A Review on Optimal Control Strategies for Magnetic Field-modulated Fractional-slot Permanent Magnet Motors in Autonomous Underwater Vehicle

doi:10.12382/bgxb.2025.0649

Abstract

Abstract:

Magnetic field-modulated fractional-slot permanent magnet motor utilizes the magnetic field modulation effect to eliminate the need for the gearbox structure in traditional electric propulsion system，which simplifies the electric propulsion system architecture and reduces mechanical noise.Furthermore，magnetic field -modulated fractional-slot permanent magnet motor is particularly suitable for the electric propulsion of AUVs due to their high power density and high torque density.Magnetic field -modulated fractional-slot permanent magnet motor can utilize multiple harmonic components of the excitation magnetic flux density to work cooperatively，significantly enhancing the motor’s torque density.However，this type of motor simultaneously modulates certain low-order harmonic components of the armature magnetic flux density.This leads to the issues such as low power factor，high harmonic losses，and significant torque ripple in magnetic field-modulated motors，negatively impacting the stealth capabilities and operational efficiency of AUVs.This paper focuses on the control strategies for torque ripple suppression，power factor improvement，and efficiency optimization from the perspective of motor optimization control.Finally，the current state of technology regarding the application of such motors in new energy power generation is summarized，marine propulsion，and electric vehicles，followed by a discussion on the key technologies and future development directions for their application in AUVs.

Key words: autonomous underwater vehicle, flux modulation effect, fractional slot, harmonic suppression, optimized control

YAO Yujie, QIAO Mingzhong, WU Bo, SUN Lucheng, WANG Kangning. A Review on Optimal Control Strategies for Magnetic Field-modulated Fractional-slot Permanent Magnet Motors in Autonomous Underwater Vehicle[J]. Acta Armamentarii, 2025, 46(S1): 250649-.

Figures/Tables 25

Table 1 Performance comparison table between permanent magnet motor and magnetic field modulation motor

电机类型	功率密度	效率	振动噪声
永磁电机	较高	全工况较高	较高
磁场调制永磁电机	高	宽转速范围高	低

Fig.1 Schematic diagram of AUV electric propulsion system

Table 2 Performance comparison table between FOC and DTC

控制策略	转矩动态响应	转矩脉动
FOC	较快	小
DTC	快	大

Fig.2 Classification diagram of torque ripple optimized control

Fig.3 Design block diagram of cascaded PIR controllers for current and speed loops

Fig.4 Multilayer architecture diagram of model predictive control for PMSM servo systems

Fig.5 Schematic diagram of model predictive control

Fig.6 Taxonomy of harmonic-oriented torque ripple suppression control techniques

Fig.7 Back-EMF waveforms and FFT analysis of phase A+/A- in hybrid-excited permanent magnet vernier motor

Fig.8 Control structure of harmonic current suppression with active compensation for HE-VPM drives

Fig.9 Harmonic injection current control flowchart

Fig.10 Modulated motor speed regulation system with active disturbance rejection iterative learning control

Fig.11 Block diagram of ILC-ADRC strategy

Table 3 Torque ripple optimization control strategy performance comparison table

特征	方法
特征	转矩补偿法	谐波优化控制	自抗扰迭代学习控制
动态响应速度	快	中	慢
复杂度	中等	高	高
参数敏感性	高	中	高
优点	实时性强，实现简单	针对性强，谐波抑制效果显著	抗干扰能力强，精度高
缺点	依赖模型和观测器，鲁棒性低	依赖模型和观测器，鲁棒性低	需要多次迭代，存储和计算资源需求高
适用场景	工业伺服系统、电动汽车驱动等实时性要求高的场合	PMSM的齿槽转矩抑制、电力推进系统的低谐波控制等	机械臂驱动、高精度转台等控制精度要求高的场景

Fig.12 Block diagram of ILC-ADRC strategy

Fig.13 Block diagram of field-weakening control with unity power factor

Fig.14 Topology of a magnetic-field-modulated linear permanent magnet motor system based on flying-capacitor open-winding

Fig.15 Classification of efficiency-optimized control strategies for electric motors

Fig.16 Block diagram of MTPA vector control system

Fig.17 Block diagram of the efficiency-optimized control system based on loss model for magnetically modulated permanent magnet motors

Fig.18 Block diagram of online search control based on minimum loss model

Table 4 Comparison of efficiency-optimized control algorithms for electric motors

