面向刚柔耦合定位平台的模型预测控制算法

doi:10.13229/j.cnki.jdxbgxb20210479

吉林大学学报(工学版) ›› 2022, Vol. 52 ›› Issue (12): 2806-2815.doi: 10.13229/j.cnki.jdxbgxb20210479

面向刚柔耦合定位平台的模型预测控制算法

杨志军¹(),高忠义¹,王丽君²,黄观新¹(),危宇泰¹

^1.广东工业大学省部共建精密电子制造技术与装备国家重点实验室，广州 510006
^2.北京科技大学工业过程知识自动化教育部重点实验室，北京 100083

收稿日期:2021-05-31 出版日期:2022-12-01 发布日期:2022-12-08
通讯作者: 黄观新 E-mail:yangzj@gdut.edu.cn;guanxinhuang@gdut.edu.cn
作者简介:杨志军（1977-），男，教授，博士. 研究方向：机电系统性能定制设计. E-mail：yangzj@gdut.edu.cn
基金资助:
国家自然科学基金项目(51875108);中央高校基本科研业务费专项资金项目(FRF-BD-19-002A)

Model predictive control algorithm for rigid⁃flexible coupling positioning stage

Zhi-jun YANG¹(),Zhong-yi GAO¹,Li-jun WANG²,Guan-xin HUANG¹(),Yu-tai WEI¹

^1.State Key Laboratory of Precision Electronic Manufacturing Technology and Equipment，Guangdong University of Technology，Guangzhou 510006，China
^2.Key Laboratory of Industrial Process Knowledge Automation，Ministry of Education，University of Science and Technology Beijing，Beijing 100083，China

Received:2021-05-31 Online:2022-12-01 Published:2022-12-08
Contact: Guan-xin HUANG E-mail:yangzj@gdut.edu.cn;guanxinhuang@gdut.edu.cn

摘要/Abstract

摘要：

针对刚柔耦合定位平台（RFCS）在运动阶段和定位阶段模型不同的特点，提出了一种扩张状态观测器辅助的模型预测控制（ESO-MPC）算法。该算法采用时域离散的差分方程对RFCS的动力学响应进行预测，并且在时域离散时引入了可调参数应对实验模型的不确定因素。通过扩张状态观测器（ESO）获取反馈信息，对RFCS的位置、速度及柔性铰链的弹性力和阻尼力进行实时观测。通过RFCS的25组点位运动实验和负载实验，对比了传统PID、前馈PID、LADRC与ESO-MPC算法的性能。实验结果表明，4种控制方案都能达到±0.1 μm的稳态误差，而ESO-MPC算法的整定时间最短，并且通过负载实验验证了ESO-MPC算法的鲁棒性。

关键词: 机械电子工程, 刚柔耦合定位平台, 模型预测控制, 扩张状态观测器

Abstract:

For the feature that the RFCS has different models in motion and positioning stage， an extended state observer assisted model predictive control （ESO-MPC） method was proposed. The time-domain discrete difference equation was used to predict the dynamic response of RFCS， and an adjustable parameter during the time-domain discretization process was introduced to deal with uncertain factors of the experimental model. The feedback information was obtained through the Expanded State Observer （ESO）， which can observe the position and speed of the RFCS as well as the spring and damping forces of the flexible hinge in real time. The performance of traditional PID， feedforward PID， LADRC and ESO-MPC was compared by 25 sets of RFCS point-to-point experiments and load experiments. The experimental results show that the four control schemes can achieve a steady-state error of ±0.1 μm， and ESO-MPC has the smallest setting time and the robustness of ESO-MPC is verified by load experiment.

Key words: mechatronic engineering, rigid-flexible coupling positioning stage, model predictive control, extended state observer

中图分类号:

TP273

杨志军,高忠义,王丽君,黄观新,危宇泰. 面向刚柔耦合定位平台的模型预测控制算法[J]. 吉林大学学报(工学版), 2022, 52(12): 2806-2815.

Zhi-jun YANG,Zhong-yi GAO,Li-jun WANG,Guan-xin HUANG,Yu-tai WEI. Model predictive control algorithm for rigid⁃flexible coupling positioning stage[J]. Journal of Jilin University(Engineering and Technology Edition), 2022, 52(12): 2806-2815.

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参数	定义	值
J_max/（m·s^-3）	最大急动度	126.45
A_max/（m·s^-2）	最大加速度	8.11
V_max/（m·s^-1）	最大速度	0.78
Q/m	行程	0.15

PID	前馈PID	LADRC	ESO-MPC
k_P=3.2×10⁴	k_P=3.2×10⁴	ω_c=800	α=900
k_I=2.0×10⁶	k_I=2.8×10⁶	ω_o=1000	m=1.4
k_D=16	k_D=17		ω_o=1000

控制算法	最小值/ms	最大值/ms	平均值/ms	众数/ms
PID	30.6	44.5	34.31	33.0
前馈PID	25.9	35.8	31.50	31.5
LADRC	5.3	44.6	27.63	35.8
ESO-MPC	0.4	29.5	14.23	29.4

负载质量/kg	最小值/ms	最大值/ms	平均值/ms	标准差
1	7.3	18.6	10.28	0.003 591 0
2	8.5	22.2	15.76	0.005 224 0
3	20.5	22.9	21.80	0.000 726 0
4	30.2	33.0	31.52	0.000 796 9

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面向刚柔耦合定位平台的模型预测控制算法

Model predictive control algorithm for rigid⁃flexible coupling positioning stage

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负载质量/kg	α	ω_c	m
1	900	1000	2.4
2	900	1000	3.4
3	900	1000	4.4
4	900	1000	5.4