Mechanism Analysis of Parasitic Torque in Electric Loading Systems

doi:10.16182/j.issn1004731x.joss.25-0228

Abstract

Abstract:

To address the issues of sources and mechanisms of parasitic torque in electric loading systems for aircraft actuator loads, a functional model of the electric loading system was established. Numerical simulations and Monte Carlo methods were employed to analyze the sources of parasitic torque and its primary influencing factors. The influence mechanisms and degrees of the system's external inputs and internal disturbances on parasitic torque were analyzed and validated through single-parameter and multi-parameter analyses. The results indicate that parasitic torque is predominantly influenced by factors such as loading command frequency, sensor signal bias, and loading motor parameters. In particular, the loading command frequency has the most significant effect on parasitic torque; a 10% change in loading command frequency causes a variation in parasitic torque at least 124 times greater than that caused by other factors.

Key words: electric loading system, parasitic torque, numerical simulation, frequency domain analysis, loading command frequency

CLC Number:

TP391.9

Sun Xiaozhe, Fu Zhenyu, Xu Zhaoke, Li Jianxin. Mechanism Analysis of Parasitic Torque in Electric Loading Systems[J]. Journal of System Simulation, 2026, 38(4): 1018-1029.

Figures/Tables 16

Fig. 1

Table 1

Parameter configuration

参数	数值
电机等效转动惯量 $J m / (k g ⋅ m 2)$	0.002 757 7
电机等效阻尼 $B m / (N ⋅ m ⋅ s / r a d)$	0.008
电机定子电阻 $R s / Ω$	0.016
电机定子电感 $L / m H$	0.099 86
永磁体磁通链 $Ψ f / W b$	0.013
极对数 $p n$	4
连接刚度 $K f / (N ⋅ m / r a d)$	1 200

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 2

Fig. 6

Fig. 7

Fig. 8

Table 3

Statistical analysis of parasitic torque simulation results under parameter variations

参数	超出标称多余力矩范围/%	比例/%	灵敏度 $(N ⋅ m / 10 %)$
电机电阻	0	0	—
电机电感	0.33	44.2	—
电机惯量	0	0	—
阻尼系数	0	0	—
电机磁通链	0.08	13	—
连接刚度	0.14	21	—
加载指令频率	361.69	82.6	0.75
转矩信号偏置	0.01	2	—
速度信号偏置	1.76	42.2	0.006
电流信号偏置	0.01	2	—
位置信号偏置	1.83	43.2	0.006
加载指令延迟	0	0	—