性能	算法
性能	MTPA	LMC	搜索控制
精度受模型影响度	高	高	低
对参数依赖度	低	高	低
算法复杂度	简单	复杂	复杂
优点	有效降低铜耗	全局效率优化	全局效率优化
缺点	部分效率优化	参数依赖度高	仅适用于稳态

Fig.19 Grid-side wind power control system

Fig.20 Internal structure diagram of a magnetically modulated in-wheel motor

Fig.21 Actual product photo of a magnetically modulated in-wheel motor

References 87

[1]	王来贺, 崔雪静. 海上无人化试验训练体系构建问题研究[J]. 兵工学报, 2024, 45(10):3445-3461. doi: 10.12382/bgxb.2023.0633
	WANG H L, CUN X J. On the construction of marine unmanned test and training system[J]. Acta Armamentarii, 2024, 45(10):3445-3461. (in Chinese) doi: 10.12382/bgxb.2023.0633
[2]	朱炜, 张大中, 孙明月. 国外超大型无人潜航器发展研究[J]. 舰船科学技术, 2024, 46(24):186-189.
	ZHU W, ZHANG D Z, SUN M Y. Research on the development of foreign extra large unmanned underwater vehicles[J]. Ship Science and Technology, 2024, 46(24):186-189. (in Chinese)
[3]	陈昭, 丁一杰, 张治强. 无人潜航器发展历程及运用优势研究[J]. 舰船科学技术, 2024, 46(23):98-102.
	CHEN Z, DING Y J, ZHANG Z Q. Research on the development history and application advantages of unmanned underwater vehicle[J]. Ship Science and Technology, 2024, 46(23):98-102. (in Chinese)
[4]	陈建勇, 陈亚杰, 高海波, 等. 新型绿色船舶电力推进系统关键技术及应用分析[J]. 船海工程, 2023, 52(6):1-7.
	CHEN J Y, CHEN Y J,GAO, H B, et al. Analysis of the key technologies and application for new green ship propulsion systems[J]. Ship & Ocean Engineering, 2023, 52(6):1-7. (in Chinese)
[5]	白刚. 无轴推进电机技术应用研究[J]. 山东工业技术, 2018(15):4.
	BAI G. Shaftless propulsion motor technology application[J]. Shandong Industrial Technology, 2018(15):4. (in Chinese)
[6]	许家群. 水下机器人永磁推进系统技术概况[J]. 机器人产业, 2021(4):58-63.
	XU J Q. Technical overview of underwater robot permanent magnet propulsion system[J]. Robot Industry, 2021(4):58-63. (in Chinese)
[7]	刘先越, 胡静, 吴晓阳, 等. 基于舰艇电力推进系统的永磁同步电机控制策略研究[J]. 江苏科技大学学报(自然科学版), 2023, 37(2):75-81.
	LIU X Y, HU J, WU X Y, et al. Research on control strategy of permanent magnets synchronous motor based on ship electric propulsion system[J]. Journal of Jiangsu University of Science and Technology(Natural Science Edition), 2023, 37(2):75-81. (in Chinese)
[8]	施伟锋, 朱倍志, 谢嘉令. 基于PSO-RBF优化的船舶六相推进电机缺相故障新型自适应滑模容错控制研究[J]. 重庆交通大学学报(自然科学版), 2023, 42(11):141-148,156.
	SHI W F, ZHU B Z, XIE J L. New adaptive sliding mode fault-tolerant control for phase failure of marine six phase propulsion motor based on PSO-RBF optimization[J]. Journal of Chongqing Jiaotong University (Natural Sciences), 2023, 42(11):141-148,156. (in Chinese)
[9]	杨怀诚, 钱树发, 郭伟, 等. 基于改进高频注入永磁推进电机控制方法研究[J]. 现代信息科技, 2025, 9(11):15-19.
	YANG H C, QIAN S F, GUO W, et al. Research on control method of permanent magnet propulsion motor based on improved high frequency injection[J]. Modern Information Technology, 2025, 9(11):15-19. (in Chinese)
[10]	胡庆南, 黄千稳. 船用永磁同步电机预定义时间滑模控制[J]. 舰船科学技术, 2025, 47(11):94-100.
	HU Q N, HUANG Q W. Predefined time sliding mode control of marine permanent magnet synchronous motor[J]. Ship Science and Technology, 2025, 47(11):94-100. (in Chinese)
[11]	冯纪超. 双三相永磁同步电机多重随机化高频振动抑制策略研究[D]. 镇江: 江苏大学, 2024.
	FENG J C. Research on multi-randomized high-frequency vibration suppression strategies for dual three-phase permanent magnet synchronous motors[D]. Zhenjiang: Jiangsu University, 2024. (in Chinese)
