high-inertia applications, it can be difficult to overcome the inertia of the rotor and accelerate the motor.Starting Algorithms for BLDC Motors:Several starting algorithms have been developed to overcome these challenges and achieve smooth and efficient motor startup. Here are some common techniques:1. Six-Step Commutation:This is the most basic starting algorithm for BLDC motors. It involves energizing the stator windings in a specific sequence to generate a rotating magnetic field. The rotor aligns itself with the magnetic field and starts rotating. However, this method can lead to cogging torque and uneven torque output.2. Sensorless Startup:This method uses an internal algorithm to estimate the rotor position without the need for a physical sensor. It utilizes the BEMF voltage generated by the motor to determine the commutation sequence. This method is more complex than sensor-based methods but provides advantages such as reduced cost and increased reliability.3. FOC (Field-Oriented Control):FOC is a advanced control technique that uses a mathematical model of the motor to control the magneticfield and torque output. It provides superior performance compared to traditional starting algorithms. FOC can minimize cogging torque, reduce torque ripple, and improve overall efficiency.4. Adaptive Starting Algorithms:Adaptive starting algorithms adjust their parameters based on the motor's operating conditions. They canoptimize startup performance for different loads and speeds. Adaptive algorithms use feedback from the motor to adjustthe commutation sequence and voltage waveform.Factors to Consider When Choosing a Starting Algorithm:Motor Parameters: The motor's voltage, current, speed, and inertia should be considered when selecting a starting algorithm.Application Requirements: The required torque, speed, and smoothness of startup should be evaluated.Cost and Complexity: Different starting algorithms have varying levels of complexity and cost.Reliability: The reliability and robustness of the algorithm under different operating conditions should be considered.中文回答：直流无刷电机启动算法。
Rotor Pole Design in Spoke-Type Brushless DC
Rotor Pole Design in Spoke-Type Brushless DC Motor by Response Surface MethodKyu-Yun Hwang1,Sang-Bong Rhee1,Byoung-Yull Yang2,and Byung-Il Kwon1 Department of Electronic,Electrical Control and Instrumentation Engineering,Hanyang University,Ansan426-791,Korea Digital Appliance R&D Center of Samsung Electronics Co.,LTD.,Suwon,KoreaThis paper proposes a novel rotor pole shape which consists of a uniform surface and an eccentric surface to make a sinusoidal mag-neticflux density in air gap in order to reduce cogging torque,torque ripple,and harmonics of back-electromotive force waveform in spoke-type brushless DC motor.In the process of design and analysis,response surface methodology and the2-Dfinite-element method are employed to obtain the rotor geometry and verify the results of the novel rotor pole shape.Index Terms—Brushless DC(BLDC)motor,cogging torque,finite-element method,response surface method,torque ripple.I.I NTRODUCTIONP ERMANENT brushless dc(BLDC)motors have been widely used due to their many advantages such as high torque and high efficiency.In particular,the spoke-type BLDC motor,which can concentrateflux from permanent magnets, has a high torque density per unit volume resulting from its high reluctance torque and structure for concentratingflux from permanent magnet.Spoke-type BLDC motors have therefore been researched for high torque application[1].However,the spoke-type BLDC motor has a serious dis-tortion of air gapflux density distribution which can increase cogging torque and torque ripple.This drawback is due to its asymmetric magnetic reluctance on the edge of the permanent magnet.To improve this,various rotor design methods have been researched.A rotor withflux barriers was proposed to reduce the distortion offlux density distribution in the air gap and to reduce cogging torque[2]–[4].Eccentric pole design was proposed to compensate the armature reaction for reducing torque ripple[5].Nevertheless,both methods have some