目前，电动汽车实现了汽车能源动力的电气化，有效缓解了全球环境污染的现状，避免了燃油车成本强依赖于国际原油价格所带来的一系列问题。因此，电动汽车成为新能源汽车里发展较快且应用较广的一种新型汽车。无刷直流电机具有功率密度较大、效率高等优点，被广泛应用于电动汽车领域。本文以电动汽车用无刷直流电机为控制对象，对其制动工况下的一些关键问题进行了研究。
       首先，在无刷直流电机数学模型的基础上，分析对比了常用的制动方法及制动调制方式。论述了制动工况下电机产生换相转矩脉动的原因，推导了不同回馈制动调制方式下换相转矩脉动的统一数学表达式，并研究了不同调制方式对电机转矩脉动及回馈制动的影响，为寻求更优的 PWM调制方式提供了理论依据。PWM-OFF-PWM 方式不存在非导通相续流引起的非换相转矩脉动，能够更好地实现车辆回馈制动。但该方式在换相过程中存在转矩脉动，因此本文提出了一种改进型 PWM-OFF-PWM 方式。推导了换相与非换相区间功率管占空比的数学表达式，当关断相和开通相的占空比满足推导公式时，能够有效抑制换相转矩脉动，从而提高了电机运行的平稳性。
       其次，基于 PWM-OFF-PWM 调制方式研究了回馈制动的原理，并建立了无刷直流电机制动系统数学模型。分析比较了四种常用的电机回馈制动策略，恒值制动电流方法能使驾驶员有较为舒适的操纵感被广泛用于电动汽车领域。为了解决电动汽车系统参数易受干扰的问题，本文提出了基于滑模控制的恒值制动电流控制策略。该策略不仅可以回馈能量，还能够精确控制制动电流，从而增加了回馈制动的安全性与汽车的舒适性。
       再次，在MATLAB/Simulink环境中搭建了电动汽车用无刷直流电机的系统仿真模型，对本文选用的调制方式、所提出的抑制换相转矩脉动方法以及回馈制动控制策略进行了验证。通过比较 PWM-OFF 与 PWM-OFF-PWM 调制方式的电流波形，验证了后者不存在非导通相续流的现象。通过对比改进前后 PWM-OFF-PWM 方法在换相区间内非换相电流及转矩的波动情况，验证了所提抑制方法的有效性。通过比较回馈制动与自然停机两种制动方式，验证了电动汽车搭载回馈制动系统能够实现能量的回收；通过比较传统 PID与滑模控制的电流波形，验证了本文控制策略具有更好的稳定性和动态响应速度。
       最后，根据控制系统的功能需求，对其硬件电路与软件程序进行了设计。搭建了电动车回馈制动控制系统实验平台，对本文提出的抑制换相转矩脉动方法以及恒值制动电流策略进行了验证。实验结果与理论分析及仿真结果一致，进一步证明了所提方法的正确性与有效性。

