Design of Cost Function without Weighting Factor for Predictive Torque Control of Surface-Mounted Permanent Magnet Synchronous Motor
Miao Yiru1, Song Pengyun2, Lü Mingcheng1, Liu Xiao1, Huang Shoudao1
1. College of Electrical and Information Engineering Hunan University Changsha 410082 China; 2. College of Electrical Engineering Southwest Minzu University Chengdu 610041 China
Abstract With high efficiency, high power density, and reliable operation, permanent magnet synchronous motors are widely used in electric vehicles, wind power generation, and high-performance servos. The research of PMSM high-performance control technology is the necessary way to improve the performance of PMSM systems. Compared with the two traditional control strategies of field-oriented control (FOC) and direct torque control (DTC), model predictive control (MPC) has the advantages of fast dynamic response, flexible objective function configuration, and easy-to-handle nonlinear constraints. MPC can be divided into model predictive current control (MPCC) and model predictive torque control (MPTC), which can directly control torque and magnetic chain by introducing torque and magnetic chain into the objective function. However, MPTC adds a weighting factor to the magnetic chain term in the cost function to regulate the degree of influence of the flux linkage term on the value of the cost function. Different weighting factors significantly impact the control performance of the motor. The currently proposed methods based on fuzzy, particle swarm, and cascade sorting all need to be revised to handle the problems of high computational power and complex implementation process. Therefore, a conversion method based on the cost function of the torque chain is proposed, which unifies the magnitudes of the two. Firstly, the discrete current, torque, and flux linkage equations of PMSM are derived. After the torque equation is substituted into the current equation and the inverse Park transformation is performed on it, the torque cost function is converted into a distance expression from the endpoint of the voltage vector to a moving line. Similarly, the cost function of the flux linkage is converted into the expression of the distance from the endpoint of the voltage vector to a moving circle. Thus, the cost function composed of torque and flux linkage is replaced by the distance cost function, avoiding the weighting coefficient design due to the non-uniformity of dimensions. Finally, the design method of the outer speed loop PI controller is presented. Simulation and experiment are carried out to compare the steady and dynamic performances of the three methods, namely NWF-PTC proposed in this paper, traditional predictive torque control (TPTC), and model predictive flux control (MPFC) proposed in Ref.[17]. NWF-PTC can consider the steady state performance of the torque and flux linkage and achieve the minimum current harmonic distortion without setting the weight coefficient. Under the two dynamic conditions of a sudden change of torque or the command value of the speed, the time of overshoot and adjustment of NWF-PTC is also slightly lower than those of the other two methods. Simulation and experimental results verify the feasibility and correctness of the proposed method. The following two conclusions are as follows: (1) The cost function of the torque and flux can be equivalent to the expression of the distance from the endpoint of the voltage vector to a moving line and a moving circle, respectively. Thus the unification of the dimensions is realized. (2) On the premise of not deteriorating the dynamic performance, the proposed method can consider the steady-state performance of torque and flux, and improve the waveform quality of the stator current.
[1] Dong Zhiping, Liu Chunhua, Song Zaixin, et al.Suppression of dual-harmonic components for five-phase series-winding PMSM[J]. IEEE Transactions on Transportation Electrification, 2022, 8(1): 121-134. [2] 刘平, 陈梓健, 苗轶如, 等. 基于开关瞬态反馈的SiC MOSFET有源驱动电路[J]. 电工技术学报, 2022, 37(17): 4446-4457. Liu Ping, Chen Zijian, Miao Yiru, et al.Active gate driver for SiC MOSFET based on switching transient feedback[J]. Transactions of China Electrotechnical Society, 2022, 37(17): 4446-4457. [3] 刘平, 李海鹏, 苗轶如, 等. 基于内置温度传感器的碳化硅功率模块结温在线提取方法[J]. 电工技术学报, 2021, 36(12): 2522-2534. Liu Ping, Li Haipeng, Miao Yiru, et al.Online junction temperature extraction for SiC module based on built-in temperature sensor[J]. Transactions of China Electrotechnical Society, 2021, 36(12): 2522-2534. [4] 王彦哲, 周胜, 王宇, 等. 中国核电和其他电力技术环境影响综合评价[J]. 