An Overview on Developments and Research of Limited Angle Torque Motor
Wang Mingjie1, Li Dawei1, Qu Ronghai1, Huang Lihao2
1. State Key Laboratory of Advanced Electromagnetic Engineering and Technology Huazhong University of Science and Technology Wuhan 430074 China; 2. AECC Aero Engine Control System Institute Wuxi 214063 China
Abstract:A limited angle torque motor (LATM) can rotate around the axis within a certain angle without requiring additional mechanical devices. LATMs are often used as electrically powered actuators, which are applied to the direct drive control with a torque requirement of less than 1 kN·m within a limited angle. Compared with traditional hydraulic and pneumatic actuators, no piping or other transmission equipment is required. Compared with the traditional electrically powered actuator of the rotary motor with gearbox, LATM has no non-linearity problem caused by the transmission mechanism and has the advantages of simple structure, convenient control, high reliability, and high torque density. Therefore, LATMs are widely used in various application fields that require only a limited rotation angle. There are many different structures of LATM and various ways to classify them. At the same time, there are similarities in the working principles of serval main topologies that have been used so far. In this paper, the working principles of each main topology are introduced by evolving the DC motor into these topologies, which leads to the relationship between output torque and rotor angle, the characteristic of most interest in applications of LATM. Then, various LATM topologies and their characteristics are presented in detail. Among these topologies, the toroidal slotless LATM and equi-polar slot LATM are the two most widely used topologies and research focuses. The torque-angle characteristic of LATM has a constant torque range (CTR), where the output torque is proportional to the input current and independent of the speed and rotor position. Thus, it is the operating range of LATM. The magnitude of CTR and the maximum output torque in the range are the two most important static performance indicators of LATM. Since CTR is affected by the cogging torque, armature reaction, and nonlinearity of the ferromagnetic material, this paper presents the application of the equivalent magnetic circuit methods, the analytical methods, the finite element method, and the decision-making methods in LATM design. Moreover, this paper discusses how to suppress the torque ripple within CTR and how to further improve the magnitude of CTR and the maximum output torque in the range. Mathematical models and control methods are indispensable to achieving precise control of LATM. The linear mathematical model can be analogous to that of a DC motor. However, accurate nonlinear mathematical models must rely on the finite element method or experimental data. Thus, robust control methods are better for obtaining the desired dynamic performance. This paper presents the application of PID and improved PID control methods in LATM control, and the application of various modern control methods considering the effects of load disturbances, motor parameter variations, and nonlinearity of the torque-angle characteristic. According to the swing scanning and positioning functions of LATM, three typical application fields- imaging system, servo valve, and aircraft attitude-are detailed in this paper, and other applications are roughly introduced. With the development of science and technology, the study of new structures, optimization of the torque-angle characteristic, loss calculation, multi-physics field coupling analysis, and testing techniques will become the main development trend in LATM research. As researchers improve motor performance, LATM will have a broader application prospect.
