文章快速检索 高级检索

Torque ripple reduction strategy for magnet suspended reactive flywheel brushless DC motor
TANG Jiqiang , WANG Yingxu , ZHOU Xinxiu
School of Instrumentation Science & Opto-electronics Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2015-07-06; Accepted: 2015-08-26; Published online: 2015-10-19 15:20
Foundation item: National Natural Science Foundation of China (61174003, 61473018, 61403015)
Corresponding author. Tel.: 010-82339273 E-mail: tjq_72@163.com
Abstract: Due to its high torque response speed, direct torque control (DTC) without flux feedback makes the torque ripple reduction of magnet suspended reactive flywheel (MSRF) brushless DC motor (BLDCM) possible, which has a small inductance. However, the bang-bang controller of the DTC causes high torque ripples. To solve this problem, the mathematic models of commutation and diode freewheeling of the inactive phase were established and the relationship between torque and phase current was obtained.Then a torque prediction method based on the established models was proposed to reduce the torque ripple effectively, and the stability and robustness were proved. While estimating the back electromotive force of the BLDCM with sliding mode observer (SMO), a smooth and continuous function with one parameter was employed to replace the sign function which leads to a higher back electromotive force estimation accuracy. Simulation and experimental results show that compared to the traditional DTC, the advanced torque control method with torque prediction and advanced SMO can significantly suppress the torque ripples and has almost the same torque response speed.
Key words: magnet suspended reactive flywheel (MSRF)     brushless DC motor (BLDCM)     torque ripple     torque prediction     sliding mode observer (SMO)     chattering

1 无刷直流电机的数学模型 1.1 基本数学模型

 图 1 无刷直流电机等效模型及驱动模型 Fig. 1 Equivalent model of BLDCM and inverter model

 (1)

1.2 绕组不同导通状态下数学模型

MSRF无刷直流电机在运行过程中，造成电机输出力矩脉动的因素主要有：① 换相；② 非导通相续流；③ 三相绕组反电动势不是标准梯形波；④ 其他因素。前2种因素能够引起转矩脉动，是因为电机导通状态发生变化。由于MSRF无刷直流电机结构经过设计，其磁密均匀而且转速一般不高，可在建立数学模型时不考虑非理想梯形波的影响。下面对无刷直流电机正常运行状态、换相状态和非导通相续流状态进行数学建模。

1.2.1 正常运行状态

 (1)

 (2)

1.2.2 换相状态

 图 2 AB→AC、AC→BC换相过程无刷直流电机等效电路 Fig. 2 Equivalent circuits of BLDCM in commutation period of AB→AC，AC→BC

 (3)

 (4)

 (2)

 (5)

1.2.3 非导通相续流状态

 图 3 不同非导通相续流情况下无刷直流电机等效电路 Fig. 3 Equivalent circuits of BLDCM with diode freewheeling of different inactive phases

 (3)
 (4)

2 改进型滑模观测器

 (5)

 (6)

 (7)

 (8)

 (6)

h(t)波形如图 4所示。可知，函数h(t)为奇函数，且t>0时，h(t)>0,t<0时，h(t)<0。此特点与符号函数类似，将符号函数替换为h(t)函数后依旧会使滑模观测器具有状态切换功能。函数h(t)有1个参数，可以根据系统需求调节λ的大小。h(t)函数在t=0处收敛至0。在系统状态进入滑模区域后，相当于减小了滑模观测器的滑模增益，减小抖振现象。

 图 4 h(t)波形(λ=1) Fig. 4 Waveform of h(t) (λ=1)

 (9)

 (7)

 (10)

 (8)

 (11)

h(t)与t符号相同，且h(t)<1。只需保证：

 (12)

 (13)

 (9)

 (10)

 (14)

3 转矩控制器 3.1 基于转矩预测的转矩控制器设计

 (15)
 (16)

Te(k+1)=Te*Te*为参考转矩。即使每个下一时刻期望转矩均为参考力矩，有

 (17)

 图 5 实际应用的无刷直流电机驱动等效电路 Fig. 5 Actual used equivalent circuit of inverter of BLDCM
3.2 控制器稳定性和鲁棒性

 (18)

 (19)

 (11)

 (12)

 (20)

 (13)

4 总体控制方案

 图 6 改进转矩控制方法的结构框图 Fig. 6 Control framework of advanced torque control method
5 仿真和实验验证 5.1 仿真验证

 图 7 400 r/min与800 r/min指令转速下绕组反电动势估计误差仿真结果 Fig. 7 Simulation results of back-EMF estimation error under command speeds of 400 r/min and 800 r/min

