基于特征模型的5阶关节伺服系统扰动补偿策略

doi:10.12382/bgxb.2022.0941

摘要/Abstract

摘要：

针对工业机器人关节伺服系统负载时变和模型不确定性问题,提出将线性扩张状态观测器和基于特征模型的全系数自适应控制相结合的控制策略。建立双惯量柔性关节动力学模型并得到关节伺服系统5阶扩张状态方程。基于该模型设计5阶线性扩张状态观测器,通过该观测器估计系统总扰动并进行扰动补偿,并证明观测器收敛性。基于特征建模的方法,通过实验数据和梯度下降法对特征参数进行辨识,并基于参数值设计全系数自适应控制律,将该控制律结合线性扩张状态观测器设计一种控制策略,对系统进行精确控制。实验结果表明,新的控制策略使系统在变负载扰动工况下的定位精度达到0.003°,正弦信号跟踪误差保持在0.92°以内,系统具有较强的鲁棒性和控制精度。

关键词: 关节伺服系统, 5阶线性扩张状态观测器, 特征建模, 全系数自适应控制, 扰动补偿

Abstract:

A control strategy combining the linear extended state observer and full coefficient adaptive control based on characteristic model is proposed for the time-varying load and model uncertainties of industrial robot joint servomechanism. A two-inertia flexible joint dynamics model is established, and the equation of the fifth-order extended state of joint servomechanism was obtained. A fifth-order linear extended state observer is designed based on the model, through which the total disturbance of the system is estimated and compensated, and the convergence of the observer is proved. Based on the method of characteristic modeling, the characteristic parameters are identified by experimental data and gradient descent method, and the full coefficient adaptive control law is designed based on the parameter values. A control strategy is designed to accurately control the system by combining the control law with the linear extended state observer. The experimental results show that the proposed control strategy is used to make the positioning accuracy of the system reach 0.003° under the condition of variable load disturbance and the sinusoidal signal tracking error keep within 0.92°. The system has strong robustness and control accuracy.

Key words: joint servomechanism, fifth-order linear extended state observer, characteristic modeling, full coefficient adaptive control, disturbance compensation

中图分类号:

TP242.2

张天艺, 郑颖, 裘信国, 季行健, 金晓航. 基于特征模型的5阶关节伺服系统扰动补偿策略[J]. 兵工学报, 2024, 45(1): 276-287.

ZHANG Tianyi, ZHENG Ying, QIU Xinguo, JI Xingjian, JIN Xiaohang. Disturbance Compensation Strategy for Fifth-order Joint Servomechanism Based on Characteristic Model[J]. Acta Armamentarii, 2024, 45(1): 276-287.

图/表 21

图1 关节伺服系统双惯量模型

Fig.1 Two-inertia model of joint servomechanism

图2 关节伺服系统动力学模型

Fig.2 Dynamic model of joint servomechanism

图3 特征模型误差验证

Fig.3 Error verification of characteristic model

表1 伺服系统参数

Table 1 Parameters of servomechanism

参数	数值
反电动势C_e/(V·rad·s^-1)	0.0764
转矩常数K_t/(N·m·A^-1)	0.112
转动惯量J_m/(kg·m²)	0.175×10^-4
定子电阻R_s/Ω	0.15
黏滞摩擦系数B/(N·m·(rad·s^-1)^-1)	0.3
减速比i	100:1
PWM功放系数K_u	8.32
额定负载惯量J_L/(kg·m²)	0.025
联轴器刚度系数k_s/(N·m·rad^-1)	3000
齿隙2θ/rad	0.00175

表2 特征参数辨识结果

Table 2 Identification results of characteristic parameters

信号	$\hat{f}_{1}$	$\hat{f}_{2}$	$\hat{g}_{0}$	$\tilde{Y} /\left(^{\circ}\right) $
	1.3461	-0.3465	3.0659×10^-5	0.026
2	1.3472	-0.3469	6.6071×10^-4	0.021
3	1.3475	-0.3481	5.8614×10^-4	0.035

