含边界层的机械臂分数阶滑模控制

刘世杰; 黄志来; 杨明星; 徐培民

含边界层的机械臂分数阶滑模控制

刘世杰^{a, b,},
黄志来^{a, b, ,},
杨明星^{a, b},
徐培民^{a, b}

a.
安徽工业大学特种重载机器人安徽省重点实验室, 马鞍山 243000
b.
机械工程学院, 马鞍山 243000

基金项目: 国家自然科学基金资助项目(52005006)

详细信息

作者简介:
刘世杰(1996−)，男，在读硕士，研究方向为动力学及控制. E-mail: liushijie9687@163.com

通讯作者:
黄志来(1983−)，男，讲师，博士，研究方向为动力学及控制. E-mail: zhilai_huang@foxmail.com

中图分类号: TP241
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- 被引次数: 0
出版历程
- 收稿日期: 2021-08-31
- 刊出日期: 2022-02-23

Fractional-order sliding mode control of robotic arms with boundary layer

LIU Shijie^{a, b
,},
HUANG Zhilai^{a, b
, ,},
YANG Mingxing^{a, b},
XU Peimin^{a, b}

a.
Anhui Province Key Laboratory of Special Heavy Load Robot
b.
School of Mechanical Engineering, Anhui University of Technology, Ma’anshan 243000, China

摘要

摘要: 针对含扰动的机械臂系统，在经典滑模控制基础上引入分数阶微积分构造分数阶滑模面，同时在趋近律中设置边界层，用饱和函数替代符号函数以削弱滑模面的抖振现象，从而获得一种含边界层的机械臂分数阶滑模控制，并通过李雅普诺夫直接法证明其收敛性. 算例以两自由度机械臂系统为被控对象，仿真结果表明，相比于经典的滑模控制，含边界层的机械臂分数阶滑模控制可通过调节微分阶次获得更好的收敛性，实现精确的轨迹跟踪.
- 滑模控制 /
- 边界层法 /
- 饱和函数 /
- 分数阶微积分 /
- 机械臂
Abstract: For the robotic arm system with perturbation, the fractional-order calculus was introduced to construct a fractional-order sliding mode surface based on classical sliding mode control. While a boundary layer had set in the reaching law, and the sign function was replaced with the saturation function to weaken chattering phenomenon of the sliding mode surface to obtain a fractional-order sliding mode control of robotic arms with boundary layer, and its convergence had proved by the direct method of Lyapunov. Example with a two-degree-of-freedom robotic arm system as the controlled object, the simulation result shows that the fractional-order sliding mode control of robotic arms with boundary layer can achieve better convergence and accurate trajectory tracking by adjusting the differential order compared with the classical sliding mode control.
- sliding mode control /
- boundary layer method /
- saturation function /
- fractional-order calculus /
- robotic arm

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图 1 饱和函数与符号函数

Figure 1. Saturation function and sign function

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图 2 轨迹跟踪

Figure 2. Trajectory tracking

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图 3 轨迹跟踪误差

Figure 3. Trajectory tracking error

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表 1 系统到达稳态时间

Table 1. System reaching steady state time

关节 SMC /s FOSMC /s
α=0.2 α=0.4 α=0.6 α=0.8

1 1.44 0.79 1.20 1.30 1.73
2 1.36 0.86 0.88 1.03 1.47

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