 图 8 指令转速为400 r/min时转矩仿真结果 Fig. 8 Simulation results of torque under command speed of 400 r/min

 图 9 单位周期内2种方法转矩结果与输出电压对比 Fig. 9 Comparison of torque and ouput voltage in one unit cycle between two methods

 图 10 指令转速为800 r/min时转矩仿真结果 Fig. 10 Simulation results of torque under command speed of 800 r/min

 图 11 改进方法转矩和控制器输出电压波形 Fig. 11 Torque and output voltage waveform of controller by advanced methool

 图 12 负载突变时转矩响应仿真结果 Fig. 12 Simulation results of torque response with step load
5.2 实验验证

 图 13 传统和改进滑模观测器的iβ跟踪结果 Fig. 13 Tracking results of iβ by traditional and advanced SMOs
 图 14 传统和改进滑模观测器对eβ的估计结果 Fig. 14 Estimation results of eβ by traditional and advanced SMOs

 图 15 传统DTC方法和改进方法转矩实验波形 Fig. 15 Tow experimental curves of troque by traditional DTC method and advanced method

 图 16 实验条件下负载突变时转矩响应曲线 Fig. 16 Response curves of torque under mutation loads in the condition of experiment

6 结 论

1) 改进滑模观测器能够有效抑制系统抖振，提高了绕组反电动势和转矩的估计精度。

2) 基于改进型滑模观测器和转矩预测相结合的改进转矩控制方法能够有效抑制MSRF无刷直流电机运行过程中的转矩脉动，提高了输出力矩的稳定性。

 [1] 巫庆辉, 邵诚, 徐占国. 直接转矩控制技术的研究现状与发展趋势[J]. 信息与控制, 2005, 34 (4) : 444 –450. WU Q H, SHAO C, XU Z G. Survey of research status quo and development trends about direct torque control[J]. Information and Control, 2005, 34 (4) : 444 –450. (in Chinese) [2] 王志强, 赵波, 周新秀. 反作用飞轮电机换相转矩脉动分析[J]. 微特电机, 2010, 38 (10) : 1 –4. WANG Z Q, ZHAO B, ZHOU X X. Commutation torque ripple analysis of brushless DC motor for reaction flywheels[J]. Small & Spacial Electrical Machines, 2010, 38 (10) : 1 –4. (in Chinese) [3] YOSHIDA M, MURAI Y, TAKADA M. Noise reduction by torque ripple suppression in brushless DC motor[C]//29th Annual IEEE Power Eletrionics Specialist Conference. Piscataway, NJ: IEEE Press, 1998, 2: 1397-1401. [4] KIM G H, KANG S J, WON J S. Analysis of the commutation torque ripple effect for BLDCM fed by HCRPWMVSI[C]//7th Annual Applied Power Electronics Conference and Exposition. Piscataway, NJ: IEEE Press, 1992: 277-284. [5] 杨进, 杨向宇. 一种减小无刷直流电机纹波转矩的新方法[J]. 微电机, 2005, 38 (1) : 9 –11. YANG J, YANG X Y. The application of tysteresis control in reducing ripple torque of brushless DC motor[J]. Micromotors, 2005, 38 (1) : 9 –11. (in Chinese) [6] 林平, 韦鲲, 张仲超. 新型无刷直流电机换相转矩脉动抑制控制方法[J]. 中国电机工程学报, 2006, 26 (3) : 153 –158. LIN P, WEI K, ZHANG Z C. A novel control scheme to suppress the commutation torque ripple in BLDCM[J]. Proceedings of the CSEE, 2006, 26 (3) : 153 –158. (in Chinese) [7] SONG J H, CHOY I. Commutation torque ripple reduction in brushless DC motor drives using a single DC current sensor[J]. IEEE Transactions on Power Electronics, 2004, 19 (2) : 312 –319. DOI:10.1109/TPEL.2003.823177 [8] 任军军. 永磁无刷直流电机的转矩脉动抑制的控制策略研究[D]. 杭州: 浙江大学, 2004. REN J J. Research on torque ripple minimization techniques for PM brushless DC motor[D]. Hangzhou: Zhejiang University, 2004(in Chinese). http://cdmd.cnki.com.cn/Article/CDMD-10613-1013106653.htm [9] 陈冬, 房建成. 非理想梯形波反电动势永磁无刷直流电机换相转矩抑制方法[J]. 中国电机工程学报, 2008, 28 (30) : 79 –83. CHEN D, FANG J C. Commutation torque ripple reduction in PM brushless DC motor with nonideal trapezoidal back EMF[J]. Proceedings of the CSEE, 2008, 28 (30) : 79 –83. (in Chinese) [10] 郭方正, 韩邦成, 刘刚. PAM调制方式下高速无刷直流电机非导通相续流抑制方法研究[J]. 