[12]	汤昊岳. 双三相永磁同步电动机及其驱动系统关键技术的研究[D]. 北京: 北京交通大学, 2023.
	TANG H Y. Research on key techniques of dual three-phase permanent magnet synchronous motor and its drive system[D]. Beijing: Beijing Jiaotong University, 2023. (in Chinese)
[13]	曹福强. 水下推进用双三相永磁同步电机驱动系统研究[D]. 哈尔滨: 哈尔滨工业大学, 2023.
	CAO F Q. Research on dual three-phase permanent magnet synchronous motor drive system for under water propulsion[D]. Harbin: Harbin Institute of Technology, 2023. (in Chinese)
[14]	柳超, 王善铭, 洪剑锋. 双三相永磁电机电磁振动分析[J]. 数字海洋与水下攻防, 2025, 8(1):36-46.
	LIU C, WANG S M, HONG J F. Electromagnetic vibration analysis of dual three-phase permanent magnet motor[J]. Digital Ocean & Underwater Warfare, 2025, 8(1):36-46. (in Chinese)
[15]	郭军, 肖峰, 郭宇峰, 等. 基于遗传算法的水下永磁无刷直流电机优化设计[J]. 现代制造技术与装备, 2025, 61(3):55-57,64.
	GUO J, XIAO F, GUO Y F, et al. Optimization design of underwater permanent magnet brushless direct current motor based on genetic algorithm[J]. Modern Manufacturing Technology and Equipment, 2025, 61(3):55-57,64. (in Chinese)
[16]	张新宇, 高良超, 南盟, 等. 电力推进永磁同步电机的无传感器控制研究[J]. 微特电机, 2024, 52(11):60-65.
	ZHANG X Y, GAO L C, NAN M, et al. Research on sensorless control of permanent magnet synchronous motor for electric propulsion[J], Small & Special Electrical Machines, 2024, 52(11):60-65. (in Chinese)
[17]	李盛雄, 刘明. 功率限制策略在船舶电力推进系统中的应用[J]. 船电技术, 2025, 45(1):21-24.
	LI S X, LIU M. Application of power limitation strategy in marine electric propulsion system[J], Marine Electric & Electronic Technology, 2025, 45(1):21-24. (in Chinese)
[18]	王广益. 基于FOC技术的永磁同步电机控制系统设计与实现[J]. 中国设备工程, 2025(11):152-155.
	WANG G Y. Design and implementation of permanent magnet synchronous motor control system based on FOC technology[J]. China Plant Engineering, 2025(11):152-155. (in Chinese)
[19]	江晓明. 集成电机推进器用无刷直流电机换相转矩脉动抑制策略研究[D]. 哈尔滨: 哈尔滨工程大学, 2018.
	JIANG X M. Control strategy for commutation torque ripple reduction of brushless DC motor in integrated motor propulsion[D]. Harbin: Harbin Engineering University, 2018. (in Chinese)
[20]	王梦缘. 六相PMSM随机调制技术及其电磁干扰影响研究[D]. 淄博: 山东理工大学, 2024.
	WANG M Y. Study on random modulation technique of six-phase PMSM and Its influence on electromagnetic interference[D]. Zibo: Shandong University of Technology, 2024. (in Chinese)
[21]	郭嘉, 胡展源, 刘天骄. 开绕组永磁同步电机在UUV电力推进系统中的应用[J]. 微电机, 2025, 58(3):62-67.
	GUO J, HU Z Y, LIU T J. Application of open winding pmsm in UUV electric propulsion system[J]. Micromotors, 2025, 58(3):62-67. (in Chinese)
[22]	CHENG M, HAN P, DU Y, et al. General airgap field modulation theory for electrical machines:principles and practice[M]. Hoboken,NJ,US: Wiley, 2023.
[23]	POUDEL B, AMIRI E, RASTGOUFARD P. Analytical investigation and heuristic optimization of surface mounted permanent magnet machines with hybrid magnetic structure[J]. IEEE Open Journal of Industry Applications, 2022, 3:152-163.
[24]	NISHANTH F, KHAMITOV A, SEVERSON E L. Design of electric machine windings to independently control multiple airgap harmonics[J]. IEEE Transactions on Industry Applications, 2024, 60(2):3039-3050.
[25]	XU L, SUN L M, ZHAO W X. Stator core loss analysis and suppression of permanent magnet vernier machines[J]. IEEE Transactions on Industrial Electronics, 2023, 70(12):12155-12167.
