非线性快速批次过程高效迭代学习预测函数控制

马乐乐; 刘向杰

doi:10.16383/j.aas.c190621

非线性快速批次过程高效迭代学习预测函数控制

doi: 10.16383/j.aas.c190621

马乐乐^1,,
刘向杰^1,

1.
华北电力大学控制与计算机工程学院北京 102206

基金项目: 国家自然科学基金(62073136, U1709211), 中国博士后科学基金(2021M701184), 国家重点研发计划(2021YFE0190900) 资助

详细信息

作者简介:
马乐乐：华北电力大学控制与计算机工程学院讲师. 2016年获得华北电力大学自动化专业学士学位. 2021年获得华北电力大学控制理论与控制工程专业博士学位. 主要研究方向为迭代学习模型预测控制及其应用.E-mail: malele@ncepu.edu.cn

刘向杰：华北电力大学控制与计算机工程学院教授. 1989年获东北大学自动控制系工业电气自动化专业学士学位. 1997年获东北大学自动化研究中心博士学位. 主要研究方向为先进控制策略在电力过程控制中的应用. 本文通信作者.E-mail: liuxj@ncepu.edu.cn

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出版历程
- 收稿日期: 2019-09-02
- 录用日期: 2020-02-07
- 网络出版日期: 2021-12-30
- 刊出日期: 2022-02-18

A High Efficiency Iterative Learning Predictive Functional Control for Nonlinear Fast Batch Processes

MA Le-Le^1
,,
LIU Xiang-Jie^1
,

1.
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206

Funds: Supported by National Natural Science Foundation of China (62073136, U1709211), China Postdoctoral Science Foundation (2021M701184), and National Key Research and Development Program of China (2021YFE0190900)

More Information

Author Bio:
MA Le-Le　Lecturer at the School of Control and Computer Engineering, North China Electric Power University. She received her bachelor degree from North China Electric Power University in 2016, and her Ph.D. degree from North China Electric Power University in 2021. Her research interest covers iterative learning model predictive control and its application

LIU Xiang-Jie　Professor at the School of Control and Computer Engineering, North China Electric Power University. He received his bachelor degree from Northeastern University in 1989, and his Ph.D. degree from the Research Center of Automation, Northeastern University in 1997. His research interest covers application of advanced control strategy in power process control. Corresponding author of this paper

摘要

摘要: 迭代学习模型预测控制(Iterative learning model predictive control, ILMPC)具备较强的批次学习能力及突出的时域跟踪性能, 在批次过程控制中发挥了重要作用. 然而对于具有强非线性的快动态批次过程, 传统的迭代学习模型预测控制很难实现计算效率与跟踪精度之间的平衡, 这给其应用带来了挑战. 对此本文提出一种高效迭代学习预测函数控制策略, 将原非线性系统沿参考轨迹线性化得到二维跟踪误差预测模型, 并在控制器设计中补偿所产生的线性化误差, 构造优化目标函数为真实跟踪误差的上界. 为加强优化计算效率, 在时域上结合预测函数控制以降低待优化变量维数, 从而有效降低计算负担. 结合终端约束集理论, 分析了迭代学习预测函数控制的时域稳定性及迭代收敛性. 通过对无人车和典型快速间歇反应器的仿真实验验证所提出算法的有效性.
- 轨迹线性化 /
- 预测函数控制 /
- 迭代学习控制 /
- 快速非线性批次过程 /
- 计算复杂度
Abstract: Iterative learning model predictive control (ILMPC) is quite popular in controlling the batch process, since it possesses not only the learning ability along batches, but also the strong time domain tracking properties. However, for a fast batch process with strong nonlinear dynamics, the application of the ILMPC is quite challengeable due to the difficulty in balancing the computational efficiency and tracking accuracy. In this paper, an efficient iterative learning predictive functional control is proposed. The original nonlinear system is linearized along reference trajectory to formulate two-dimensional tracking-error based predictive model. The linearization error is compensated to formulate the objective function as the norm bound of the real tracking error. For enhancing control efficiency, predictive functional control is incorporated to reduce the dimension of optimized variable so as to cut down computation burden effectively. The stability and convergence of this iterative learning predictive functional control with terminal constraint are analyzed. The simulations of unmanned ground vehicle and typical fast batch reactor verify the effectiveness of the proposed control algorithm.
- Trajectory linearization /
- predictive functional control (PFC) /
- iterative learning control (ILC) /
- nonlinear fast batch processes /
- computation complexity