de-fections.The former has poor performance due to the loss in flux barriers,and the latter is only suitable for motor rotation in one direction.This paper presents a novel rotor pole shape for making a sinusoidal distributedflux density in the air gap withoutflux barrier for the bidirectional rotating BLDC motor. To obtain better performance,the rotor pole shape is designed with response surface methodology(RSM)during the design process[6]–[9].Results of the proposed rotor pole shape are analyzed and compared with the initial model.II.R OTOR P OLE S HAPE D ESIGN OF BLDC M OTORA.Design Method of Rotor Pole ShapeThe arc shape of the d-axis’s rotor varies to allow for reducing cogging torque and torque ripple,as shown in Fig.1(b).The proposed rotor pole shape has a more sinusoidally distributedDigital Object Identifier10.1109/TMAG.2007.892616Color versions of one or more of thefigures in this paper are available online at.Fig.1.Topology of initial and proposed model.(a)Initial model.(b)Proposedmodel.(c)Enlarge part I.flux density in the air gap and effectively reduces the magneticsaturation on the upper permanent magnet.As a result,it caneffectively reduce cogging torque,torque ripple,and harmonicsof the back-electromotive force(back-EMF).Therefore,so as to make sinusoidally distributedflux densityin the air gap and to concentrate the more effectiveflux in a uni-form surface,the rotor pole shape was varied and divided intothree parts.These consist of two end parts of eccentric surfacesand one uniform surface.Table I and Fig.1(a)show specifica-tions of the brushless dc motor and the rotor pole shape of theinitial model,respectively.Fig.2shows how to make the ec-centric surface simply by moving the axis from the circle center(0,0)with radius L(the same axis that moves the rotor)to thepolar coordinate(r,theta1),(r,theta2)as shown in part I,partIII in Fig.2.Finally,part II determines the uniformity of thesurface;it does not change the center.Through this method of 0018-9464/$25.00©2007IEEETABLE IS PECIFICATION OF B RUSHLESS DC MOTORFig.2.Variation of rotor shape according to moving the center (0,0).(a)Part I.(b)PartIII.Fig.3.Plot of flux lines in initial and proposed model.(a)Flux lines in initial model.(b)Flux lines in proposed model.moving the center,eccentric surfaces have a curvature equaltobecause the eccentric surface is results from moving a circle with radius L,and having the rotor pole shape with an air gap of length R on the upper end of permanent magnet.This shape has a more sinusoidal distributed air-gap flux density than the initial model as shown in Fig.3(a)and (b).The initial model has a distortion of magnetic flux density distribution due to the magnetic saturation in the air gap between on the upper edge of permanent magnet and adjacent stator teeth as shown in Fig.3(a).But the proposed model is not seriously affected by the distortion of magnetic flux density in the air gap,because it reduces magnetic saturation by changing flux lines as shown in Fig.3(b).Concentrating the flux in the center,amount of effective flux is increasing,and thus the air-gap flux distribution is changed more sinusoidally.So,it has an increment of average torque and a reduction of coggingtorque.Fig.4.Design parameters of spoke-type BDLC having unequal air gap.B.Design ParametersEccentric surface is given according to the change in the circle ’s center;Fig.4shows the whole rotor shape.To optimize the design of the rotor pole shape,RSM is employed.Prior to optimization,the,response value and design parameter have to be determined.The response value is selected as cogging torque which is largely in fluenced by the permanent magnet and variation of reluctance.Design parameters are simply selected A,B,and C in place of changing r,theta,and angle of the uniform surface,to simplify the application to RSM as shown in Fig.4.Design parameter A,as a part of uniform surface among the electric angle of 180,is con fined to have a value more than 27.If the uniform surface is too small,it can cause a reduction of effective flux because of saturation on the surface,which has a relatively shorter flux