[26]	ZHENG S Y, ZHU X Y, XU L, et al. Multi-objective optimization design of a multi-permanent-magnet motor considering magnet characteristic variation effects[J]. IEEE Transactions on Industrial Electronics, 2022, 69(4):3428-3438.
[27]	王笔谈, 赵文良, 刘聪, 等. 基于磁场调制原理的双三相聚磁式永磁同步电机转矩性能分析[J]. 中国电机工程学报, 2025, 45(13):5328-5341.
	WANG B T, ZHAO W L, LIU C, et al. Torque performance analysis of dual three-phase flux concentrated permanent magnet synchronous machine from perspective of magnetic field modulation principle[J]. Proceedings of the CSEE, 2025, 45(13):5328-5341. (in Chinese).
[28]	程明, 马钲洲, 花为, 等. 电机气隙磁场调制统一理论研究进展与展望[J]. 中国电机工程学报, 2025, 45(4):1220-1236.
	CHENG M, MA Z, HUA W, et al. Research progresses and prospects of general airgap field modulation theory for electrical machines[J]. Proceedings of the CSEE, 2025, 45(4):1220-1236. (in Chinese)
[29]	凌志健, 顾友壮, 赵文祥, 等. 基于能量法的磁场调制电机结构演化及转矩提升机理[J]. 中国电机工程学报, 2025, 45(8):3236-3247.
	LING Z J, GU Y Z, ZHAO W X, et al. Topology evolution and torque improvement mechanism of magnetic field modulated machine based on energy analysis method[J]. Proceedings of the CSEE[J]. 2025, 45(8):3236-3247. (in Chinese)
[30]	刘晓, 卢萌, 林娉婷, 等. 双磁场调制磁齿轮电机磁场调制机理研究[J]. 电机与控制学报, 2022, 26(10):34-40.
	LIU X, LU M, LING P T, et al. Operation principle analysis of flux modulation in dual-flux-modulated magnetic gear machine[J]. Electric Machines and Control, 2022, 26(10):34-40. (in Chinese)
[31]	EL-REFAIE A M. Fractional-slot concentrated-windings synchronous permanent magnet machine:opportunities and challenges[J]. IEEE Transactions on Industrial Electronics, 2010, 57(1):107-121.
[32]	GURAKUQ D, GERLING D. Analysis of different PM machines with concentrated windings and flux barriers in stator core[C]// Proceedings of the International Conference on Electrical Machines.Berlin, Germany:IEEE,2014:375-384.
[33]	白宇航. 电动拖拉机用磁场调制永磁轮毂电机模型预测直接转矩控制策略研究[D]. 镇江: 江苏大学, 2024.
	BAI Y H. Research on model predictive direct torque control strategy of flux-modulated permanent magnet hub motor for electric tractors[D]. Zhenjiang: Jiangsu University, 2024. (in Chinese)
[34]	刘志良, 俱鑫, 李泽文. 适用于缓解双馈感应发电机电磁转矩脉动的新型矢量控制[J]. 电源学报, 2023, 21(3):148-155. doi: 10.13234/j.issn.2095-2805.2023.3.148
	LIU Z L, JU X, LI Z W. Novel vector control for electromagnetic torque ripple mitigation of doubly-fed induction generator[J]. Journal of power supply, 2023, 21(3):148-155. (in Chinese) doi: 10.13234/j.issn.2095-2805.2023.3.148
[35]	孙东阳, 申文强, 孟繁易, 等. 基于自适应准谐振控制的DFIG-GSC次同步振荡抑制策略研究[J]. 电机与控制学报, 2022, 26(12):63-73.
	SUN D Y, SHEN W Q, MENG F Y, et al. Research on sub-synchronous oscillation suppression strategy of DFIG-GSC based on adaptive quasi-resonant control[J]. Electric Machines and Control, 2022, 26(12):63-73. (in Chinese)
[36]	赵探探. 无刷双馈电机异步-同步特性分析及其控制策略研究[D]. 武汉: 华中科技大学, 2023.
	ZHAO T T. Research on asynchronous-synchronous characteristics of brushless doubly-fed machine and its control strategy[D]. Wuhan: Huazhong University of Science and Technology, 2023. (in Chinese)
[37]	李祥林. 基于磁齿轮原理的场调制永磁风力发电机及其控制系统研究[D]. 南京: 东南大学, 2015.