王铭杰, 李大伟, 曲荣海, 黄礼浩. 有限转角力矩电机及其研究发展综述[J]. 电工技术学报, 2023, 38(6): 1486-1505.
Wang Mingjie, Li Dawei, Qu Ronghai, Huang Lihao. An Overview on Developments and Research of Limited Angle Torque Motor. Transactions of China Electrotechnical Society, 2023, 38(6): 1486-1505.
[1] 桂竞存. 有限转角无刷直流力矩电机[J]. 电工电能新技术, 1984, 3(3): 45-49. Gui Jingcun.Limited angle brushless DC torque motor[J]. Advanced Technology of Electrical Engin- eering and Energy, 1984, 3(3): 45-49. [2] 徐加甫. 有限转角力矩电动机[J]. 自动化仪表, 1982, 3(4): 27-29, 62. Xu Jiafu.Finite angle torque motor[J]. Process Auto- mation Instrumentation, 1982, 3(4): 27-29, 62. [3] 谢果良, 杨媛霞, 张吟蓉. 高性能有限转角电动机发展概况[J]. 微电机, 1988, 21(1): 24-28. Xie Guoliang, Yang Yuanxia, Zhang Yinrong.Develop- ment survey of high performance finite angle motor[J]. Mcromotors Servo Technique, 1988, 21(1): 24-28. [4] Dawson C, Bolton H R.Performance prediction of a wide-angle limited-motion rotary actuator[J]. Pro- ceedings of the Institution of Electrical Engineers, 1978, 125(9): 895-898. [5] Huber J E, Fleck N A, Ashby M F.The selection of mechanical actuators based on performance indices[J]. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 1997, 453(1965): 2185-2205. [6] Bolton H R, Shakweh Y.Performance prediction of laws's relay actuator[J]. IEE Proceedings B Electric Power Applications, 1990, 137(1): 1-13. [7] 徐殿国, 白凤强, 张相军, 等. 形状记忆合金执行器研究综述[J]. 电工技术学报, 2022, 37(20): 5144-5163. Xu Dianguo, Bai Fengqiang, Zhang Xiangjun, et al.A review of the research on shape memory alloy actuators[J]. Transactions of China Electrotechnical Society, 2022, 37(20): 5144-5163. [8] Bolton H R. Design aspects of electromagnetic actuators[C]//IEE Colloquium on Magnetic Materials for Sensors and Actuators (Digest No.1994/183), London, UK, 2002: 6/1-6/5. [9] Ahmed F S.Analysis, modeling, identification and control of pancake DC torque motors: application to automobile air path actuators[J]. Mechatronics, 2012, 22(2): 195-212. [10] Chen S L, Kamaldin N, Teo T J, et al.Towards comprehensive modeling and large angle tracking control of a limited angle torque actuator with cylindrical Halbach[J]. IEEE/ASME Transactions on Mechatronics, 2016, 21(1): 431-442. [11] Yu Guodong, Xu Yongxiang, Zou Jibin, et al.Modeling and analysis of limited-angle torque motor considering nonlinear effects[J]. IEEE Transactions on Transportation Electrification, 2020, 6(4): 1457-1465. [12] 宋恩哲, 姚崇, 孙军, 等. 有限转角直流力矩电机作为柴油机调速执行机构的控制策略研究[J]. 内燃机工程, 2009, 30(1): 45-50. Song Enzhe, Yao Chong, Sun Jun, et al.Design and research of LABLTM's controlling strategy for diesel engine speed actuator[J]. Chinese Internal Com- bustion Engine Engineering, 2009, 30(1): 45-50. [13] Qiu Yihui, Perreault D J, Kassakian J G, et al.A custom-designed limited-angle actuator for an electro- mechanical engine valve drive part I: conceptual design[C]//5th IET International Conference on Power Electronics, Machines and Drives (PEMD 2010), Brighton, UK, 2010: 1-6. [14] Qiu Yihui, Perreault D J, Kassakian J G, et al.A custom-designed limited-angle actuator for an elec- tromechanical engine valve drive part Ⅱ: fabrication and evaluation[C]//5th IET International Conference on Power Electronics, Machines and Drives (PEMD 2010), Brighton, UK, 2010: 1-6. [15] Farhad T, Hosein F, Mojtaba A.Gray-box modeling of a pneumatic servo-valve[J]. Acta Polytechnica Hungarica, 2010, 7(5): 129-142. [16] Jang G H, Seo S W, Kim C W, et al.Self-aligning limited-angle rotary torque PM motor for control valve: design and experimental verification[J]. IEEE Transactions on Applied Superconductivity, 2020, 30(4): 1-5. [17] Tsai C C, Lin S C, Huang H C, et al.Design and control of a brushless DC limited-angle torque motor with its application to fuel control of small-scale gas turbine engines[J]. Mechatronics, 2009, 19(1): 29-41. [18] 何松波, 顾鸿祥. 