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图 1 参考轨迹邻域示意图

Fig. 1 The neighborhoods along reference trajectory

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图 2 ILPFC控制框图

Fig. 2 The control scheme of the ILPFC

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图 3 ILPFC可行域形成过程

Fig. 3 The forming process of feasible region of ILPFC

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图 4 UGV系统跟踪误差时变终端不变集

Fig. 4 The time-varying tracking error terminal invariant set of UGV control system

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图 5 ILPFC控制下状态跟踪曲线

Fig. 5 The state tracking trajectories under the ILPFC

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图 6 ILPFC控制下控制输入曲线

Fig. 6 The trajectories of control inputs under the ILPFC

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图 7 UGV系统${\boldsymbol{\theta}}$变化曲线和MSE变化曲线

Fig. 7 The change curves of ${\boldsymbol{\theta}}$ and MSE of UGV control system

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图 8 UGV系统分别在ILPFC、ILMPC和mp-ILMPC控制下第9批次的运动跟踪曲线

Fig. 8 The motion curve of UGV during the 9th batch under the ILPFC, ILMPC and mp-ILMPC

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图 9 间歇反应器系统跟踪误差时变终端不变集

Fig. 9 The time-varying tracking error terminal invariant set of batch reactor control system

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图 10 ILPFC控制下反应温度跟踪曲线

Fig. 10 The trajectories of the reaction temperature $ T$ under the ILPFC

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图 11 ILPFC控制下反应物A浓度跟踪曲线

Fig. 11 The trajectories of the concentration $ {C_A}$ under the ILPFC

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图 12 ILPFC控制下冷却剂温度曲线

Fig. 12 The trajectories of the coolant stream temperature $ {T_j}$ under the ILPFC

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图 13 间歇反应器系统$ {\boldsymbol{\theta}} $变化曲线和MSE变化曲线

Fig. 13 The change curves of $ {\boldsymbol{\theta}} $ and MSE of batch reactor control system

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图 14 第20批次ILPFC、ILMPC和mp-ILMPC控制下反应温度跟踪曲线

Fig. 14 The tracking trajectories of the reaction temprature under the ILPFC, ILMPC and mp-ILMPC in the 20th batch

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图 15 阶跃初始批次输入下ILPFC温度跟踪曲线

Fig. 15 The tracking trajectories of the reaction temprature $ T$ under the ILPFC with a step input in the initial batch

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表 1 ILPFC、ILMPC及mp-ILMPC计算量和跟踪误差比较

Table 1 The comparison of computation time and tracking errors between ILPFC, ILMPC and mp-ILMPC

控制时域	ILPFC平均计算时间 (s) (Hessian矩阵维数)	ILMPC平均计算时间 (s) (Hessian矩阵维数)	mp-ILMPC平均计算时间 (s)	ILPFC 平均 MSE	ILMPC 平均 MSE	mp-ILMPC 平均 MSE
10	0.083 (2 × 2)	0.158 (20 × 20)	0.162	3.051	2.878	3.053
15	0.041 (2 × 2)	0.185 (30 × 30)	0.191	2.988	2.734	2.984
20	0.064 (2 × 2)	0.211 (40 × 40)	0.216	2.845	2.627	2.840

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表 2 ILPFC、ILMPC及mp-ILMPC计算量和跟踪误差比较

Table 2 The comparison of computation time and tracking errors between ILPFC, ILMPC and mp-ILMPC

控制时域	ILPFC平均计算时间 (s) (Hessian 矩阵维数)	ILMPC平均计算时间 (s) (Hessian 矩阵维数)	mp-ILMPC平均计算时间 (s)	ILPFC 平均 MSE	ILMPC 平均 MSE	mp-ILMPC 平均 MSE
10	0.067 (3 × 3)	0.108 (10 × 10)	0.197	5.974	5.602	5.992
15	0.052 (3 × 3)	0.255 (15 × 15)	0.361	5.568	5.227	5.603
20	0.061 (3 × 3)	0.412 (20 × 20)	0.502	5.113	4.895	5.121

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