	LI X L. Research on field modulated permanent magnet machine and its control system for direct drive wind power generation[D]. Nanjing: Southeast University, 2015. (in Chinese)
[38]	NAVID M, MOHAMMAD R A P, IMAN S. A detailed comparison between FOC and DTC methods of a permanent magnet synchronous motor drive[J]. Journal of Electrical & Electronic Engineering, 2015, 3(2):92-100.
[39]	项子旋, 鞠昊, 朱孝勇, 等. 以谐波为导向的轮辐式磁场调制永磁轮毂电机转速波动抑制研究[J]. 电机与控制学报, 2024, 28(9):125-138.
	XIANG Z X, JU H, ZHU X Y, et al. Research on speed fluctuation suppression of harmonic-oriented spoke-type flux-modulated permanent magnet in-wheel motor[J]. Electric Machines and Control, 2024, 28(9):125-138. (in Chinese)
[40]	XIA C L, JI B N, YAN Y. Smooth speed control for low-speed high-torque permanent-magnet synchronous motor using proportional-integral-resonant controller[J]. IEEE Transactions on Industrial Electronic, 2015, 62(4):2123.
[41]	FEI Q, DENG Y T, LI H W, et al. Speed ripple minimization of permanent magnet synchronous motor based on model predictive and iterative learning controls[J]. IEEE Access, 2019, 7:31791.
[42]	SPARGO C M, B.C.MECROW B C, WIDMER J D. A seminumerical finite-Element postprocessing torque ripple analysis technique for synchronous electric machines utilizing the air-gap maxwell stress tensor[J]. IEEE Transactions on Magnetics, 2017, 50(5):1-9.
[43]	郭培遥, 梁建伟, 王昕华, 等. 辐条式磁齿轮电机齿槽转矩抑制[J]. 电机与控制应用, 2023, 50(7):66-73,80.
	GUO P Y, LIANG J W, WNAG X H, et al. Cogging torque suppression of spoke magnetic gear motor. electric machines & control application, 2023, 50(7):66-73,80. (in Chinese)
[44]	高永超. 电动汽车用永磁同步电机谐波抑制策略研究[D]. 淄博: 山东理工大学, 2023.
	GAO Y C. Research on harmonic suppression strategy of permanent magnet synchronous motor for electric vehicle[D]. Zibo: Shandong University Of Technology, 2023. (in Chinese)
[45]	李佳润, 陈勇, 陈光, 等. 基于比例谐振自抗扰控制的电机谐波抑制与噪声优化[J]. 电子测量技术, 2024, 47(9):18-25.
	LI J R, CHEN Y, CHEN G, et al. Harmonic suppression and noise optimization of electric machines based on proportional resonance self-immunity control[J]. Electronic Measurement Technology, 2024, 47(9):18-25. (in Chinese)
[46]	袁彬. 基于分数阶重复控制的永磁同步电机谐波电流控制技术研究[D]. 南京: 东南大学, 2023.
	YUAN L. Research on harmonic current control of permanent magnet synchronous motor based on fractional repetitive control[D]. Nanjing: Southeast University, 2023. (in Chinese)
[47]	YU Z X, KONG W B, JIA S F, et al. Harmonic current suppression control strategy for hybrid excited vernier PM machines[C] //Proceedings of the IEEE International Electric Machines and Drives Conference (IEMDC).Miami,FL,USA:IEEE, 2017.
[48]	黄超, 熊璐, 官岑旭, 等. 轮毂驱动电机谐波注入抑制转矩脉动研究[J]. 微特电机, 2025, 53(5):8-12.
	HUANG C, XIONG LU, GUAN C X, et al. Research on torque ripple suppression in in-wheel drive motors through harmonic current injection[J]. Small & Special Electrical Machines, 2025, 53(5):8-12. (in Chinese)
[49]	AMIRIAN M A, RASHIDI A, SAGHAEIAN NEJAD S M, et al. Multiple reference frame control of permanent magnet synchronous motor with non-sinusoidal back EMF using adaptive notch filter[C]// Proceedings of the 2015 23rd Iranian Conference on Electrical Engineering,Tehran, Iran:IEEE,2015:1480-1485.