清华大学学报(自然科学版), 2021, 61(4): 377-384. Wang Yanzhe, Zhou Sheng, Wang Yu, et al.Com-prehensive assessment of the environmental impact of China’s nuclear and other power generation tech-nologies[J]. Journal of Tsinghua University (Science and Technology), 2021, 61(4): 377-384. [5] Xiao Meng, Shi Tingna, Yan Yan, et al.Predictive torque control of permanent magnet synchronous motors using flux vector[J]. IEEE Transactions on Industry Applications, 2018, 54(5): 4437-4446. [6] 秦艳忠, 阎彦, 陈炜, 等. 永磁同步电机参数误差补偿-三矢量模型预测电流控制[J]. 电工技术学报, 2020, 35(2): 255-265. Qin Yanzhong, Yan Yan, Chen Wei, et al.Three-vector model predictive current control strategy for permanent magnet synchronous motor drives with parameter error compensation[J]. Transactions of China Electrotechnical Society, 2020, 35(2): 255-265. [7] Petkar S G, Eshwar K, Thippiripati V K.A modified model predictive current control of permanent magnet synchronous motor drive[J]. IEEE Transactions on Industrial Electronics, 2021, 68(2): 1025-1034. [8] Niu Feng, Chen Xi, Huang Shaopo, et al.Model predictive current control with adaptive-adjusting timescales for PMSMs[J]. CES Transactions on Elec-trical Machines and Systems, 2021, 5(2): 108-117. [9] Zhang Xiaoguang, Hou Benshuai.Double vectors model predictive torque control without weighting factor based on voltage tracking error[J]. IEEE Transactions on Power Electronics, 2018, 33(3): 2368-2380. [10] 李家祥, 汪凤翔, 柯栋梁, 等. 基于粒子群算法的永磁同步电机模型预测控制权重系数设计[J]. 电工技术学报, 2021, 36(1): 50-59, 76. Li Jiaxiang, Wang Fengxiang, Ke Dongliang, et al.Weighting factors design of model predictive control for permanent magnet synchronous machine using particle swarm optimization[J]. Transactions of China Electrotechnical Society, 2021, 36(1): 50-59, 76. [11] 梅杨, 易高. 间接矩阵变换器-异步电机调速系统模型预测控制权重系数自整定方法[J]. 电工技术学报, 2020, 35(18): 3938-3948. Mei Yang, Yi Gao.A weighting factor self-tuning method in model prediction control for indirect matrix converter with induction motor system[J]. Transa-ctions of China Electrotechnical Society, 2020, 35(18): 3938-3948. [12] Alireza Davari S, Khaburi D A, Kennel R.An improved FCS-MPC algorithm for an induction motor with an imposed optimized weighting factor[J]. IEEE Transactions on Power Electronics, 2012, 27(3): 1540-1551. [13] Kodumur Meesala R E, Kunisetti V P K, Kumar Thippiripati V. Enhanced predictive torque control for open end winding induction motor drive without weighting factor assignment[J]. IEEE Transactions on Power Electronics, 2019, 34(1): 503-513. [14] Norambuena M, Rodriguez J, Zhang Zhenbin, et al.A very simple strategy for high-quality performance of AC machines using model predictive control[J]. IEEE Transactions on Power Electronics, 2018, 34(1): 794-800. [15] Zhang Yongchang, Zhang Boyue, Yang Haitao, et al.Generalized sequential model predictive control of IM drives with field-weakening ability[J]. IEEE Transa-ctions on Power Electronics, 2019, 34(9): 8944-8955. [16] Kusuma E, Eswar K M R, Vinay Kumar T. An effective predictive torque control scheme for PMSM drive without involvement of weighting factors[J]. IEEE Journal of Emerging and Selected Topics in Power Electronics, 2021, 9(3): 2685-2697. [17] 陈炜, 曾思坷, 张国政, 等. 永磁同步电机改进型三矢量模型预测转矩控制[J]. 电工技术学报, 2018, 33(增刊2): 420-426. Chen Wei, Zeng Sike, Zhang Guozheng, et al.Improved three-vector model predictive torque con-trol of permanent magnet synchronous motor[J]. Transactions of China Electrotechnical Society, 2018, 33(S2): 420-426. [18] 张晓光, 张亮, 侯本帅. 永磁同步电机优化模型预测转矩控制[J]. 中国电机工程学报, 2017, 37(16): 4800-4809, 4905. Zhang Xiaoguang, Zhang Liang, Hou Benshuai.Improved model predictive torque control of per-manent magnet synchronous motor[J]. Proceedings of the CSEE, 2017, 37(16): 4800-4809, 4905. [19] 赵勇, 黄文新, 林晓刚, 等. 基于权重系数消除和有限控制集优化的双三相永磁容错电机快速预测直接转矩控制[J]. 电工技术学报, 2021, 36(1): 3-14. Zhao Yong, Huang Wenxin, Lin Xiaogang, et al.Fast predictive direct torque control of dual three-phase permanent magnet fault tolerant machine based on weighting factor elimination and finite control set optimization[J]. Transactions of China Electrotech-nical Society, 2021, 36(1): 3-14. [20] 夏长亮, 张天一, 周湛清, 等. 结合开关表的三电平逆变器永磁同步电机模型预测转矩控制[J]. 电工技术学报, 2016, 31(20): 83-92, 110. Xia Changliang, Zhang Tianyi, Zhou Zhanqing, et al.Model predictive torque control with switching table for neutral point clamped three-level inverter-fed permanent magnet synchronous motor[J]. Transa-ctions of China Electrotechnical Society, 2016, 31(20): 83-92, 110. [21] Zhang Yongchang, Yang Haitao.Model-predictive flux control of induction motor drives with switching instant optimization[J]. IEEE Transactions on Energy Conversion, 2015, 30(3): 1113-1122. [22] 於锋, 朱晨光, 吴晓新, 等. 基于矢量分区的永磁同步电机三电平双矢量模型预测磁链控制[J]. 电工技术学报, 2020, 35(10): 2130-2140. Yu Feng, Zhu Chenguang, Wu Xiaoxin, et al.Two-vector-based model predictive flux control of three-level based permanent magnet synchronous motor with sector subregion[J]. Transactions of China Electrotechnical Society, 2020, 35(10): 2130-2140.
2023, Vol. 38 