line than the eccentric surface.Design parameter B,expressing how much the eccentric surface is curved,equals the curvature of the circle with radius L resulting from changing from the center ofrotor.This value of curvature willbe.If design parameter B is selected as the value of curvature,its value is too low,so selected as L in order to use a larger value.This selection is reasonable;as it employs all values of curvatures in con fined range.Design parameter C signi fies the air-gap length R on the upper edge of the permanent magnet.To operate at high speed,it is con fined to lower than 1.68mm to prevent from separating permanent magnets with considering mechanical stiffness.Given these condition constraints and the in fluence of object function such as cogging torque,the range of design parameters are expressed by arrayof factorial design [6].The factorial design is applied to obtain more reasonable and objective design area for RSM as shown in Fig.5.And then,central composite design (CCD)is employed as the experimental design method to estimate the regression [7].For rotation of the design,the valueof is 1.682.The com-plete list of all factors is provided in Table II.C.Response Surface Method (RSM)The main process in RSM can be expressed as (1),(2),and (3).Equation (1)shows the simple relation between design pa-rameters and responseparameters(1)where is output of themodel,are normalized de-sign parameters for A,B,and C respectively.Through the resultHWANG et al.:ROTOR POLE DESIGN IN SPOKE-TYPE BRUSHLESS DC MOTOR1835Fig.5.Main effects plot for cogging torque.TABLE IID ESIGN P ARAMETERS INCCDfrom CCD,second-order polynomial approximation is given asfollows:(2)whereare estimated by a regression from experi-ments,is the error estimate.To determine the precision of this regression equation from CCD,the coef ficient ofdeterminationis used as shown in(3)(3)where SSR and SST are given asfollows:(4)where is number of total experiments inCCD,is actual responsevalue,is average value,and is the response value from the regression equation.D.Analysis of the ResultIn this paper,the second-order polynomial approximation which shows the relation between suggested parameters and cogging torque can be obtained as shown in(5)(5)where coef ficient ofdetermination is 0.9510and it indicates that 95.10%of the total variation can be explained by the re-gression equation.The optimum result also can be obtainedasFig. 6.Predicted response surface in CCD.(a)x =0:1668(A =27:5496[mm ]).(b)x =01:6820(B =43[mm ]).(c)x =1:6820(C =1:73[mm ]).TABLE IIIR ESULT OF P ROPOSED M ODEL BY 2-DFEMshown in Fig.6by RSM and Table III is obtained by 2-D fi-nite-element method (FEM),and shows not only each of char-acteristic values both initial model and the proposed model,but also an aspect with variation in the response surface through regression of the variable design parameter.To see the surface response to changing two design parameters,designparameter is held as the optimum value,(oror )in order to see the response value of each parameter.In the casewheremm,mm,in other words a circle in which its radius of 43mm cur-vature is moved from rotor ’s center (0,0)to polarcoordinatemmmm ,cogging torque is considerably reduced about 89.9[%]compared with the initial model by results of RSM or 2-D FEM.And the average torque is also increased about 16.66%.In the optimum shape,although the total of air-gap flux den-sity is decreased due to the increased air-gap length,the rotor ’s ef ficiency is almost sustained as 79%because of the reduction1836IEEE TRANSACTIONS ON MAGNETICS,VOL.43,NO.4,APRIL2007parison of the air-gap magnetic flux densitywaveform.parison of the back-EMFwaveform.parison of the cogging torque.of magnetic saturation and less losses near the edge of the per-manent magnet,and the increment of the effective flux.Also,Figs.7and 8show the air-gap flux density and back-EMF wave-form in one pole.Throughout these figures,the proposed model has a more sinusoidal flux density waveform and ef ficiently re-duces the harmonics of back-EMF waveforms in one pole.The cogging torque and the torque ripple are respectively