自屏蔽式音圈电机[J]. 计算机研究与发展, 1984, 21(4): 27-34, 17. He Songbo, Gu Hongxiang.Self-shielding voice coil motor[J]. Journal of Computer Research and Develop- ment, 1984, 21(4): 27-34, 17. [19] 柴嘉伟, 贵献国. 音圈电机结构优化及应用综述[J]. 电工技术学报, 2021, 36(6): 1113-1125. Chai Jiawei, Gui Xianguo.Overview of structure optimization and application of voice coil motor[J]. Transactions of China Electrotechnical Society, 2021, 36(6): 1113-1125. [20] 尹达一. 有限转角驱动机构在国外航天遥感系统中的应用[J]. 红外, 2003, 24(5): 5-10. Yin Dayi.Application of finite angle driving mechanism to foreign space remote sensing systems[J]. Infrared, 2003, 24(5): 5-10. [21] 李勇, 王亮, 张波, 等. 航空用盘式绕组旋转式音圈电机的热应力与热变形分析[J]. 电工技术学报, 2015, 30(12): 181-185. Li Yong, Wang Liang, Zhang Bo, et al.Analysis of thermal stress and deformation of disk winding rotary voice coil motor used in space[J]. Transactions of China Electrotechnical Society, 2015, 30(12): 181-185. [22] 褚立新, 林辉. 基于积分反推原理的天线定向伺服技术研究[J]. 中国空间科学技术, 2008, 28(1): 54-59. Chu Lixin, Lin Hui.Study of antenna pointing servo system based on integral back-stepping scheme[J]. Chinese Space Science and Technology, 2008, 28(1): 54-59. [23] 骆光照, 王鹏, 吴梅, 等. 直接驱动电动舵机的混合H2/H∞ 控制器设计[J]. 西北工业大学学报, 2004, 22(5): 649-652. Luo Guangzhao, Wang Peng, Wu Mei, et al.Mixed H2/H∞ control of direct-drive electromechanical actuator (EMA)[J]. Journal of Northwestern Poly- technical University, 2004, 22(5): 649-652. [24] 林莘, 李永祥, 马跃乾, 等. 高压断路器新型电机操动机构的动态特性分析[J]. 电机与控制学报, 2009, 13(2): 216-221, 226. Lin Xin, Li Yongxiang, Ma Yueqian, et al.Dynamic characteristics analysis on novel motor actuator of high voltage circuit breaker[J]. Electric Machines and Control, 2009, 13(2): 216-221, 226. [25] 王强, 王喜太, 张晓玉. 基于微电机的下肢康复训练系统的研究与开发[J]. 微电机, 2010, 43(1): 18-20. Wang Qiang, Wang Xitai, Zhang Xiaoyu.Research and development of rehabilitative exercises systems of lower limbs based on micro-motor[J]. Micromotors, 2010, 43(1): 18-20. [26] 陈益广, 刘均喜. 磁阻反应式有限转角电机特性分析[J]. 电工技术学报, 2017, 32(5): 19-25. Chen Yiguang, Liu Junxi.The characteristic analysis of limited angle reluctance motor[J]. Transactions of China Electrotechnical Society, 2017, 32(5): 19-25. [27] 郭志强, 余红英, 刘琛. 基于模糊PID的高速振镜电机控制[J]. 微特电机, 2019, 47(4): 61-65. Guo Zhiqiang, Yu Hongying, Liu Chen.High-speed galvanometer motor control based on fuzzy PID[J]. Small & Special Electrical Machines, 2019, 47(4): 61-65. [28] Zhang Y, Smith I R, Kettleborough J G.Performance evaluation for a limited-angle torque motor[J]. IEEE/ ASME Transactions on Mechatronics, 1999, 4(3): 335-339. [29] 何松波. 有限转角电机[J]. 微特电机, 1976, 4(3): 16-31. He Songbo.Finite angle motor[J]. Small & Special Machines, 1976, 4(3): 16-31. [30] 禹国栋. 集中绕组有限转角力矩电机及其特性的研究[D]. 哈尔滨: 哈尔滨工业大学, 2017. [31] Dawson C, Bolton H R.Limited motion rotary actuators of the toroidal-stator, permanent-magnet rotor type[J]. IEE Proceedings B Electric Power Applications, 1982, 129(4): 190-198. [32] 刘华源, 王自强, 杨帆. 一种有限转角力矩电机的设计方法[J]. 微电机, 2013, 46(1): 17-20, 66. Liu Huayuan, Wang Ziqiang, Yang Fan.A limited angle torque motor design[J]. Micromotors, 2013, 46(1): 17-20, 66. [33] Yu Zheyan, Wang Ziqiang. Analysis and simulation of a limited-angle torque motor[J]. Applied Mechanics and Materials, 2014, 668/669: 601-606. [34] 刘杰, 赵友坤, 范雪蕾, 等. 一种定子双励磁有限转角力矩电机设计[J]. 微电机, 2019, 52(8): 20-22. Liu Jie, Zhao Youkun, Fan Xuelei, et al.The invention relates to a stator double excitation torque motor with limited turning angle[J]. Micromotors, 2019, 52(8): 20-22. [35] 姜保军, 周鹏飞. 一种永磁有限转角电机的磁场分析[J]. 