图4 关节伺服系统控制结构

Fig.4 Control structure of joint servomechanism

图5 位置反馈量的频域特性曲线

Fig.5 Frequency domain characteristic curve of position feedback quantity

图6 控制器输出的频域特性曲线

Fig.6 Frequency domain characteristic curve of controller output

图7 实验平台

Fig.7 Experimental platform

图8 阶跃响应曲线

Fig.8 Step response curve

图9 阶跃跟踪误差

Fig.9 Step tracking error

图10 特征模型误差

Fig.10 Characteristic model error

图11 C4位置和速度估计误差

Fig.11 Position and velocity estimated errors of C4

图12 连续阶跃响应曲线

Fig.12 Continuous step response curves

图13 连续阶跃跟踪误差

Fig.13 Continuous step tracking error

图14 正弦跟踪曲线

Fig.14 Sinusoidal tracking curve

图15 正弦跟踪误差

Fig.15 Sinusoidal tracking error

表3 性能指标

Table 3 Performance indicators(°)

控制器	指标
控制器	M_e	μ	σ
C1	9.025	5.155	2.394
C2	8.736	0.821	0.842
C3	4.699	1.285	0.939
C4	1.952	0.594	0.295

图16 正弦跟踪曲线

Fig.16 Sinusoidal tracking curve

图17 正弦跟踪误差

Fig.17 Sinusoidal tracking error

表4 性能指标

Table 4 Performance indicators(°)

控制器	指标
控制器	M_e	μ	σ
C1	25.436	15.698	7.026
C2	14.176	8.926	3.977
C3	11.461	2.834	1.850
C4	10.221	0.629	1.193