微电机, 2009, 42 (8) : 42 –46. GUO F Z, HAN B C, LIU G. Research on suppression for diode freewheeling of inactive phase in high-speed BLDCM using PAM strategy[J]. Micromotors, 2009, 42 (8) : 42 –46. (in Chinese) [11] OZTURK S B, TOLIYAT H A. Direct torque control of brushless DC motor with non-sinusoidal back-EMF[C]//IEEE IEMDC 2007: Proceedings of the International Electric Machines and Drives Conference. Piscataway, NJ: IEEE Press, 2007. [12] 林海, 梁中, 闫茂德, 等. 无刷直流电机改进型直接转矩控制研究[J]. 电气传动, 2014, 44 (8) : 11 –14. LIN H, LIANG Z, YAN M D, et al. Improved direct torque control in brushless DC motor drives[J]. Electric Drive, 2014, 44 (8) : 11 –14. (in Chinese) [13] 安群涛, 孙立志, 刘超, 等. 无刷直流电机的磁链自控直接转矩控制[J]. 中国电机工程学报, 2010, 30 (12) : 86 –92. AN Q T, SUN L Z, LIU C, et al. Flux linkage self-control based direct torque control of brushless DC motor[J]. Proceedings of the CSEE, 2010, 30 (12) : 86 –92. (in Chinese) [14] 朱俊杰, 粟梅, 王湘中, 等. 分段式滑模变结构无刷直流电机直接转矩控制[J]. 仪器仪表学报, 2013, 34 (11) : 2634 –2640. ZHU J J, SU M, WANG X Z, et al. Direct-torque-control of brushless DC motors based on segmented sliding-mode-variable-structure[J]. Chinese Journal of Scientific Instrument, 2013, 34 (11) : 2634 –2640. (in Chinese) [15] 郭鸿浩, 周波, 左广杰, 等. 无刷直流电机反电势自适应滑模观测[J]. 中国电机工程学报, 2011, 31 (21) : 142 –149. GUO H H, ZHOU B, ZUO G J, et al. Adaptive sliding-mode observer for back electromotive force estimation of brushless DC motor[J]. Proceedings of the CSEE, 2011, 31 (21) : 142 –149. (in Chinese) [16] 郭鸿浩, 周波, 左广杰, 等. 无刷直流电机转矩观测与电感自适应辨识[J]. 中国电机工程学报, 2011, 31 (33) : 151 –158. GUO H H, ZHOU B, ZUO G J, et al. Torque estimation and adaptive inductance identication for brushless DC motor[J]. Proceedings of the CSEE, 2011, 31 (33) : 151 –158. (in Chinese) [17] 周衍, 张兴华. 一种简易的无刷直流电动机直接转矩控制[J]. 微特电机, 2014, 42 (7) : 54 –60. ZHOU Y, ZHANG X H. A kind of simplified direct torque control for brushless DC motor[J]. Small & Spacial Electrical Machines, 2014, 42 (7) : 54 –60. (in Chinese) [18] 李珍国, 章松发, 周生海, 等. 考虑转矩脉动最小化的无刷直流电机直接转矩控制系统[J]. 电工技术学报, 2014, 29 (1) : 139 –146. LI Z G, ZHANG S F, ZHOU S H, et al. Direct torque control of brushless DC motor considering torque ripple minimization[J]. Transaction of China Electrotechnical Sociaty, 2014, 29 (1) : 139 –146. (in Chinese) [19] 王晓远, 田亮, 冯华. 无刷直流电机直接转矩模糊控制研究[J]. 中国电机工程学报, 2006, 26 (15) : 134 –138. WANG X Y, TIAN L, FENG H. Study of the fuzzy control on direct torque control for brushless BLDCM[J]. Proceedings of the CSEE, 2006, 26 (15) : 134 –138. (in Chinese) [20] 许鹏, 郭桂芳, 曹军义, 等. 直流无刷电机神经网络直接转矩控制[J]. 中国电机工程学报, 2009, 29 (Suppl.) : 192 –196. XU P, GUO G F, CAO J Y, et al. Neural network control on direct torque control for brushless DC motor[J]. Proceedings of the CSEE, 2009, 29 (Suppl.) : 192 –196. (in Chinese)

#### 文章信息

TANG Jiqiang, WANG Yingxu, ZHOU Xinxiu

Torque ripple reduction strategy for magnet suspended reactive flywheel brushless DC motor

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(7): 1377-1387
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0451