重庆交通大学学报(自然科学版), 2020, 39(8): 119-124. Jiang Baojun, Zhou Pengfei.Magnetic field analysis of a permanent magnet limited angle motor[J]. Journal of Chongqing Jiaotong University (Natural Science), 2020, 39(8): 119-124. [36] Cheng Ming, Hua Wei, Zhang Jianzhong, et al.Overview of stator-permanent magnet brushless machines[J]. IEEE Transactions on Industrial Elec- tronics, 2011, 58(11): 5087-5101. [37] Evans S A, Smith I R, Kettleborough J G.Static and dynamic analysis of a permanent magnet rectilinear Laws' relay actuator[J]. IEE Proceedings-Electric Power Applications, 1999, 146(1): 11-16. [38] Evans S A, Smith I R, Kettleborough J G.Permanent- magnet linear actuator for static and reciprocating short-stroke electromechanical systems[J]. IEEE/ASME Transactions on Mechatronics, 2001, 6(1): 36-42. [39] 桂竞存. 稀土永磁有限转角力矩电机的设计计算[J]. 微电机, 1986, 19(1): 14-18. Gui Jingcun.Design and calculation of rare earth permanent magnet finite angle torque motor[J]. Mcromotors Servo Technique, 1986, 19(1): 14-18. [40] Murali Krishna P, Kannan N.Brushless DC limited angle torque motor[C]//Proceedings of International Conference on Power Electronics, Drives and Energy Systems for Industrial Growth, New Delhi, India, 2002: 511-516. [41] Zarandi R N, Kelk H M, Toorani F, et al.Com- prehensive design of a toroidally-wound limited angle torque motor[J]. International Review of Electrical Engineering, 2011, 6(1): 198-206. [42] Roohnavazfar M, Houshmand M, Nasiri-Zarandi R, et al.Using axiomatic design theory for selection of the optimum design solution and manufacturing process plans of a limited angle torque motor[J]. Journal of Manufacturing Science and Engineering, 2014, 136(5): 051009. [43] Nasiri-Zarandi R, Mirsalim M, Cavagnino A.Analysis, optimization, and prototyping of a brushless DC limited-angle torque-motor with segmented rotor pole tip structure[J]. IEEE Transactions on Industrial Electronics, 2015, 62(8): 4985-4993. [44] Wu Shuai, Zhao Xiangyu, Li Xiao, et al.Preliminary design and optimization of toroidally wound limited angle servo motor based on a generalized magnetic circuit model[J]. IEEE Transactions on Magnetics, 2016, 52(9): 1-9. [45] Hekmati P, Yazdanpanah R, Mirsalim M, et al.Radial-flux permanent-magnet limited-angle torque motors[J]. IEEE Transactions on Industrial Elec- tronics, 2017, 64(3): 1884-1892. [46] Wu Shuai, Zhao Xiangyu, Jiao Zongxia, et al.Multi-objective optimal design of a toroidally wound radial-flux halbach permanent magnet array limited angle torque motor[J]. IEEE Transactions on Indu- strial Electronics, 2017, 64(4): 2962-2971. [47] Li Yong, Ma Pengcheng, Wang Qian, et al.Analysis, modeling, and verification of limited angle torque motors with irregular slot numbers for performance improvement[J]. IEEE Transactions on Energy Con- version, 2020, 35(2): 1004-1013. [48] Yazdanpanah R.Analytical study, design and opti- mization of radial-flux PM limited-angle torque motors[J]. Scientia Iranica, 2020, 29(4): 1975-1982. [49] Ma Pengcheng, Wang Qian, Li Yong, et al.Operational range extension method for limited-angle torque motors with irregular slot numbers[J]. IET Electric Power Applications, 2021, 15(5): 570-578. [50] Ma Pengcheng, Wang Qian, Li Yong, et al.Research on torque ripple suppression of the slotted limited angle torque motor[J]. IEEE Transactions on Mag- netics, 2021, 57(2): 1-6. [51] 王海燕, 张雪英, 王真, 等. 分数槽绕组有限转角电动机的设计及仿真[J]. 