[50]	FLIELLER D., NGUYEN N K, WIRA P, et al. A self-learning solution for torque ripple reduction for non-sinusoidal permanent-magnet motor drives based on artificial neural networks[J]. IEEE Transactions on Industrial Electronics, 2014, 61(2):655-666.
[51]	LAI C Y, FENG G D, LAKSHMI VARAHA IYER K, et al. Genetic algorithm-based current optimization for torque ripple reduction of interior PMSMs[J]. IEEE Transactions on Industry Applications, 2017, 53(5):4493-4503.
[52]	马铭遥, 余发, 杨晴晴, 等. 基于注入分段式谐波电流抑制开关磁阻电机转矩脉动的控制策略[J]. 中国电机工程学报, 2018, 38(1):285-291.
	MA M Y, YU F, YANG Q Q, et al. Control strategy of minimizing torque ripples of the switched reluctance motor by injecting piecewise harmonic currents[J]. Proceedings of the CSEE, 2018, 38(1):285-291. (in Chinese)
[53]	马嘉杰, 孙培德. 基于四桥臂的三次谐波注入式永磁同步电机转矩密度优化[J]. 微特电机, 2021, 49(1):1-4.
	MA J J, SUN P D. Torque density optimization of third harmonic injection permanent magnet synchronous motor based on four-leg[J]. Small & Special Electrical Machines, 2021, 49(1):1-4. (in Chinese)
[54]	袁浩仁, 周福强, 孙江宏. 基于负载转矩观测器的永磁同步电机改进线性自抗扰控制方法[J]. 电子测量技术, 2025, 48(9):36-43.
	YUAN H R, ZHOU F Q, SUN J H. Improved linear active disturbance rejection control of PMSM based on load torque observation[J]. Electronic Measurement Technology, 2025, 48(9):36-43. (in Chinese)
[55]	闫宏亮, 史王晨. 基于改进分数阶自抗扰的永磁同步电机转速控制策略研究[J]. 现代制造工程, 2025(4):151-158.
	YAN H L, SHI W C. Research on PMSM control strategy based on improved fractional order active disturbance rejection[J]. Modern Manufacturing Engineering, 2025(4):151-158. (in Chinese)
[56]	高云雷, 王玉彬, 黄瑛. 基于自抗扰迭代学习控制的双定子磁场调制电机转矩脉动抑制策略[J]. 电机与控制应用, 2021, 48(6):10-16.
	GAO Y L, WNAG Y,B, HUANG Y. Torque ripple suppression strategy of field-modulation double-stator motor based on ILC-ADRC[J]. Electric Machines & Control Application, 2021, 48(6):10-16. (in Chinese)
[57]	吴磊磊. 三相表贴式磁场调制永磁电机的研究[D]. 武汉: 华中科技大学, 2018.
	WU L L. Research on three phase surface-mounted magnetic-field modulated permanent magnet machines[D].Wuhan:Huazhong University of Science and Technology 2018. (in Chinese)
[58]	宋鑫鑫, 赵文祥, 成瑀. 开绕组磁场调制永磁直线电机的单位功率因数弱磁控制[J]. 电工技术学报, 2021, 36(5):893-901.
	SONG X X, ZHAO W X, CHENG Y. Unity power factor field weakening control of field-modulated permanent magnet linear modulation motor with open winding[J]. Transactions of China Electrotechnical Society, 2021, 36(5):893-901. (in Chinese)
[59]	冯雷, 张志锋. 改进的IPMSM单张表转矩转速二维查表法[J]. 微特电机, 2022, 50(2):47-51,58.
	FENG L, ZHANG Z F. Improvement of IPMSM single table torque speed 2D look-up table method[J], 2022, 50(2):47-51,58. (in Chinese)
[60]	SUN T F, WANG J B, CHEN X. Maximum torque per ampere (MTPA) control far interior permanent magnet synchronous machine drives based on virtual signal injection[J]. IEEE Transactions on Power E1ectranics 2015, 30(9):5036-5045
[61]	贝承荣, 鲁文其, 鲁玉军, 等. 基于变遗忘因子递推最小二乘法的永磁同步电机电参数辨识[J]. 电子科技, 2025, 38(9):9-19.
	BEI C R, LU W Q, LU Y J, et al. Electrical parameter identification of permanent magnet synchronous motor based on recursive least squares method with variable forgetting factor[J]. Electronic Science and Technology, 2025, 38(9):9-19 (in Chinese)
[62]	沈建新, 张雨馨, 王云冲, 等. 自寻优最大转矩电流比矢量控制连载之一:同步电动机动态寻优MTPA控制技术综述[J]. 微特电机, 2022, 50(9):1-6.