shown in Figs.9and 10for the initial model and the proposed model.As shown,the proposed model can effectively reduce cogging torque and torque ripple for the reason just explained,which are the near sinusoidal flux density waveform,the reduction of magnetic saturation near the edge of the permanentmagnet.parison of the torque ripple.III.C ONCLUSIONThis paper proposes a novel rotor pole shape which consists of eccentric surfaces and uniform surface,to reduce cogging torque,torque ripple,and harmonics of the back-EMF wave-form for bidirectional rotating and the three-phase BLDC motor.This novel rotor includes eccentric surface,which has a smooth variation of reluctance that can make a near sinusoidal magnetic flux waveform in air gap.It causes a reduction of losses between upper edge of permanent magnet and adjacent stator teeth,and increment of the effective flux by concentrating the flux.As a result,the optimum pole shape using RSM has good characteristics with respect to cogging torque,torque ripple,and average torque compared with the initial model,and it is veri fied by 2-D FEM.R EFERENCES[1]B.K.Lee,G.H.Kang,J.Hur,and D.W.You,“Design of spoke typeBLDC motors with high power density for traction applications,”in Proc.Industry Applications Conf.,Oct.2004,vol.2,3–7,no.2,pp.1068–1074.[2]B.Y.Yang,K.Y.Yun,and B.I.Kwon,“Designing method of fluxbarriers in rotor for reducing cogging torque,”in COMPUMAG2005,Shenyang,China,June 2005,IV-26,PG1-7.[3]D.H.Kim,I.H.Park,J.H.Lee,and C.E.Kim,“Optimal shape de-sign of iron core to reduce cogging torque of IPM motor,”IEEE Trans.Magn.,vol.39,no.3,pp.1456–1459,May 2003.[4]T.U.Jung and H.Nam,“Rotor design to improve starting performanceof line-start synchronous reluctance motor,”J.Elect.Eng.Technol.,vol.1,no.3,Sep.2006.[5]P.Zheng,Y.Liu,T.Wang,and S.Cheng,“Pole optimization of brush-less DC motor,”in Annu.Meeting.Conf.Rec.39th IAS ,Oct.2004,vol.2,3–7,pp.1063–1067.[6]D.C.Montgomery ,Design and Analysis of Experiments .New York:Wiley,2001.[7]A.I.Khuri and J.A.Cornell ,Response Surfaces:Designs and Ana-lyzes .New York:Marcel Dekker,1996.[8]S.I.Kim,J.P.Hong,Y.K.Kim,H.Nam,and H.I.Cho,“Optimaldesign of slotless-type PMLSM considering multiple responses by re-sponse surface methodology,”IEEE Trans.Magn.,vol.42,no.4,pp.1219–1222,Apr.2006.[9]X.K.Gao,T.S.Low,Z.J.Liu,and S.X.Chen,“Robust design fortorque optimization using response surface methodology,”IEEE Trans.Magn.,vol.38,no.2,pp.1141–1144,Mar.2002.Manuscript received October 27,2006(e-mail:bikwon@hanyang.ac.kr).。
BLDC_原理与驱动
・Torque/电流比最大控制 ・电压饱和时控制
9
第九页，编辑于星期五：四点 三十二分。
BLDCM驱动原理-Basic Block
BASIC BLOCK of INVERTER
10
第十页，编辑于星期五：四点 三十二分。
BLDCM 120度驱动原理-导通顺序
六个开关管交替导通,任一时刻,只有两相导通
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以此类推
11
第十一页，编辑于星期五：四点 三十二分。
BLDCM驱动原理-启动方法
五步启动法： 占空比与时间值存入EEPROM
TIMING CHART Motor Current
IPM
BLDCM驱动原理-BEMF检测
BEMF 的产生及特征
120度通电:对其中两相通电，第三相会产生反电势； 关系式：
N每相绕组的圈数 ;l转子的长度;r转子的半径;B 转子的磁通密度；电机的角速度
特征： 在任一相的反电势过零点，都有反电势Ea+Eb+Ec=0; 在同一通电周期内，每相有两个反电势过零点；
rcarrier周波数2motor变频波电流5次7次多pwmpulse数4次为止可能减少torqueripple电压利用率位相管理每60度但转极突极比较周密连续量例如每1度在电流最适宜控制中的基准电流位相commutation重复区间的12基准电流0位相規準分析手法过度现象电流连续量dq模式分析正弦波驱动优点损失降低噪音降低过负载提升位置sensorless驱动时电流位相调整容易vector控制?torque电流比最大控制?电压饱和时控制motor控制需要用正弦波
脉动转矩研究
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• 气隙中标量磁位满足拉普拉斯方程，永磁体内标量 磁位满足泊松方程。求解得气隙中磁密径向分量
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齿槽转矩的分类
1.646
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• 该类齿槽转矩波形的周期数取决于定子槽数和转子 槽数的组合。
• 该项齿槽转矩与定、转子槽数的配合有关，可以 通过合理选择定转子槽数的配合削弱齿槽转矩。
齿槽转矩的分类
h 4 m 2m 1n 1k 1B rm sn ss k i2 m n Z 1s p s2 im k n ( p k s 2 s 1 )
• 第5、6项齿槽转矩由Br2 ()的谐波、定子齿槽和转 子齿槽引起的磁密谐波共同产生产生的。
• 周期数取决于极数，定子槽数和转子槽数。
削弱齿槽转矩的方法
斜槽和斜极是削弱齿槽转矩最有效的方法
• 采用斜一个定子齿距的方法不能消除永磁 同步电动机中的所有齿槽转矩分量。
ANALYTICAL CALCULATION OF COGGING TORQUE IN BRUSHLESS DC MOTOR
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1 Research Scholar, Electrical Engineering Department, Jadavpur University, Kolkata – 700032, INDIA E-mail: bharatkar_sachin@. 2 Professor, Department of Electrical Engineering, Jadavpur University, Kolkata – 700032, INDIA E-mail: dchatterjee@ee.jdvu.ac.in.
