基于三角函数正交性的永磁伺服系统机械参数辨识

doi:10.12382/bgxb.2022.0130

摘要/Abstract

摘要：

为抑制永磁伺服系统机械参数不确定对系统控制性能的影响,提出一种利用三角函数正交性进行机械参数辨识的方法。给电机施加两个不同幅值、相同角频率的机械角速度指令,通过正弦、余弦函数在不同区间内的积分实现系统摩擦系数与转动惯量的解耦,在提高辨识精度的同时消除了不定负载转矩对黏滞摩擦系数、库仑摩擦系数和转动惯量辨识结果的影响。利用辨识得到的机械参数值对负载转矩进行观测,并针对系统的摩擦转矩、负载转矩进行对应的前馈补偿。仿真和实验结果均验证了该方法的有效性,机械参数辨识误差在1%左右,进行前馈补偿后转速环的控制性能得到一定的提升。

关键词: 永磁伺服系统, 三角函数正交特性, 机械参数辨识, 不定负载转矩, 补偿

Abstract:

To mitigatethe impact of uncertain mechanical parameters on the control performance of apermanent magnet servo system, a method of mechanical parameter identification using the orthogonality of trigonometric functions is proposed. This method applies two mechanical angular velocity commands with different amplitudes but the same angular frequency to the motor.Itdecouples the friction coefficient and moment of inertia of the system through the integration of sine and cosine functions in different intervals, enhancing identification accuracy and eliminating uncertainty. The effect of load torque on the identification results of viscous friction coefficient, Coulomb friction coefficient and moment of inertia is investigated. At the same time, the load torque is observed by using the mechanical parameter values obtained from the identification, and the corresponding feed-forward compensation is performed for the friction torque and load torque of the system. The simulation and experimental results have verified the effectiveness of the method, with a mechanical parameter identification error of about 1%.The control performance of the speed loop is improved to a certain extent after the feed-forward compensation.

Key words: permanent magnet servo system, orthogonal characteristics of trigonometric functions, mechanical parameter identification, uncertain load torque, compensation

朱其新, 姜晨艳, 张国平, 朱永红. 基于三角函数正交性的永磁伺服系统机械参数辨识[J]. 兵工学报, 2023, 44(6): 1820-1828.

ZHU Qixin, JIANG Chenyan, ZHANG Guoping, ZHU Yonghong. Identification of Mechanical Parameters of Permanent Magnet Servo System Based on Orthogonal Characteristics of Trigonometric Function[J]. Acta Armamentarii, 2023, 44(6): 1820-1828.

图/表 16

图1 参数辨识及前馈补偿控制框图

Fig.1 Control block diagram of parameter identification and feedforward compensation

表1 参数设置

Table 1 Parameter setting

标识符	数值
R_s/Ω	1.5
L_d/H	0.0048
L_q/H	0.0048
φ_f/Wb	0.109
J/(kg·m²)	2.75×10^-4
B/(N·m·s·rad^-1)	0.0012
p_n	4
C/(N·m)	0.248

图2 转速指令

Fig.2 Speed instruction

图3 系统摩擦系数辨识

Fig.3 Identification of system friction coefficients

图4 转动惯量辨识

Fig.4 Moment of inertia identification

表2 机械参数辨识结果

Table 2 Identification results of mechanical parameters

参数	辨识值	真实值	误差/%
J/(kg·m²)	2.7526×10^-4	2.75×10^-4	0.95
B/(N·m·s·rad^-1)	0.001202	0.0012	0.17
C/(N·m)	0.2477	0.248	0.93

图5 负载转矩观测

Fig.5 Load torque observation

图6 无前馈补偿的转速误差

Fig.6 Speed error without feedforward compensation

图7 有摩擦前馈补偿的转速误差

Fig.7 Speed error with friction feedforward compensation

图8 有负载转矩前馈补偿的转速误差

Fig.8 Speed error with load torque feedforward compensation

图9 有摩擦前馈补偿和负载前馈补偿的转速误差

Fig.9 Speed error with load torque and friction feedforward compensation

图10 实验平台

Fig.10 Experimental platform

表3 电机参数

Table 3 Parameter of the motor

标识符	数值
R_s/Ω	4.08
L_d/H	0.00408
L_q/H	0.00408
转矩常数/(N·m·A^-1)	0.55
J/(kg·m²)	0.34×10^-4
p_n	5
转速/(r·min^-1)	3000

图11 辨识实验结果

Fig.11 Experimental identification results

图12 摩擦补偿前的波形

Fig.12 Speed error without feedforward compensation

图13 摩擦补偿后的波形

Fig.13 Speed error with feedforward compensation

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