	SHENG J X, ZHANG Y X, WANG Y C, et al. Self-optimizing MTPA vector control part 1:a review of dynamic mtpa control for synchronous motor[J]. Small & Special Electrical Machines, 2022, 50(9):1-6. (in Chinese)
[63]	LI K, WANG Y. Maximum torque per ampere (MTPA) control for IPMSM drives using signal injection and an mtpa control law[J]. IEEE Transactions on Industrial Informatics, 2019, 15(10):5588-5598.
[64]	KIRSCHEN D S, NOVOTNY D W, LIPO T A. On-line efficiency optimization of a variable frequency induction motor drive[J]. IEEE Transactions on Industry Applications, 1985, IA 21(3):610-616
[65]	刘凯, 张阔, 花为, 等. 基于变载波频率的永磁同步电机驱动系统效率优化控制[J]. 东南大学学报(自然科学版), 2024, 54(3):724-729.
	LIU K, ZHANG K, HUA W, et al. Efficiency optimization control of permanent magnet synchronous motor drive system based on variable carrier frequency[J]. Journal of Southeast University(Natural Science Edition), 2024, 54(3):724-729. (in Chinese)
[66]	孙博文, 陈建明, 周成, 等. 电动汽车用内置式永磁同步电机驱动系统效率优化研究[J]. 控制与信息技术, 2021, 472(4):25-30.
	SUN B W, CHEN J M, ZHOU C, et al. Research on efficiency optimization of interior permanent magnet synchronous motor drive system for electric vehicle[J]. Control and Information Technology, 2021, 472(4):25-30. (in Chinese)
[67]	王柄东, 王道涵, 王晓姬, 等. 交流调磁型永磁同步电机磁通协同调控最大转矩铜耗比控制[J]. 电工技术学报, 2024, 39(12):3630-3645.
	WANG B D, WNAG D H, WANG X J, et al. A maximum torque per copper loss control for AC Flux-regulation permanent magnet synchronous motor with magnetic flux co-regulation[J]. Transactions of China Electrotechnical Society, 2024, 39(12):3630-3645. (in Chinese)
[68]	赵子安, 王一帆, 李凤姣, 等. 考虑铁损的同步磁阻电机最小损耗控制策略[J]. 电机与控制学报, 2023, 27(11):1-9.
	ZHAO Z A, WANG Y F, LIU F J, et al. Minimum losses control strategy of synchronous reluctance motors considering iron losses[J]. Electric Machines and Control, 2023, 27(11):1-9. (in Chinese)
[69]	贺鸿彬, 何龙, 颜秉洋, 等. 感应电机损耗最小化预测控制策略研究[J]. 微特电机, 2024, 52(3):54-59.
	HE H B, HE L, YAN B Y, et al. Research on predictive control strategy for minimizing induction motor losses[J]. Small & Special Electrical Machines, 2024, 52(3):54-59. (in Chinese)
[70]	徐奇伟, 龙学汉, 苗轶如, 等. 永磁同步电机双矢量模型预测控制的计算量优化方法研究[J]. 电机与控制学报, 2025, 29(5):19-30.
	XU Q W, LONG X H, MIAO T R, et al. Double-vector model predictive current control for PMSM drive system with low calculation burden[J]. Electric Machines and Control, 2025, 29(5):19-30. (in Chinese)
[71]	王红, 于新红. 一种永磁同步电机效率优化控制策略研究[J]. 电子设计工程, 2023, 31(16):16-20.
	WANG H, Yu X H. Research on an efficiency optimization control strategy of permanent magnet synchronous motor[J]. Electronic Design Engineering, 2023, 31(16):16-20. (in Chinese)
[72]	XIAO R X, YANG X, LI J, et al. Loss minimization control for interior permanent magnet synchronous motor in a wide speed range// Proceedings of the 2021 IEEE 4th International Electrical and Energy Conference (CIEEC). Wuhan,China:IEEE, 2021,1-6.
[73]	梁策, 张兵, 朱建阳. 基于IPSO-BPNN的电机控制方法研究[J]. 机床与液压, 2025, 53(7):81-87.
	LIANG C, ZHANG B, ZHU J Y, Research on motor control method based on IPSO-BPNN[J]. Machine Tool & Hydraulics, 2025, 53(7):81-87. (in Chinese)
[74]	戚云飞. 异步电机能效在线检测与效率优化关键技术[J]. 防爆电机, 2025, 60(3):65-68.
	QI Y F. Key technologies of efficiency on-line detection and optimization of induction motor[J]. Explosion-Proof Electric Machine, 2025, 60(3):65-68. (in Chinese)