微特电机, 2009, 37(8): 9-11. Wang Haiyan, Zhang Xueying, Wang Zhen, et al.Design and simulation of fractional slot winding in limited angle motor[J]. Small & Special Electrical Machines, 2009, 37(8): 9-11. [52] Christian M.A new multipurpose servo valve for fast applications[C]//SAE Technical Paper Series, Detroit, Michigan, USA, 1994, 103: 1097-1103. [53] Bianchi N, Bolognani S.Design techniques for reducing the cogging torque in surface-mounted PM motors[C]//Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy (Cat. No.00CH37129), Rome, Italy, 2002: 179-185. [54] Yu Guodong, Zou Jibin, Xu Yongxiang, et al.Estimation of maximum angular operation range for permanent-magnet slotted limited-angle torque motor[J]. IEEE Transactions on Magnetics, 2015, 51(11): 1-5. [55] Yu Guodong, Zou Jibin, Xu Yongxiang, et al.Torque performance improvement of a radial-flux slotted limited-angle torque motor by tapered tooth-tip[J]. IEEE Transactions on Applied Superconductivity, 2016, 26(7): 1-5. [56] Yu Guodong, Xu Yongxiang, Zou Jibin, et al.Analysis and experimental validation of dynamic performance for slotted limited-angle torque motor[J]. IEEE Transactions on Magnetics, 2017, 53(11): 1-5. [57] Yu Guodong, Xu Yongxiang, Zou Jibin, et al.Development of a radial-flux slotted limited-angle torque motor with asymmetrical teeth for torque performance improvement[J]. IEEE Transactions on Magnetics, 2019, 55(7): 1-5. [58] 于浩. 等极槽有限转角电机力矩特性优化与热问题研究[D]. 哈尔滨: 哈尔滨工业大学, 2020. [59] 禹国栋, 徐永向, 邹继斌, 等. 等极槽式有限转角力矩电机磁场解析计算与恒转矩区间分析[J]. 中国电机工程学报, 2021, 41(7): 2538-2546. Yu Guodong, Xu Yongxiang, Zou Jibin, et al.Analytical calculation of magnetic field and constant torque range analysis of slotted limited-angle torque motor with identical pole-slot number[J]. Proceedings of the CSEE, 2021, 41(7): 2538-2546. [60] Yu Guodong, Xu Yongxiang, Lin Tianyu, et al.Nonlinear EMC modeling and analysis of permanent- magnet slotted limited-angle torque motor[J]. IEEE Transactions on Industrial Electronics, 2021, 68(9): 8507-8518. [61] Yu Hao, Yu Guodong, Xu Yongxiang, et al.Torque performance improvement for slotted limited-angle torque motors by combined SMA application and GA optimization[J]. IEEE Transactions on Magnetics, 2021, 57(2): 1-5. [62] Zou Jibin, Yu Guodong, Xu Yongxiang, et al.Development of a limited-angle torque motor with a moving coil[J]. IEEE Transactions on Magnetics, 2016, 52(7): 1-5. [63] Smith K J, Graham D J, Neasham J A.Design and optimization of a voice coil motor with a rotary actuator for an ultrasound scanner[J]. IEEE Transactions on Industrial Electronics, 2015, 62(11): 7073-7078. [64] Choi Y M, Ahn D H, Gweon D G, et al.Halbach magnetic circuit for voice coil motor in hard disk drives[J]. Journal of Magnetics, 2010, 15(3): 143-147. [65] Xu Zhaoping, Chang Siqin.Improved moving coil electric machine for internal combustion linear gen- erator[J]. IEEE Transactions on Energy Conversion, 2010, 25(2): 281-286. [66] Hiemstra D B, Parmar G, Awtar S.Performance tradeoffs posed by moving magnet actuators in flexure-based nanopositioning[J]. IEEE/ASME Transa- ctions on Mechatronics, 2014, 19(1): 201-212. [67] Wu Shuai, Jiao Zongxia, Yan Liang, et al.Develop- ment of a direct-drive servo valve with high- frequency voice coil motor and advanced digital controller[J]. IEEE/ASME Transactions on Mechatronics, 2014, 19(3): 932-942. [68] McCann R A, Suriano J R. Optimized design and 3D finite element analysis of a rotary actuator[C]//IAS '95. Conference Record of the 1995 IEEE Industry Applications Conference Thirtieth IAS Annual Meeting, Orlando, FL, USA, 2002: 492-497. [69] Ahmed F S, Laghrouche S, Bagdouri M E.Pancake type DC limited angle torque motor: modeling and identification, application to automobile air path actuators[J]. IFAC Proceedings Volumes, 2010, 43(7): 431-436. [70] Lee E C, Kwon S O, Lee H Y, et al.Effects of rotor pole angle on torque characteristics of a limited-angle torque motor[C]//2017 IEEE International Electric Machines and Drives Conference (IEMDC), Miami, FL, USA, 2017: 1-6. [71] Hekmati P, Mirsalim M.Design and analysis of a novel axial-flux slotless limited-angle torque motor with trapezoidal cross section for the stator[J]. IEEE Transactions on Energy Conversion, 2013, 28(4): 815-822. [72] 马瑞卿, 刘景林, 刘卫国. 具有磁阻效应的永磁式有限转角无刷力矩电动机[J]. 