机械臂模糊超螺旋二阶滑模轨迹跟踪控制

doi:10.16182/j.issn1004731x.joss.21-0066

系统仿真学报 ›› 2022, Vol. 34 ›› Issue (6): 1343-1352.doi: 10.16182/j.issn1004731x.joss.21-0066

• 仿真模型/系统置信度评估技术 • 上一篇下一篇

机械臂模糊超螺旋二阶滑模轨迹跟踪控制

杜宝林(), 朱大昌(), 盘意华

广州大学机械与电气工程学院，广东广州 510006

收稿日期:2021-01-22 修回日期:2021-03-21 出版日期:2022-06-30 发布日期:2022-06-16
通讯作者: 朱大昌 E-mail:15119698824@163.com;zdc98998@gzhu.edu.cn
作者简介:杜宝林(1997-)，男，硕士生，研究方向为机器人非线性控制。E-mail：15119698824@163.com
基金资助:
国家自然科学基金(51905115);广州市教育局高校科研项目(202032821)

Fuzzy Super-twisting Second Order Sliding Mode Trajectory Tracking Control for Robotic Manipulator

Baolin Du(), Dachang Zhu(), Yihua Pan

School of Mechanical and Electrical Engineering, Guangzhou University, Guangzhou 510006, China

Received:2021-01-22 Revised:2021-03-21 Online:2022-06-30 Published:2022-06-16
Contact: Dachang Zhu E-mail:15119698824@163.com;zdc98998@gzhu.edu.cn

摘要/Abstract

摘要：

针对工业机械臂模型误差和外部干扰等不确定性因素对末端轨迹跟踪精度的影响，设计了一种新的模糊自适应超螺旋二阶滑模轨迹跟踪控制方法。基于机械臂动力学模型，设计一种新的非奇异终端滑模面，采用超螺旋算法设计二阶滑模控制律；为解决滑模控制只能在已知扰动边界的情况下对匹配扰动进行补偿问题，结合模糊推理算法实现对系统未知不确定性的在线补偿，采用Lyapunov理论证明了闭环控制系统的稳定性。仿真与实验对比表明：该控制方法可使机械臂在复杂不确定性因素下实现末端轨迹精确跟踪，并对系统抖振现象进行有效抑制。

关键词: 二阶滑模控制, 模糊推理算法, 不确定机械臂, 轨迹跟踪

Abstract:

A fuzzy super-twisting second order sliding mode control method is proposed for the uncertainties of the model error and external disturbance on the trajectory tracking accuracy of robotic manipulator. Based on the dynamic model of the robotic, a new non-singular terminal sliding mode manifold is designed, and an improved super-twisting algorithm is used to design the second order sliding mode controller. In order to solve the problem that the matching disturbance can only be compensated under the condition of the known disturbance boundary in the sliding mode control, the fuzzy logic algorithm is used to carryout the online compensation for uncertainty of the system. The stability of the closed-loop control system is guaranteed by Lyapunov theory. The simulation and experiment results show that the proposed controller can track the trajectory accurately under the uncertainty of the robotic and can effectively suppress the chattering phenomenon of the system.

Key words: second order sliding mode control, fuzzy reasoning algorithm, uncertain robotic manipulator, trajectory tracking

中图分类号:

TP273

杜宝林, 朱大昌, 盘意华. 机械臂模糊超螺旋二阶滑模轨迹跟踪控制[J]. 系统仿真学报, 2022, 34(6): 1343-1352.

Baolin Du, Dachang Zhu, Yihua Pan. Fuzzy Super-twisting Second Order Sliding Mode Trajectory Tracking Control for Robotic Manipulator[J]. Journal of System Simulation, 2022, 34(6): 1343-1352.

图/表 13

表1

模糊控制规则

$s$	$s ˙$
$s$	NB	NM	ZO	PM	PB
NB	PB	PB	PB	PM	ZO
NM	PB	PM	PM	ZO	NM
ZO	PM	PM	ZO	NM	NM
PM	PM	ZO	NM	NM	NM
PB	ZO	NM	NB	NB	NB

表1

图1

图2

表2

三自由度机械臂模型参数

连杆	质量 $m i$ /kg	长度 $L i$ /m	质心距离 $r i$ /m	惯量 $I i$ /(kg·m²)
1	1.50	0	0	0.35
2	1.50	0.20	0.10	0.30
3	1.00	0.20	0.10	0.30

表2

图3

图4

图5

表3

各控制器性能参数

性能指标	PID	NTSMC	本文方法
关节1跟踪误差 $\| \| e 1 \| \| R M S$ /rad	0.021 7	0.018 4	0.008 8
关节2跟踪误差 $\| \| e 2 \| \| R M S$ /rad	0.035 2	0.021 0	0.013 0
关节3跟踪误差 $\| \| e 3 \| \| R M S$ /rad	0.029 6	0.023 8	0.014 4
关节1输出力矩 $\| \| τ 1 \| \| R M S$ /(N·m)	0.617 9	4.268 3	1.258 7
关节2输出力矩 $\| \| τ 2 \| \| R M S$ /(N·m)	4.655 8	5.923 9	3.400 7
关节3输出力矩 $\| \| τ 3 \| \| R M S$ /(N·m)	1.710 3	2.743 5	1.290 8

表3

图6

图7

图8

图9

表4

各控制器性能参数(实验条件下)

控制器	PID	NTSMC	本文方法
关节1跟踪误差 $\| \| e 1 \| \| R M S$ /rad	0.022 8	0.020 3	0.009 1
关节2跟踪误差 $\| \| e 1 \| \| R M S$ /rad	0.035 9	0.025 7	0.013 2
关节1输出力矩 $\| \| τ 1 \| \| R M S$ /(N·m)	1.163 8	1.802 5	1.169 6
关节2输出力矩 $\| \| τ 2 \| \| R M S$ /(N·m)	4.211 0	4.828 3	4.321 9

表4

参考文献 16

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机械臂模糊超螺旋二阶滑模轨迹跟踪控制

Fuzzy Super-twisting Second Order Sliding Mode Trajectory Tracking Control for Robotic Manipulator

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$s$	$s ˙$
$s$	NB	NM	ZO	PM	PB
NB	PB	PB	PB	PM	ZO
NM	PB	PM	PM	ZO	NM
ZO	PM	PM	ZO	NM	NM
PM	PM	ZO	NM	NM	NM
PB	ZO	NM	NB	NB	NB

$s$	$s ˙$
$s$	NB	NM	ZO	PM	PB
NB	PB	PB	PB	PM	ZO
NM	PB	PM	PM	ZO	NM
ZO	PM	PM	ZO	NM	NM
PM	PM	ZO	NM	NM	NM
PB	ZO	NM	NB	NB	NB

$s$	$s ˙$
$s$	NB	NM	ZO	PM	PB
NB	PB	PB	PB	PM	ZO
NM	PB	PM	PM	ZO	NM
ZO	PM	PM	ZO	NM	NM
PM	PM	ZO	NM	NM	NM
PB	ZO	NM	NB	NB	NB