At present, electric vehicles have realized the electrification of vehicle energy and power,effectively alleviating the status quo of global environmental pollution, and avoiding a series of problems caused by the strong dependence of the cost of fuel vehicles on international crude oil prices. Therefore, electric vehicles have become a new type of vehicle that has developed rapidly and is widely used in new energy vehicles. Brushless DC motors have the advantages of high power output and high efficiency, and are widely used in the field of electric vehicles. This article focuses on brushless DC motors for electric vehicles and explores some of the important issues related to their braking conditions.
Firstly, based on the mathematical model of brushless DC motor, the commonly used braking methods and braking modulation methods are analyzed and compared. The reasons for the commutation torque ripple of the motor under braking conditions are discussed, the unified mathematical expression of the commutation torque ripple under different regenerative braking
modulation methods is deduced, and the effects of different modulation methods on the motor torque ripple and feedback are studied. The influence of braking provides a theoretical basis for
seeking a better PWM modulation method. The PWM-OFF-PWM method does not have the non-commutation torque ripple caused by the non-conductive freewheeling, which can better realize the vehicle regenerative braking. However, this method has torque ripple during the commutation process, this paper proposes an improved PWM-OFF-PWM method. The formulas of the duty cycle of switching tube in the commutation period and that during
non-commutation period is derived. When the duty cycle of the outgoing and incoming phases meets the derivation formula, the commutation torque ripple can be effectively suppressed, so
as to improve the stability of the motor operation.
Secondly, the principle of feedback braking is studied based on PWM-OFF-PWM modulation, and the mathematical model of Brushless DC motor braking system is established. Four common motor feedback braking strategies are analyzed and compared. The constant value braking current method can make the driver have a more comfortable control feeling and is widely used in the field of electric vehicles. In order to solve the problem that electric vehicle system parameters are easily disturbed, a constant braking current control strategy based on sliding mode control is proposed in this paper. This strategy can not only regenerate energy, but also precisely control the braking current, thereby increasing the safety of regenerative braking and the comfort of the car.
Then, the system simulation model of the brushless DC motor for electric vehicles is built in the MATLAB/Simulink environment, and the modulation method selected in this paper, the proposed method to suppress the commutation torque ripple and the regenerative braking control strategy are verified. By comparing the current waveforms of PWM-OFF and PWM-OFF-PWM modulation, it is verified that there is no non-conducting phase freewheeling in the latter. By comparing the fluctuations of the non-commutation current and torque in the commutation interval of the PWM-OFF-PWM method before and after the improvement, the effectiveness of the proposed suppression method is verified. By comparing the two braking methods of regenerative braking and natural stop, it is verified that the electric vehicle equipped with regenerative braking system can realize energy recovery. By comparing the current waveforms of traditional PID and sliding mode control, it is verified that the control strategy in this paper has better stability and dynamic response speed.
Finally, according to the functional requirements of the control system, its hardware circuit and software program are designed. An experimental platform for the regenerative braking control system for electric vehicles is built, and the method of suppressing commutation torque ripple and the strategy of constant braking current proposed in this paper are verified from different aspects. The experimental results are consistent with the theoretical analysis and simulation results, which prove the correctness and effectiveness of the method.

[1] Mutoh N, Hayano Y, Yahagi H, et al. Electric braking control methods for electric vehicles with independently driven front and rear wheels[J]. IEEE Transactions on Industrial Electronics, 2007, 54(2): 1168-1176.

[2] 张丽, 朱孝勇, 左月飞. 电动汽车用转子永磁型无刷电机与控制系统容错技术综述[J]. 中国电机工程学报, 1875, 39(6): 1792-1802.

[3] 宋哲, 王友仁, 鲁世红, 等. 一种电动车用无刷直流电机混合回馈制动控制方法[J]. 电工技术学报, 2016, 31(6): 74-80.

[4] Palmer C. 电动汽车市场加速发展[J]. Engineering, 2021, 7(2): 13-18.

[5] 谭建成. 永磁无刷直流电机技术[M]. 机械工业出版社, 2018.

[6] 曲荣海, 秦川. 电动汽车及其驱动电机发展现状与展望[J]. 南方电网技术, 2016, 10(3): 82-86.

[7] 陈真. 永磁无刷直流电机转矩脉动抑制方法研究[D]. 东北大学, 2015.

[8] 王大方, 卜德明, 朱成, 等. 一种减小无刷直流电机换相转矩脉调制方法[J]. 电工技术学报, 2014, 29(5): 160-166.

[9] Lin Y K, Lai Y S. Pulsewidth modulation technique for BLDCM drives to reduce commutation torque ripple without calculation of commutation time[J]. IEEE Transactions on Industry Applications, 2011, 47(4): 1786-1793.

[10] Xia K, Ye Y, Ni J, et al. Model predictive control method of torque ripple reduction for BLDC motor[J]. IEEE Transactions on Magnetics, 2019, 56(1): 1-6.

[11] Xia C, Wang Y, Shi T. Implementation of finite-state model predictive control for commutation torque ripple minimization of permanent-magnet brushless DC motor[J]. IEEE Transactions on Industrial Electronics, 2012, 60(3): 896-905.

[12] 王培侠, 姜卫东, 王金平, 等. 基于电流滞环控制的无刷直流电机多状态换相转矩脉动抑制方法[J]. 电工技术学报, 2018, 33(22): 5261-5272.

[13] Jiang W, Wang P, Ni Y, et al. Multimode current hysteresis control for brushless DC motor in motor and generator state with commutation torque ripple reduction[J]. IEEE Transactions on Industrial Electronics, 2017, 65(4): 2975-2985.

[14] 盛田田, 王晓琳, 顾聪, 等. 一种使用重叠换相法的无刷直流电机平均转矩控制[J]. 中国电机工程学报, 2015, 35(15): 3939-3947.