微特电机, 2005, 33(7): 5-8. Ma Ruiqing, Liu Jinglin, Liu Weiguo.Permanent magnet limited angle brushless torque motor based on reluctance effect[J]. Small & Special Machines, 2005, 33(7): 5-8. [73] 樊战亭, 刘卫国, 贺安超. 有限转角力矩电动机转矩分析和优化[J]. 微特电机, 2012, 40(2): 1-3. Fan Zhanting, Liu Weiguo, He Anchao.Limited angle torque motor torque analysis and optimization[J]. Small & Special Electrical Machines, 2012, 40(2): 1-3. [74] Li Xiao, Wu Shuai, Jiao Zongxia, et al.Design and analysis of a Limited angle torque motor with dual Halbach arrays[C]//2015 IEEE International Confer- ence on Advanced Intelligent Mechatronics (AIM), Busan, Korea (South), 2015: 401-406. [75] Dawson C, Bolton H R.Design of a class of wide- angle limited-rotation rotary actuators[J]. Proceedings of the Institution of Electrical Engineers, 1979, 126(4): 345-350. [76] 张守首, 郭思源. 基于子域分析模型的实心转子感应电机磁场解析[J]. 电工技术学报, 2021, 36(20): 4285-4296. Zhang Shoushou, Guo Siyuan.Analytical solution of magnetic field in solid rotor induction machine based on subdomain model[J]. Transactions of China Electrotechnical Society, 2021, 36(20): 4285-4296. [77] 赵士豪, 陈进华, 张驰, 等. 不均匀气隙表贴式永磁同步电机磁场解析计算[J]. 电工技术学报, 2022, 37(14): 3502-3513. Zhao Shihao, Chen Jinhua, Zhang Chi, et al.Analytical calculation of magnetic field of permanent magnet synchronous motor with uneven air gap structure[J]. Transactions of China Electrotechnical Society, 2022, 37(14): 3502-3513. [78] Gutfrind C, Dufour L, Liebart V, et al.An approach to the prototyping of an optimized limited stroke actuator to drive a low pressure exhaust gas recir- culation valve[J]. Sensors, 2016, 16(5): 735. [79] 孙毅, 蔡顺, 林迎前, 等. 永磁辅助同步磁阻电机顶层优化设计(英文)[J]. 电工技术学报, 2022, 37(9): 2306-2318. Sun Yi, Cai Shun, Lin Yingqian, et al.Top-level design pattern of pm-assisted synchronous reluctance machines[J]. Transactions of China Electrotechnical Society, 2022, 37(9): 2306-2318. [80] Bramerdorfer G.Multiobjective electric machine optimization for highest reliability demands[J]. CES Transactions on Electrical Machines and Systems, 2020, 4(2): 71-78. [81] 张文晶, 徐衍亮, 李树才. 新型盘式横向磁通永磁无刷电机的结构原理及设计优化[J]. 电工技术学报, 2021, 36(14): 2979-2988. Zhang Wenjing, Xu Yanliang, Li Shucai.Structure principle and optimization of a novel disk transverse flux permanent magnet brushless motor[J]. Transa- ctions of China Electrotechnical Society, 2021, 36(14): 2979-2988. [82] Widdowson G P, Howe D, Evison P R.Computer- aided optimization of rare-earth permanent magnet actuators[C]//International Conference on Computa- tion in Electromagnetics, London, UK, 1991: 93-96. [83] Roohnavazfar M, Houshmand M, Zarandi R N, et al.Optimization of design parameters of a limited angle torque motor using analytical hierarchy process and axiomatic design theory[J]. Production & Manu- facturing Research, 2014, 2(1): 400-414. [84] 胡小飞, 刘超, 王毅, 等. 单相无刷有槽有限转角电机的分析与优化[J]. 电工技术学报, 2019, 34(13): 2744-2751. Hu Xiaofei, Liu Chao, Wang Yi, et al.Analysis and optimization of single phase brushless slotted limited angle torque motor[J]. Transactions of China Elec- trotechnical Society, 2019, 34(13): 2744-2751. [85] 郭立志, 郑楚良, 王和. 半浸油式有限转角力矩电机的设计与仿真[J]. 微特电机, 2021, 49(1): 22-25. Guo Lizhi, Zheng Chuliang, Wang He.Design and simulation of semi-immersed limited angle torque motor[J]. Small & Special Electrical Machines, 2021, 49(1): 22-25. [86] Ionică I, Modreanu M, Boboc C, et al.Tridimensional modeling for a DC, limited angle, torque motor of size 16[C]//2016 International Conference and Expo- sition on Electrical and Power Engineering (EPE), Iasi, Romania, 2016: 235-239. [87] Krishnan S, Sreejith M R, Sajeev K A, et al.A comparative design approach of a novel wide angle torque motor for pointing mechanism for space application[C]//2018 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Chennai, India, 2019: 1-5. [88] 刘有恩, 刘勇, 葛红岩, 等. 