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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (1): 10-20    DOI: 10.3785/j.issn.1008-973X.2023.01.002
    
Contour error control of two-axis system based on LSTM and Newton iteration
Hua HUANG1(),Qiu-ge ZHAO1,Zai-xing HE2,Jia-ran LI1
1. School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2. School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China
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Abstract  

An approach of contour error prediction based on long short-term memory neural network (LSTM) and Newton iteration and the contour error compensation by transforming the task coordinate system was proposed in order to address the problem that the accuracy of two-axis motion was affected by contour error. The feature contour and data were extracted from the control system of the two-axis motion platform, and the contour error was obtained by Newton’s method, which was employed as the training data of LSTM neural network. Then a more accurate prediction model of contour error was obtained. The predicted contour error was compensated to the reference contour through feedforward control by transforming the task coordinate system so as to improve the contour control performance. The random NRBUS curve was used to verify its generalization by comparing PID, ILC and neural network. The experimental results show that the proposed approach can effectively predict and control the contour error, and has good potential application value in the precision motion control.

Key words： two-axis motion control      contour error      long short-term memory neural network      feedforward compensation     
Received: 09 August 2022      Published: 17 January 2023
CLC:  TP 391  
Fund:  国家自然科学基金资助项目(51965037，51565030)
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Hua HUANG
Qiu-ge ZHAO
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Jia-ran LI
Cite this article:

Hua HUANG,Qiu-ge ZHAO,Zai-xing HE,Jia-ran LI. Contour error control of two-axis system based on LSTM and Newton iteration. Journal of ZheJiang University (Engineering Science), 2023, 57(1): 10-20.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.01.002     OR     https://www.zjujournals.com/eng/Y2023/V57/I1/10


基于LSTM与牛顿迭代的两轴系统轮廓误差控制

针对轮廓误差影响运动系统精度的问题，提出结合长短期记忆神经网络(LSTM)和牛顿迭代法对轮廓误差进行预测、通过转换任务坐标系对轮廓误差进行补偿的方法. 在运动平台上提取特征轮廓与数据，将牛顿迭代法应用于对轮廓误差的计算，通过计算出的轮廓误差对优化后的LSTM神经网络进行训练，建立更准确的轮廓误差预测模型. 通过转换任务坐标系，将预测的轮廓误差作为前馈补偿到参考轮廓中，提高轮廓控制性能. 通过试验对比PID、迭代法和神经网络法，利用随机NRBUS轨迹验证泛化性，表明提出的方法能够有效地预测并控制轮廓误差，在精密运动控制领域有良好的应用前景.


关键词： 两轴运动控制,  轮廓误差,  长短期记忆神经网络,  前馈补偿 
Fig.1 Dynamic model of uniaxial servo system
Fig.2 Control model of feed servo system
Fig.3 Two-axis motion system
Fig.4 Schematic diagram of contour error of two axis platform
Fig.5 Simulation test of contour error estimation
${{i} }$ $\|{\boldsymbol{\varepsilon } }({ {\hat {{t} } } })\|$ ${{i} }$ $\| {\boldsymbol{\varepsilon } }({ {\hat {{t} } } })\|$
1 0.918 7 6 0.796 4
2 0.861 3 7 0.795 9
3 0.820 9 8 0.795 4
4 0.798 8 9 0.795 4
5 0.797 1 10 0.795 4
Tab.1 Simulation results of contour error calculation
Fig.6 LSTM neural network framework
Fig.7 Flow chart of LSTM neural network training
Fig.8 Random NURBS A
Fig.9 Contour error prediction deviation of LSTM neural network under different training characteristics
特征 ${{\varepsilon } }{'_{\max } }$/μm ${{\varepsilon } }{'_{ {{\rm{rms}}} } }$/μm
A 49.4 25.0
B 24.9 12.6
C 10.4 5.0
Tab.2 Comparison of contour error prediction effect of LSTM neural network under different training characteristics
Fig.10 Schematic diagram of converting task coordinate system
Fig.11 Contour error control block diagram
Fig.12 Block diagram of overall control strategy
Fig.13 Comparison of contour error estimation deviation
Fig.14 Random NURBS B
Fig.15 Comparison of contour error
方法 ${\left| { { {\boldsymbol{\varepsilon } }_{\rm{d}}} } \right|_{ \rm{rms} } }$/μm ${\left| { { {\boldsymbol{\varepsilon } }_{\rm{d}}} } \right|_{ {\max} } }$/μm
C1 109.1 489
C2 83.5 468
C3 93.7 150
C4 11.4 195
C5 8.2 76.6
C6 9.1 75.4
Tab.3 Comparison of contour error control
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