[15] 陈健, 于慎波. 一种减小无刷直流电动机噪声的 PWM 调制方法[J]. 电工技术学报, 2016, 31(9): 129-136.

[16] 王大方, 朱洪彪, 金毅, 等. 抑制 BLDCM 换相转矩脉动的超前换相控制策略[J]. 电机与控制学报, 2018, 22(10): 77-86.

[17] Lin Y K, Lai Y S. Pulsewidth modulation technique for BLDCM drives to reduce commutation torque ripple without calculation of commutation time[J]. IEEE Transactions on Industry Applications, 2011, 47(4): 1786-1793.

[18] 殷帅, 吕彩琴, 马铁华. 抑制无刷直流电机换相转矩脉动的新型电流控制[J]. 电机与控制学报, 2015, 19(8): 47-52.

[19] 夏鲲, 董斌, 卢晶. 一种基于电流反馈的分段式 PWM 控制无刷直流电机转矩波动抑制方法[J]. 电工技术学报, 2017, 32(17): 172-179.

[20] 李珍国, 王江浩, 高雪飞, 等. 一种合成电流控制的无刷直流电机转矩脉动抑制系统[J]. 中国电机工程学报, 2015, 35(21): 5592-5599.

[21] 夏鲲, 朱琳玲, 曾彦能, 等. 基于准 Z 源网络的永磁无刷直流电机换相转矩脉动抑制方法[J]. 中国电机工程学报, 2015, 35(4): 971-978.

[22] Li X, Xia C, Cao Y, et al. Commutation torque ripple reduction strategy of Z-source inverter fed brushless DC motor[J]. IEEE Transactions on Power Electronics, 2016, 31(11): 7677-7690.

[23] Viswanathan V, Jeevananthan S. Approach for torque ripple reduction for brushless DC motor based on three-level neutral-point-clamped inverter with DC–DC converter[J]. IET Power Electronics, 2015, 8(1): 47-55.

[24] Chen W, Liu Y, Li X, et al. A novel method of reducing commutation torque ripple for brushless DC motor based on Cuk converter[J]. IEEE Transactions on Power Electronics, 2016, 32(7): 5497-5508.

[25] Yao X, Zhao J, Wang J, et al. Commutation torque ripple reduction for brushless DC motor based on an auxiliary step-up circuit[J]. IEEE Access, 2019, 7: 138721-138731.

[26] Viswanathan V, Seenithangom J. Commutation torque ripple reduction in the BLDC motor using modified SEPIC and three-level NPC inverter[J]. IEEE Transactions on Power Electronics, 2017, 33(1): 535-546.

[27] 曹彦飞, 陆海天, 李新旻, 等. 基于无电感升压拓扑的无刷直流电机电流控制策略[J]. 电工技术学报, 36(6): 1249-1258.

[28] 朱俊杰, 刘浩然, 蒋峰, 等. 无刷直流电机转矩脉动抑制系统的新型拓扑研究[J]. 电工技术学报, 2018, 33(17): 4060-4068.

[29] 姚绪梁, 赵继成, 王景芳, 等. 一种基于辅助升压前端的无刷直流电机换相转矩脉动抑制方法研究[J]. 中国电机工程学报, 2020, 40(9): 3021-3031.

[30] Shi T, Guo Y, Song P, 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, 2009, 57(10): 3483-3490.

[31] 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.

[32] Shi T, Cao Y, Jiang G, et al. A torque control strategy for torque ripple reduction of brushless DC motor with nonideal back electromotive force[J]. IEEE Transactions on Industrial Electronics, 2017, 64(6): 4423-4433.

[33] 徐会风, 苏少平, 杜庆诚. 一种新型零矢量的二三导通无刷直流电机直接转矩控制系统研究[J]. 西安交通大学学报, 2020, 54(4): 85-92.

[34] 陆可, 蔡广瀚, 向南辉, 等. 基于电压矢量注入的无刷直流电机换相转矩脉动抑制方法[J]. 中国电机工程学报, 2021, 41(10): 3592-3601.

[35] Sheng T, Wang X, Zhang J, et al. Torque-ripple mitigation for brushless DC machine drive system using one-cycle average torque control[J]. IEEE Transactions on Industrial Electronics, 2014, 62(4): 2114-2122.