大角位移有限转角力矩电机辅助齿的设计与优化[J]. 现代机械, 2021(3): 47-52. Liu Youen, Liu Yong, Ge Hongyan, et al.Design and optimization of auxiliary gear tooth for limited angle torque motor with large angular displacement[J]. Modern Machinery, 2021(3): 47-52. [89] 曾子元, 刘有恩, 吴和远, 等. 一种双余度有限转角力矩电机的设计研究[J]. 现代机械, 2019(6): 17-21. Zeng Ziyuan, Liu Youen, Wu Heyuan, et al.Design of a dual redundancy limited angle torque motor[J]. Modern Machinery, 2019(6): 17-21. [90] 谢冰川, 张岳, 徐振耀, 等. 基于代理模型的电机多学科优化关键技术综述[J]. 电工技术学报, 2022, 37(20): 5117-5143. Xie Bingchuan, Zhang Yue, Xu Zhenyao, et al.Review on multidisciplinary optimization key tech- nology of electrical machine based on surrogate models[J]. Transactions of China Electrotechnical Society, 2022, 37(20): 5117-5143. [91] Lee J S, Choi G.Modeling and hardware-in-the-loop system realization of electric machine drives—a review[J]. CES Transactions on Electrical Machines and Systems, 2021, 5(3): 194-201. [92] Smith I R, Kettleborough J G, Zhang Y.Simplified modelling and dynamic analysis of a Laws’ relay actuator[J]. Mechatronics, 1999, 9(5): 463-475. [93] Ahmed F S, Laghrouche S, El Bagdouri M.Overview of the modelling techniques of actuator non-linearities in the engine air path[J]. Proceedings of the Institu- tion of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2013, 227(3): 443-454. [94] Qiao Yue, Zhao Tianyi, Gui Xianguo.Overview of position servo control technology and development of voice coil motor[J]. CES Transactions on Electrical Machines and Systems, 2022, 6(3): 269-278. [95] 赵华伟. 有限转角力矩电机作为柴油机电子调速执行机构的设计与研究[D]. 哈尔滨: 哈尔滨工程大学, 2008. [96] Jagadeeshwaran A, Padma S, Shankar S V, et al.Development of limited angle brushless torque motor control drive for scan mirror mechanism[J]. Inter- national Journal of Engineering and Technology, 2013, 5(5): 3907-3913. [97] Precup R E, Balint A D, Radac M B, et al.Back- tracking search optimization algorithm-based approach to PID controller tuning for torque motor systems[C]// 2015 Annual IEEE Systems Conference (SysCon) Proceedings, Vancouver, BC, Canada, 2015: 127-132. [98] Chen Jianchi, Prempain E, Wu Qinghua.Observer- based nonlinear control of a torque motor with perturbation estimation[J]. International Journal of Automation and Computing, 2006, 3(1): 84-90. [99] 许辉, 王自强. 基于神经网络的有限转角力矩电动机滑模控制[J]. 微特电机, 2015, 43(11): 39-42, 48. Xu Hui, Wang Ziqiang.Sliding mode controller of limited angel torque motor based on neural network[J]. Small & Special Electrical Machines, 2015, 43(11): 39-42, 48. [100] Zhang Y, Smith I R, Kettleborough J G.Accurate tracking control of a limited angle torque motor[J]. Electric Machines & Power Systems, 1999, 27(11): 1191-1199. [101] Du Chunyang, Li Tiecai, Cao Zhengcai.Accurate tracking control of a limited angle torque motor[C]// 38th IAS Annual Meeting on Conference Record of the Industry Applications Conference, Salt Lake City, UT, USA, 2004: 744-748. [102] 武志涛, 李帅, 程万胜. 基于扩展滑模扰动观测器的永磁直线同步电机定结构滑模位置跟踪控制[J]. 电工技术学报, 2022, 37(10): 2503-2512. Wu Zhitao, Li Shuai, Cheng Wansheng.Fixed structure sliding mode position tracking control for permanent magnet linear synchronous motor based on extended sliding mode disturbance observer[J]. Transactions of China Electrotechnical Society, 2022, 37(10): 2503-2512. [103] 韩国强, 陆哲, 吴孟霖, 等. 基于改进滑模控制策略的开关磁阻电机直接瞬时转矩控制方法[J]. 电工技术学报, 2022, 37(22): 5740-5755. Han Guoqiang, Lu Zhe, Wu Menglin, et al.Direct instantaneous torque control method for switched reluctance motor based on an improved sliding mode control strategy[J]. Transactions of China Electro- technical Society, 2022, 37(22): 5740-5755. [104] 魏惠芳, 王丽梅. 永磁直线同步电机自适应模糊神经网络时变滑模控制[J]. 