[75]	URASAKI N, SENJYU T, UEZATO K. Neural network based high efficiency drive for interior permanent magnet synchronous motors compensating EMF constant variation[C]// Proceedings of Power Conversion Conference.Osaka,Japan:IEEE, 2002,1273-1278.
[76]	CAVALLARO C, TOMMASO A, MICELI R, et al. Efficiency enhancement of permanent-magnet synchronous motor drives by online loss minimization approaches[J]. IEEE Transactions on Industrial Electronics, 2005, 52(4):1153-1160
[77]	张立伟, 温旭辉, 郑琼林. 异步电机用混合式模糊搜索效率优化控制研究[J]. 中国电机工程学报, 2007, 254(27):83-87.
	ZHANG L W, WEN X H, ZHENG Q L. Fuzzy logic based hybrid search control strategy for efficiency optimization control of induction motors[J]. Proceedings of the CSEE, 2007, 254(27):83-87. (in Chinese)
[78]	曲星宇, 朱振康. 内置式永磁同步电机无传感器最小损耗控制[J]. 组合机床与自动化加工技术, 2024(11):94-98.
	QU X Y, ZHU Z K. Interior sensorless minimum loss control for permanent magnet synchronous motors[J]. Modular Machine Tool & Automatic Manufacturing Technique. 2024(11):94-98. (in Chinese)
[79]	汪谦松, 夏链, 韩江. 改进人群搜索算法优化的直线电机模糊PID控制[J]. 合肥工业大学学报(自然科学版), 2022, 45(4):458-463,474.
	WANG Q S, XIA L, HAN J. Fuzzy PID control of linear motor optimized by improved seeker optimization algorithm[J]. Journal of Hefei University of Technology(Natural Science), 2022, 45(4):458-463,474. (in Chinese)
[80]	NASIR U M, ZOU H B, AZEVEDO F. Online loss-minimization-based adaptive flux observer for direct torque and flux control of PMSM drive[J]. IEEE Transactions on Industry Applications, 2015, 52(1):425-431.
[81]	ZHAO Y, REN X, FAN X G, et al. A high power factor permanent magnet vernier machine with modular stator and yokeless rotor[J]. IEEE Transactions on Industrial Electronics, 2023, 70(7):7141-7152.
[82]	张长国. 磁场调制式无刷双馈风力发电机特性研究[D]. 南京: 东南大学, 2022.
	ZHANG C G. Research on characteristics of field modulated brushless doubly-fed generators for wind turbine[D]. Nanjing: Southeast University, 2022. (in Chinese)
[83]	姜永将. 永磁磁场调制无刷双馈风力发电机的设计与分析[D]. 南京: 东南大学, 2019.
	JIANHG Y J. Design and analysis of brushless doubly-fed generator based on permanent magnet field modulation[D]. Nanjing: Southeast University, 2019. (in Chinese)
[84]	王腾光. 磁场调制型永磁轮毂电机设计分析与多目标综合优化研究[D]. 镇江: 江苏大学, 2024.
	WNAG T G. Design analysis and multi-objective comprehensive optimization research of magnetic field modulation permanent magnet hub motor[D]. Zhenjiang: Jiangsu University, 2024. (in Chinese)
[85]	蒋敏. 磁场调制变漏磁永磁轮毂电机多变工况设计与优化研究[D]. 镇江: 江苏大学, 2024.
	JIANG M. Research on design and optimization under driving cycle of magnetic field modulated variable leakage permanent magnet hub motor[D]. Zhenjiang: Jiangsu University, 2024. (in Chinese)
[86]	曲荣海, 李大伟, 赵钰. 磁场调制电机的由来、发展与挑战[J]. 中国电机工程学报, 2024, 44(18):7361-7381.
	QU R H, LI D W, ZHAO Y. The origin, development and challenge of flux modulation machine[J]. Proceedings of the CSEE, 2024, 44(18):7361-7381. (in Chinese)
[87]	罗正豪, 宋启. 一种船舶推进的双定子单转子场调制超导电机[J]. 船电技术, 2024, 44(9):5-10.
	LUO Z H, SONG Q. A double-stator single-rotor field modulated superconducting motor for ship propulsion[J]. Marine Electric & Electronic Technology, 2024, 44(9):5-10. (in Chinese)