参考文献 20

[1]	牟方厉, 吴丹, 董云飞. 具有多层感知器力矩补偿的机器人自抗扰控制[J]. 控制理论与应用, 2020, 37(6): 1397-1405.
	MOU F L, WU D, DONG Y F. Active disturbance rejection control with multilayer perceptron compensating network for robot systems[J]. Control Theory and Applications, 2020, 37(6): 1397-1405. (in Chinese)
[2]	王立新, 赵丁选, 刘福才, 等. 电液比例伺服力加载自抗扰控制[J]. 机械工程学报, 2020, 56(18): 216-225. doi: 10.3901/JME.2020.18.216
	WANG L X, ZHAO D X, LIU F C, et al. Active disturbance rejection control for electro-hydraulic proportional servo force loading[J]. Journal of Mechanical Engineering: 2020, 56(18): 216-225. (in Chinese)
[3]	徐驰, 赵希梅. 永磁直线同步电动机智能递归非奇异终端滑模控制[J]. 控制理论与应用, 2022, 39(7): 1242-1250.
	XU C, ZHAO X M. Intelligent recursive nonsingular terminal sliding mode control of permanent magnet linear synchronous motor[J]. Control Theory & Applications, 2022, 39(7): 1242-1250. (in Chinese)
[4]	聂守成, 钱林方, 陈志群, 等. 基于干扰观测器的弹丸协调器电液伺服系统自适应滑模控制[J]. 兵工学报, 2020, 41(9): 1745-1751. doi: 10.3969/j.issn.1000-1093.2020.09.006
	NIE S C, QIAN L F, CHEN Z Q, et al. Adaptive sliding mode control based on disturbance observer for bullets coordinator electro-hydraulic servo system[J]. Acta Armamentarii, 2020, 41(9): 1745-1751. (in Chinese)
[5]	苗双全, 张宝泉, 王明超, 等. 基于扰动观测器的机载光电稳定平台自适应指数时变滑模控制[J]. 兵工学报, 2022, 43(7): 1636-1645. doi: 10.12382/bgxb.2021.0229
	MIAO S Q, ZHANG B Q, WANG M C, et al. Adaptive exponential time-varying sliding mode control based on disturbance observer for photoelectric stabilized airborne platform[J]. Acta Armamentarii, 2022, 43(7): 1636-1645. (in Chinese)
[6]	丁力, 姚勇, 巢渊, 等. 面向水质采样的绳驱动空中机械臂抗干扰控制[J]. 农业机械学报, 2022, 53(8):452-458.
	DING L, YAO Y, CHAO Y, et al. Disturbance rejection control for cable-driven aerial manipulator applied on water samples[J]. Transactions of the Chinese Society for Agricultural Machinery, 2022, 53(8): 452-458. (in Chinese)
[7]	王会明, 张扬, 王雪闯. 移动机器人的线性自抗扰控制设计与实验验证[J]. 控制理论与应用, 2022, 39(7): 1289-1296.
	WANG H M, ZHANG Y, WANG X C. Design and implementation of linear active disturbance rejection control for mobile robots[J]. Control Theory & Applications, 2022, 39(7): 1289-1296. (in Chinese)
[8]	于欣波, 贺威, 薛程谦, 等. 基于扰动观测器的机器人自适应神经网络跟踪控制研究[J]. 自动化学报, 2019, 45(7): 1307-1324.
	YU X B, HE W, XUE C Q, et al. Disturbance observer-based adaptive neural network tracking control for robots[J]. Acta Automatica Sinica, 2019, 45(7): 1307-1324. (in Chinese)
[9]	WU H X, HU J, XIE Y C. Characteristic model-based all-coefficient adaptive control method and its applications[J]. IEEE Transactions on Systems, Man, and Cybernetics, 2007, 37(2): 213-221.
[10]	吴宏鑫, 胡军, 解永春. 基于特征模型的智能自适应控制[M]. 北京: 中国科学技术出版社, 2009.
	WU H X, HU J, XIE Y C. Characteristic model-based intelligent adaptive control[M]. Beijing: Science and Technology Press of China, 2009. (in Chinese)
[11]	孟斌, 唐青原, 吴宏鑫. 特征模型理论及其在火星气动捕获制导中的应用[J]. 中国科学:技术科学, 2020, 50(5): 483-492.
	MENG B, TANG Q Y, WU H X. Characteristic model and its applications in mars aerocapture guidance[J]. Scientia Sinica Technologica, 2020, 50(5): 483-492. (in Chinese) doi: 10.1360/SST-2019-0304 URL
[12]	李超, 何英姿, 胡勇. 基于特征模型的挠性航天器接触消旋控制[J]. 空间控制技术与应用, 2022, 48(2):54-61.
	LI C, HE Y Z, HU Y. Characteristic model-based contact racemization control for flexible spacecraft[J]. Aerospace Control and Application, 2022, 48(2): 54-61. (in Chinese)
[13]	张世俊, 邢琰. 参数不确定机器人关节特征建模与自适应控制研究[J]. 载人航天, 2019, 25(5): 625-630.
	ZHANG S J, XING Y. Research on joint characteristics modeling and adaptive control of robot with uncertain parameters[J]. Manned Spaceflight, 2019, 25(5):625-630. (in Chinese)
[14]	高熠, 吴益飞, 关妍. 基于特征模型的双电机伺服系统2阶离散滑模控制[J]. 机械设计与制造工程, 2020, 49(3): 29-34.
	GAO Y, WU Y F, GUAN Y. Second-order discrete sliding mode control of the double-motor servo system based on feature model[J]. Machine Design and Manufacturing Engineering, 2020, 49(3):29-34. (in Chinese)
[15]	王翔, 吴益飞, 高阳, 等. 基于扩展状态观测器的伺服系统特征建模和自适应滑模控制[J]. 南京理工大学学报(自然科学版), 2019, 43(3): 261-268,274.
	WANG X, WU Y F, GAO Y, et al. Extended state observer-based characteristic modeling and adaptive sliding-mode control for servo system[J]. Journal of Nanjing University of Science and Technology, 2019, 43(3): 261-268, 274. (in Chinese)
[16]	HUANG Y, XUE W C. Active disturbance rejection control: methodology and theoretical analysis[J]. ISA Transactions, 2014, 53(4): 963-976. doi: 10.1016/j.isatra.2014.03.003 pmid: 24742958
[17]	ZHANG H, ZHAO S, GAO Z. An active disturbance rejection control solution for the two-mass-spring benchmark problem[C]// Proceedings of the American Control Conference.Boston,MA,US:IEEE, 2016:1566-1571.
[18]	ISKANDAR M, OTT C, EIBERGER O, et al. Joint-level control of the DLR lightweight robot SARA[C]// Proceedings of 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems. Piscataway,NJ, US: IEEE, 2020: 8903-8910.
[19]	ZUO Z Y, JU X L, DING Z T. Control of gear transmission servo systems with asymmetric deadzone nonlinearity[J]. IEEE Transactions on Control Systems Technology, 2016, 24(4): 1472-1479. doi: 10.1109/TCST.2015.2493119 URL
[20]	吴宏鑫, 王颖, 解永春. 非线性系统的特征建模与控制方法[J]. 控制工程, 2002(6):1-7.
	WU H X, WANG Y, XIE Y C. Characteristic modeling and control method of nonlinear system[J]. Control Engineering, 2002(6):1-7. (in Chinese)