电工技术学报, 2022, 37(4): 861-869. Wei Huifang, Wang Limei.Adaptive fuzzy neural network time-varying sliding mode control for permanent magnet linear synchronous motor[J]. Transactions of China Electrotechnical Society, 2022, 37(4): 861-869. [105] 汤恩生, 原劲鹏. 基于锁相环的摆动扫描控制系统模型分析[J]. 中国空间科学技术, 2013, 33(6): 74-80. Tang Ensheng, Yuan Jinpeng.Model analysis of PLL swing scanning control system[J]. Chinese Space Science and Technology, 2013, 33(6): 74-80. [106] 王劲强. 星载相机扫描镜控制系统研究[D]. 长沙: 国防科学技术大学, 2004. [107] 刘晓玮. 扫描型热像仪扫描控制技术研究[D]. 西安: 西安工业大学, 2013. [108] 刘晓玮, 江婷婷, 李扬, 等. 基于DSP的光机扫描控制技术[J]. 兵工自动化, 2015, 34(2): 86-89. Liu Xiaowei, Jiang Tingting, Li Yang, et al.Technique of scanning control based on DSP[J]. Ordnance Industry Automation, 2015, 34(2): 86-89. [109] Scattolini R, Siviero C, Mazzucco M, et al.Modeling and identification of an electromechanical internal combustion engine throttle body[J]. Control Engin- eering Practice, 1997, 5(9): 1253-1259. [110] Parlikar T A, Chang W S, Qiu Y H, et al.Design and experimental implementation of an electromagnetic engine valve drive[J]. IEEE/ASME Transactions on Mechatronics, 2005, 10(5): 482-494. [111] Qiu Yihui, Perreault D J, Keim T A, et al.Nonlinear system modeling, optimal cam design, and advanced system control for an electromechanical engine valve drive[J]. IEEE/ASME Transactions on Mechatronics, 2012, 17(6): 1098-1110. [112] 肖然, 周明, 郝守刚. 有限转角直流力矩电机位置伺服驱动器设计[J]. 微电机, 2008, 41(1): 37-39, 42. Xiao Ran, Zhou Ming, Hao Shougang.Design of position servo driver for DC limited angle torque motor[J]. Micromotors Servo Technique, 2008, 41(1): 37-39, 42. [113] 胡小飞, 王毅, 苏静静, 等. 旋转直驱伺服阀用有限转角电机的设计与研究[J]. 微特电机, 2021, 49(11): 25-29. Hu Xiaofei, Wang Yi, Su Jingjing, et al.Design and research of a lmited-angle torque motor for the rotate direct drive valve[J]. Small & Special Electrical Machines, 2021, 49(11): 25-29. [114] 付华军. 某新型RDDV伺服阀的设计与仿真分析[J]. 液压与气动, 2014(1): 45-48. Fu Huajun.Design and simulation analysis of new RDDV servovalve[J]. Chinese Hydraulics & Pneu- matics, 2014(1): 45-48. [115] Yu Jue, Zhuang Jian, Yu Dehong.Modeling and analysis of a rotary direct drive servovalve[J]. Chinese Journal of Mechanical Engineering, 2014, 27(5): 1064-1074. [116] Zhang Xinhua, Wang Tianyi, Huang Jian, et al.Design of a novel limited angle toque motor with compound Halbach array for electric direct-drive servo system in aerospace vehicle[C]//2019 22nd International Conference on Electrical Machines and Systems (ICEMS), Harbin, China, 2019: 1-6. [117] Zou Jibin, Yu Guodong, Xu Yongxiang, et al.Development of a slotless limited-angle torque motor for reaction wheels torque measurement system[J]. IEEE Transactions on Magnetics, 2014, 50(11): 1-4. [118] 李永祥, 林莘, 徐建源. 高压断路器有限转角永磁电机操动机构两种定子结构[J]. 电工技术学报, 2010, 25(5): 61-68. Li Yongxiang, Lin Xin, Xu Jianyuan.Two stator structures of limited angle permanent magnet motors for operating mechanism on high voltage circuit breaker[J]. Transactions of China Electrotechnical Society, 2010, 25(5): 61-68. [119] 王筠. 有限转角测速发电机设计[J]. 微特电机, 2004, 32(2): 16-17. Wang Yun.The design of the limited angle tacho- generator[J]. Small & Special Machines, 2004, 32(2): 16-17. [120] 马瑞卿, 刘卫国, 罗兵. 双余度有限转角力矩电动机控制技术[J]. 微电机(伺服技术), 2000, 33(3): 24-26, 34. Ma Ruiqing, Liu Weiguo, Luo Bing.Controlling of dual-redundancy limited angle torque motor[J]. Micro- motors (Servo Technique), 2000, 33(3): 24-26, 34. [121] Zhou You, Li Dawei, Huang Lihao, et al.Design of a limited-angle torque motor with magnetic zero- returner for aviation fuel valve[C]//2020 International Conference on Electrical Machines (ICEM), Gothenburg, Sweden, 2020: 654-660. [122] Overboom T T, Jansen J W, Lomonova E A, et al.Design and optimization of a rotary actuator for a two- degree-of-freedom z ϕ -module[J]. IEEE Transactions on Industry Applications, 2010, 46(6): 2401-2409.