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基于混合集成建模的硅单晶直径自适应非线性预测控制

任俊超 刘丁 万银

任俊超, 刘丁, 万银. 基于混合集成建模的硅单晶直径自适应非线性预测控制. 自动化学报, 2020, 46(5): 1004−1016 doi: 10.16383/j.aas.c190798
引用本文: 任俊超, 刘丁, 万银. 基于混合集成建模的硅单晶直径自适应非线性预测控制. 自动化学报, 2020, 46(5): 1004−1016 doi: 10.16383/j.aas.c190798
Ren Jun-Chao, Liu Ding, Wan Yin. Hybrid integrated modeling based adaptive nonlinear predictive control of silicon single crystal diameter. Acta Automatica Sinica, 2020, 46(5): 1004−1016 doi: 10.16383/j.aas.c190798
Citation: Ren Jun-Chao, Liu Ding, Wan Yin. Hybrid integrated modeling based adaptive nonlinear predictive control of silicon single crystal diameter. Acta Automatica Sinica, 2020, 46(5): 1004−1016 doi: 10.16383/j.aas.c190798

基于混合集成建模的硅单晶直径自适应非线性预测控制

doi: 10.16383/j.aas.c190798
基金项目: 国家自然科学基金重点项目(61533014)资助
详细信息
    作者简介:

    任俊超:西安理工大学博士研究生. 分别于2014年、2017年获西安理工大学学士和硕士学位. 主要研究方向为数据驱动建模、优化与控制.E-mail: renjc425x@163.com

    刘丁:西安理工大学教授, 博士生导师. 1982年获陕西机械学院学士学位, 1997年获西安交通大学工学博士学位. 主要研究方向为信号处理, 智能控制, 复系统建模与控制. 本文通信作者.E-mail: liud@xaut.edu.cn

    万银:西安理工大学博士研究生. 分别于2016年、2019年获西安理工大学学士和硕士学位. 主要研究方向为复杂系统建模、仿真与分析.E-mail: yinwan690212@163.com

Hybrid Integrated Modeling Based Adaptive Nonlinear Predictive Control of Silicon Single Crystal Diameter

Funds: Supported by the Key Program of National Natural Science Foundation of China (61533014)
  • 摘要: 大尺寸、电子级直拉硅单晶生长过程中物理变化复杂、多场多相耦合、模型不确定且存在大滞后和非线性等特性, 因此如何实现硅单晶直径控制是一个具有理论意义和实际价值的问题. 本文结合工程实际提出一种基于混合集成建模的晶体直径自适应非线性预测控制方法. 首先, 为了准确辨识晶体直径模型, 提出基于互相关函数的时滞优化估计方法和基于Lipschitz商准则与模型拟合优度的模型阶次辨识方法; 其次, 基于“分而治之”原理构建晶体直径混合集成模型. 其中, 采用小波包分解(Wavelet packet decomposition, WPD)方法将原始数据分解成若干个子序列, 以减少其非平稳性和随机噪声. 极限学习机(Extreme learning machine, ELM)和长短时记忆网络(Long-short-term memory networks, LSTM)分别建立近似(低频)子序列和细节(高频)子序列的预测模型, 最终晶体直径预测输出由各子序列的预测结果汇总而成; 然后, 针对晶体直径混合集成模型失配问题以及目标函数难以求解问题, 提出一种基于蚁狮优化(Ant lion optimizer, ALO)的自适应非线性预测控制策略. 最后, 基于工程实验数据仿真分析, 验证了所提建模及控制方法的有效性.
  • 图  1  Cz法硅单晶生长工艺流程

    Fig.  1  Cz silicon single crystal growth process

    图  2  基于WPD-ELM-LSTM的混合集成建模框架

    Fig.  2  Hybrid integrated modeling framework based on WPD-ELM-LSTM

    图  3  基于WPD-ELM-LSTM的晶体直径自适应NMPC结构

    Fig.  3  Crystal diameter adaptive NMPC structure based on WPD-ELM-LSTM

    图  4  Cz法硅单晶生长过程和晶体直径测量系统

    Fig.  4  Cz silicon single crystal growth process and crystal diameter measurement system

    图  5  原始晶体直径与加热器功率实验数据

    Fig.  5  Experimental data of raw crystal diameter and heater power

    图  6  晶体直径原始数据分解结果

    Fig.  6  Crystal diameter raw data decomposition results

    图  7  时滞阶次$d$辨识结果

    Fig.  7  Time delay order $d$ identification results

    图  8  不同建模方法的晶体直径预测效果及评价指标对比

    Fig.  8  Comparison of prediction effect and evaluation index of crystal diameter by different modeling methods