eliminated at low speed by employing current control based on direct current sensing. In [2] and [3], it was concluded that it could not be compensated for by current chopping in the two-phase switching mode if the magnitude of the phase back-EMF is > 25% of the dc link voltage. In [4], two methods viz. overlapping conduction and PWM chopping were proposed, but because of first method torque ripple still results due to the difficulty in optimizing the overlap time. The second method significantly increases the system complexity and switching loss. In [5], commutation torque ripple was shown to result from the voltage between the neutral point of the inverter and the neutral point of the motor, which affects phase current during commutation. Adaptive torque-ripple control was proposed for BLDC motors in [6]. A commutation-torque-ripple reduction method for low cost application was presented in [7]. An alternative approach for minimizing torque ripple due to phase current commutation in a BLDC motor was developed in [8]. In [9], torque pulsations due to the interactions of the back-EMFs and currents and also due to commutation is reduced by employing torque controller. The application of direct toque control to a three- phase BLDC drive operating in 1200 electrical conduction mode was proposed in [10]. The performance of a direct toque controlled BLDC drive has also been compared with that of a PWM currentand without current shaping [11]. The estimation of the instantaneous electromagnetic torque was reported in [12]. The influence of PWM and cogging on the steady-state performance of a direct toque controlled BLDC drive was investigated in [13]. The commutation torque ripple minimization in direct toque controlled BLDC drive was presented in [14]. In this paper, an analytical study of commutation process is derived for inverters for both 1200 and 1800 conduction mode. It is seen that for 1200 conduction mode, due to increase in commutation time at higher speeds, the torque ripple increases and hence will not be suitable at higher speeds. Also, for 1800 conduction mode for the inverters, the commutation time increases at lower
1-4244-2405-4/08/$20.00 ©2008 IEEE
289
2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Abstract—This paper describes the reduction in torque ripple due to phase commutation of brushless dc motors. With two-phase 1200 electrical conduction for the inverter connected to the conventional three-phase BLDC machine, the commutation torque ripple occurs at every 60 electrical degrees when a change over from one phase to another occurs. This effect increases the commutation time at higher speeds which increases the torque ripple. The torque ripple is reduced by changing the switching mode from 1200 to a dual switching mode with 1200 switching at lower speeds and 1800 electrical for the inverter at higher speeds. KeywordsüBrushless dc motor, current commutation, torque ripple, electric vehicle.
I.
INTRODUCTION
The recent progress in the area of magnetic materials and power semiconductors has improved the performance of brushless dc motors significantly. Its advantages are high power to weight ratio, high torque to current ratio, high dynamics-flexible control for variable speed operation, reduced maintenance due to absence of mechanical commutators (brushless-type) etc. These features have made brushless dc motors to be one of the best choices to replace conventional brush-type dc motors for many high performance applications. Brushless dc motors, having trapezoidal back emf waveform, when fed with rectangular stator current produces theoretically constant torque. However, in practice, torque ripple may exist due to several reasons e.g. toque ripple due to cogging, e.m.f. waveform imperfections, supply current ripple resulting from PWM inverters and from phase current commutation. It is desirable to minimize the torque ripple in a brushless dc (BLDC) drive to remove unacceptable speed ripple, vibration and acoustic noise. Thus in the past one decade, research effort was on to reduce such undesirable torque ripple in the machine. The cogging torque attenuation is mainly achieved by slot skewing or by changing the magnet’s dimensions and positioning [1]. However, the torque ripple arising out from phase current commutation is one of the major problems for the BLDC drives. In [2], it was shown that the commutation torque ripple might reach 50% of the average torque, but it could be