Table 3

Fig. 9

Table 4

Table 5

Fig. 10

Fig. 11

References 20

[1]	刘晓琳, 王静. 飞机舵机电动加载系统的非线性干扰抑制方法[J]. 计算机测量与控制, 2024, 32(6): 85-90, 110.
	Liu Xiaolin, Wang Jing. Nonlinear Interference Suppression Methods for Aircraft Rudder Electric Loading System[J]. Computer Measurement & Control, 2024, 32(6): 85-90, 110.
[2]	Huang Jing, Song Zhenkun, Wu Jiale, et al. Parameter Adaptive Sliding Mode Force Control for Aerospace Electro-hydraulic Load Simulator[J]. Aerospace, 2023, 10(2): 160.
[3]	Zhang Jianwei, Fan Yuanxun, Cao Dawei, et al. Backstepping Sliding Mode Control of Electric Linear Load Simulator[J]. Journal of Physics: Conference Series, 2021, 1754(1): 012111.
[4]	Li Bing, Gao Yeye, Luo Fei, et al. Research on Surplus Torque Restrain of Electrical Load Simulator Based on Compound Control[C]//2021 40th Chinese Control Conference (CCC). Piscataway: IEEE, 2021: 6744-6748.
[5]	刘宇豪. 基于自抗扰控制的电动负载模拟器加载策略研究[D]. 北京: 北京交通大学, 2023.
	Liu Yuhao. Research on Loading Strategy of Electric Load Simulator Based on Active Disturbance Rejection Control[D]. Beijing: Beijing Jiaotong University, 2023.
[6]	Zheng Yanbin, Yu Zhenglin, Ma Guoqing. Nonlinear Disturbance Observer Backstepping Control for Electric Dynamic Load Simulator[J]. Journal of Physics: Conference Series, 2020, 1676(1): 012182.
[7]	王浩. 舵面负载模拟系统控制策略研究[D]. 北京: 北京交通大学, 2021.
	Wang Hao. Research on Control Strategy of Rudder Surface Load Simulation System[D]. Beijing: Beijing Jiaotong University, 2021.
[8]	潘卫东, 沈烽, 王厚浩, 等. 电动直线负载模拟器反步控制器设计与研究[J]. 自动化与仪器仪表, 2022(3): 217-221.
	Pan Weidong, Shen Feng, Wang Houhao, et al. Design and Research of Backstepping Controller for Electric Linear Load Simulator[J]. Automation & Instrumentation, 2022(3): 217-221.
[9]	Dai Changhua, Chen Guoying, Zong Changfu, et al. Precise Compound Control of Loading Force for Electric Load Simulator of Electric Power Steering Test Bench[J]. Chinese Journal of Mechanical Engineering, 2022, 35(1): 8.
[10]	朱红, 齐蓉, 李玉忍. 电动加载实验台多余力消除方法[J]. 电力系统及其自动化学报, 2005, 17(3): 55-58.
	Zhu Hong, Qi Rong, Li Yuren. Elimination Method of Plus Torque on the Electric Load Test-bed[J]. Proceedings of the CSU-EPSA, 2005, 17(3): 55-58.
[11]	李成功, 靳红涛, 焦宗夏. 电动负载模拟器多余力矩产生机理及抑制[J]. 北京航空航天大学学报, 2006, 32(2): 204-208.
	Li Chenggong, Jin Hongtao, Jiao Zongxia. Mechanism and Suppression of Extraneous Torque of Motor Driver Load Simulator[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(2): 204-208.
[12]	方强. 被动式力矩伺服控制系统设计方法及应用研究[D]. 哈尔滨: 哈尔滨工业大学, 2006.
	Fang Qiang. Research on Design Method for Passive Torque Servo Control System and Its Application[D]. Harbin: Harbin Institute of Technology, 2006.
[13]	孙晓哲, 侯东, 杨建忠. 双余度机电作动器力纷争机理及敏感性[J]. 航空学报, 2023, 44(增1): 195-206.
	Sun Xiaozhe, Hou Dong, Yang Jianzhong. Mechanism and Sensitivity of Force Fight in Dual Redundant Electromechanical Actuators[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 195-206.
[14]	刘晓琳, 李晋恺. 舵机电动负载模拟器迭代学习控制[J]. 北京航空航天大学学报, 2024, 50(9): 2727-2738.
	Liu Xiaolin, Li Jinkai. Iterative Learning Control of Electric Load Simulator of Aircraft Steering Gear[J]. Journal of Beijing University of Aeronautics and Astronautics, 2024, 50(9): 2727-2738.
[15]	Zhang Pan, Shi Zhaoyao, Yu Bo, et al. Research on a Sensorless ADRC Vector Control Method for a Permanent Magnet Synchronous Motor Based on the Luenberger Observer[J]. Processes, 2024, 12(5): 906.
[16]	Yuan Qingqing, Xiao Rongyan, Wang Jingxia, et al. Double-virtual-vector-based Model Predictive Torque Control for Dual Three-phase PMSM[J]. Electronics, 2025, 14(1): 50.
[17]	代明光, 齐蓉. 具有控制时滞的电动加载系统迭代学习复合控制[J]. 北京航空航天大学学报, 2020, 46(2): 340-349.
	Dai Mingguang, Qi Rong. Composite Iterative Learning Control for Electric Dynamic Loading System with Control Time Delay[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(2): 340-349.
[18]	Li Jianying, Li Weidong, Liang Heng, et al. A Review of the Research on Electro-hydraulic Load Simulator and Characteristics with Improvement Methods[J]. Recent Patents on Engineering, 2024, 18(3): 45-56.
[19]	Ahn Hyeongki, Kim Sangkyeum, Park Jihoon, et al. Adaptive Quick Sliding Mode Reaching Law and Disturbance Observer for Robust PMSM Control Systems[J]. Actuators,2024, 13(4): 136.
[20]	Chen Shaotang, Namuduri C, Mir S. Controller-induced Parasitic Torque Ripples in a PM Synchronous Motor[J]. IEEE Transactions on Industry Applications, 2002, 38(5): 1273-1281.

分类	影响多余力矩的因素	表现形式
加载电机参数误差	电机电阻电机电感电机惯量阻尼系数电机磁通链	电阻误差30% 电感误差10% 转动惯量误差10% 阻尼系数误差30% 磁通链误差6%
联轴器	连接刚度	连接刚度误差25%
加载指令	加载指令频率	加载频率范围0~5 Hz
控制器及传感器误差	转矩信号偏置速度信号偏置电流信号偏置位置信号偏置加载指令延迟	2%的转矩信号偏置 2%的速度信号偏置 2%的电流信号偏置 2%的位置信号偏置 1 kHz内的传输速率

参数	结果	原因
电机电阻	相位差约6°	与控制器零极点无法对消产生附加极点
电机电感
阻尼系数
电机惯量	相位差约6°，敏感度0.002 9
连接刚度	相位差约6°，敏感度0.012	改变系统增益
电机磁通链	相位差约6°	改变系统增益
加载指令频率	相位差0.49°~178°	PI控制器无法响应高频指令及扰动
转矩信号偏置	相位差约6°	积分器累积误差，响应速度降低
电流信号偏置
速度信号偏置
位置信号偏置
加载指令延迟		引入延迟环节

参数	主频率/Hz	主频率幅值	THD/%
电机电阻	1	3.863	1.79
电机电感	1	3.863	1.79
电机惯量	1	3.863	1.79
摩擦系数	1	3.862	1.80
电机磁通链	1	3.874	1.80
连接刚度	1	3.863	1.73
加载指令频率	4.98	8.339	9.79
转矩信号偏置	1	3.866	1.80
速度信号偏置	1	3.875	1.84
电流信号偏置	1	3.867	1.80
位置信号偏置	1	3.862	1.81
加载指令延迟	1	3.871	1.83