    图  9  自适应NMPC和常规NMPC的晶体直径设定值跟踪效果

    Fig.  9  Crystal diameter setpoint tracking effect of adaptive NMPC and conventional NMPC

    图  10  晶体直径控制性能指标和模型参数估计性能指标收敛曲线

    Fig.  10  Convergence curve of crystal diameter control performance index and model parameter estimation performance index

    图  11  所提自适应NMPC与常规PID的晶体直径控制结果

    Fig.  11  The crystal diameter control results of the proposed adaptive NMPC and conventional PID

    图  12  时滞阶次变化时所提自适应NMPC与常规PID的晶体直径控制结果

    Fig.  12  Crystal diameter control results of adaptive NMPC and conventional PID for delay order variation

    表  1  原始实验数据集的统计特性

    Table  1  Statistical characteristics of the raw experimental data set

    数据集数量MeanMaxMinStd
    晶体直径 (mm)
    总样本5 000208.92212.57206.160.66
    训练集3 800208.92212.57206.160.72
    测试集1 200208.92209.83208.060.41
    加热器功率 (kW)
    总样本5 00070.5272.5168.370.80
    训练集3 80070.2072.3268.370.59
    测试集1 20071.5672.5170.440.40
    下载: 导出CSV

    表  2  基于Lipschitz商准则的输入变量个数辨识结果

    Table  2  Identification results of the number of input variables based on Lipschitz quotient criterion

    $\Gamma (m + 1,m)$$\Gamma (4,3)$$\Gamma (5,4)$$\Gamma (6,5)$$\Gamma (7,6)$$\Gamma (8,7)$$\Gamma (9,8)$$\Gamma (10,9)$$\Gamma (11,10)$
    指标值0.01450.01050.00880.00710.01410.00710.00330.0003
    下载: 导出CSV

    表  3  不同阶次组合的模型拟合优度结果

    Table  3  Goodness-of-fit of the models with different order combinations

    不同阶次组合$({n_u},{n_y})$(1,3)(2,2)(3,1)
    模型拟合优度值Fit99.913299.908599.9090
    下载: 导出CSV

    表  4  模型性能评价指标

    Table  4  Model performance evaluation index

    指标定义公式
    MAE平均绝对值误差${\rm MAE} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\left| {f(i) - \hat f(i)} \right|} $
    MAPE平均绝对百分
    比误差
    ${\rm MAPE} = \dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N {\left| {\frac{ {f(i) - \hat f(i)} }{ {f(i)} } } \right|} \times 100{\rm{\% } }$
    RMSE均方根误差${\rm RMSE} = \sqrt {\dfrac{1}{N}\displaystyle\sum\limits_{i = 1}^N { { {(f(i) - \hat f(i))}^2} } } $
    下载: 导出CSV

    表  5  不同预测方法的参数设置

    Table  5  Parameter setting of different prediction methods

    预测方法参数设置
    ELM20 个隐含节点数, 激活函数 sigmoid
    LSTM200 个隐含节点数, 学习率 0.005, 训练轮次 200
    WPD-ELM20 个隐含节点数, 激活函数 sigmoid
    WPD-LSTM200 个隐含节点数, 学习率 0.005, 训练轮次 200
    WPD-ELM-LSTMELM: 27 个隐含节点数, 激活函数 sigmoid; LSTM: 185 个隐含节点数, 学习率 0.005, 训练轮次 200
    下载: 导出CSV

    表  6  不同预测模型的晶体直径预测指标

    Table  6  Prediction index of crystal diameter based on different prediction models

    模型MAE (mm)MAPE (%)RMSE (mm)
    ELM0.01970.00940.0258
    LSTM0.08780.04200.1131
    WPD-ELM0.01720.00820.0228
    WPD-LSTM0.04310.02060.0627
    WPD-ELM-LSTM0.00960.00460.0125
    下载: 导出CSV

    表  7  不同晶体直径预测模型的训练计算时间

    Table  7  Training calculation time of different crystal diameter prediction models

    预测模型训练计算时间 (s)
    ELM0.0828
    LSTM304.4786
    WPD-ELM0.2752
    WPD-LSTM972.6920
    WPD-ELM-LSTM601.1670
    下载: 导出CSV

    表  8  基于不同预测模型的晶体直径预测控制计算时间

    Table  8  Calculation time of crystal diameter predictive control based on different prediction models

    预测模型平均控制量更新时间 (s)
    ELM (常规NMPC)0.4512
    LSTM (常规NMPC)0.4899
    WPD-ELM-LSTM (常规NMPC)0.6841
    WPD-ELM-LSTM (自适应NMPC)7.3113
    下载: 导出CSV
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  • 收稿日期:  2019-11-20
  • 录用日期:  2020-03-16
  • 网络出版日期:  2020-06-01
  • 刊出日期:  2020-06-01

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