[36] 李珍国, 孙启航, 王鹏磊, 等. 基于转子永磁体磁场定向的无刷直流电机转矩脉动抑制[J]. 电工技术学报, 2020, 35(14): 2987-2996.

[37] Sakai A. Toyota braking system for hybrid vehicle with regenerative system[J]. EVS-13, 1997: 231-234.

[38] Ogura M, Aoki Y, Mathison S. The Honda EV PLUS regenerative braking system[C]// Proceeding of the 14th International Electric Vehicle Symposium. 1997.

[39] Yuan Y, Zhang J, Lv C, et al. Design and performance analysis of a novel regenerative braking system for electrified passenger vehicles[J]. SAE International Journal of Materials and Manufacturing, 2016, 9(3): 699-706.

[40] 潘铮. 分布式驱动电动汽车电液混合制动自适应分频控制研究[D]. 上海交通大学, 2020.

[41] 熊觉振. 复合电源纯电动汽车再生制动控制策略研究[D]. 湖南大学, 2020.

[42] Long B, Lim S T, Ryu J H, et al. Energy-regenerative braking control of electric vehicles using three-phase brushless direct-current motors[J]. Energies, 2013, 7(1): 99-114.

[43] 朱飞白. 电液制动系统能量回收控制策略研究[D]. 吉林大学, 2020.

[44] 曾小华, 陈虹旭, 宋大凤, 等. 基于电机最优回馈转矩曲线的制动控制策略[J]. 汽车工程, 2021, 43(2): 162-170.

[45] 曹彦飞. 永磁无刷直流电机转矩控制策略研究[D]. 天津大学, 2019.

[46] 贾喆武, 张庆湖, 王东. 环形绕组无刷直流电机的四象限运行分析[J]. 电工技术学报, 2020, 35(18): 3821-3829.

[47] 边春元, 段鹏飞, 肖鸿权, 等. 一种用于无刷直流电机回馈制动的 PWM 调制方式[J]. 中国电机工程学报, 2019, 39(17): 5247-5256.

[48] 胡庆波, 郑继文, 吕征宇. 混合动力中无刷直流电机反接制动 PWM 调制方式的研究[J]. 中国电机工程学报, 2007, 27(30): 87-91.

[49] 宋哲, 王友仁, 鲁世红, 等. 一种电动车用无刷直流电机混合回馈制动控制方法[J]. 电工技术学报, 2016, 31(6): 74-80.

[50] 韩晨阳. 无刷直流电机制动调制方式的转矩脉动特性研究[D]. 西安科技大学, 2020.

[51] 段鹏飞. 无刷直流电机回馈制动控制系统的研究与设计[D]. 东北大学, 2017.

[52] 傅涛. 电动汽车用大功率无刷直流电机控制关键技术研究[D]. 天津大学, 2016.

[53] 李竟成. 电动汽车驱动控制与再生制动研究[D].西安交通大学, 2003.

[54] 黄斐梨, 王耀明, 姜新建, 等. 电动汽车永磁无刷直流电机驱动系统低速能量回馈制动的研究[J]. 电工技术学报, 1995 (3): 28-31.

[55] 赵辉, 李铁才, 孙立志, 等. 电池供电的永磁电动机系统的再生制动[J]. 电机与控制学报, 1999, 3(4): 207-210.

[56] 王晓远, 傅涛. 基于模型预测控制策略的电动车用无刷直流电机回馈制动的研究[J]. 电工技术学报, 2017, 32(9): 16-23.

[57] 陈志梅. 滑模变结构控制理论及应用[M]. 电子工业出版社, 2012.

[58] Hong-xing W, Shu-Kang C, Shu-mei C. A controller of brushless DC motor for electric vehicle[C]//2004 12th Symposium on Electromagnetic Launch Technology. IEEE, 2004: 528-533.

[59] Emadi A. Modeling and analysis of multiconverter DC power electronic systems using the generalized state-space averaging method[J]. IEEE Transactions on Industrial Electronics, 2004, 51(3): 661-668.

[60] Mattavelli P, Rossetto L, Spiazzi G. Small-signal analysis of DC-DC converters with sliding mode control[J]. IEEE Transactions on Power Electronics, 1997, 12(1): 96-102.

[61] Wang Y, Zhang X, Yuan X, et al. Position-sensorless hybrid sliding-mode control of electric vehicles with brushless DC motor[J]. IEEE Transactions on Vehicular Technology, 2010, 60(2): 421-432.