PTFE间歇聚合反应过程变周期动态经济优化控制

doi:10.11949/0438-1157.20220454

化工学报 ›› 2022, Vol. 73 ›› Issue (9): 3973-3982.DOI: 10.11949/0438-1157.20220454

PTFE间歇聚合反应过程变周期动态经济优化控制

王雪松¹(), 曾祥宇¹, 薄翠梅¹(), 汤舒淇¹, 董超¹, 李俊¹, 张泉灵², 金晓明³, 叶胜利⁴

^1.南京工业大学电气工程与控制科学学院，江苏南京 211816
^2.南京工业大学智能制造研究院，江苏南京 211816
^3.浙江大学控制科学与工程学院，浙江杭州 310027
^4.东华工程科技股份有限公司，安徽合肥 230041

收稿日期:2022-03-29 修回日期:2022-06-01 出版日期:2022-09-05 发布日期:2022-10-09
通讯作者: 薄翠梅
作者简介:王雪松(1996—)，男，硕士研究生，wangxuesong@njtech.edu.cn
基金资助:
国家重点研发计划项目(2019YFB1705800);国家自然科学基金项目(62173178)

Dynamic economic optimal control for PTFE batch polymerization process with free terminal

Xuesong WANG¹(), Xiangyu ZENG¹, Cuimei BO¹(), Shuqi TANG¹, Chao DONG¹, Jun LI¹, Quanling ZHANG², Xiaoming JIN³, Shengli YE⁴

^1.College of Electrical Engineering and Control Science, Nanjing Tech University, Nanjing 211816, Jiangsu, China
^2.Institute of Intelligent Manufacturing, Nanjing Tech University, Nanjing 211816, Jiangsu, China
^3.College of Control Science and Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China
^4.East China Engineering Science and Technology Co. , Ltd. , Hefei 230041, Anhui, China

Received:2022-03-29 Revised:2022-06-01 Online:2022-09-05 Published:2022-10-09
Contact: Cuimei BO

摘要/Abstract

摘要：

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性，提出了一种基于自由终端的动态经济优化控制方法。首先，将生产周期作为一个自由度纳入优化变量建立动态经济优化问题，采用改进控制变量参数化方法，控制输入被离散为可变长度的片状序列，便可将动态经济优化问题转换为非线性规划(NLP)问题；然后，采用基于梯度下降的内点罚函数法求解NLP问题，通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间；最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析，仿真结果表明本方法单位经济效益更高，生产周期更短，突显了间歇生产的灵活性。

关键词: 聚四氟乙烯, 间歇聚合反应, 自由终端, 经济优化控制, 动态实时优化

Abstract:

Polytetrafluoroethylene (PTFE) batch polymerization production mode can meet the market demand of small batch, multi-purpose and high quality products. Aiming at the strong nonlinearity and large time delay in the PTFE polymerization process, a dynamic economic optimization control method based on free terminal is proposed in this paper. Firstly, the dynamic economic optimization problem is established by integrating the production cycle as a degree of freedom into the optimization variable. The control inputs are discretized into piece-wise sequences by using improved control variable parameterization method, and the dynamic economic optimization problem can be transformed into a nonlinear programming (NLP) problem. Then, the NLP problem is solved based on the penalty function method of gradient descent, and the rolling optimization control method in the free prediction time domain is used to optimize the control input and terminal time. Finally, compared with PI control and nonlinear model predictive control, the simulation results show that free terminal dynamic economic optimization control method has higher economic benefit and shorter production cycle, which highlights the flexibility of batch production.

Key words: PTFE, batch polymerization, free terminal, economic optimization control, dynamic real-time optimization

中图分类号:

TP 3

王雪松, 曾祥宇, 薄翠梅, 汤舒淇, 董超, 李俊, 张泉灵, 金晓明, 叶胜利. PTFE间歇聚合反应过程变周期动态经济优化控制[J]. 化工学报, 2022, 73(9): 3973-3982.

Xuesong WANG, Xiangyu ZENG, Cuimei BO, Shuqi TANG, Chao DONG, Jun LI, Quanling ZHANG, Xiaoming JIN, Shengli YE. Dynamic economic optimal control for PTFE batch polymerization process with free terminal[J]. CIESC Journal, 2022, 73(9): 3973-3982.

图/表 11

表1 PTFE聚合反应中存在的反应

Table 1 The existing reactions of PTFE polymerization reaction

反应类型	反应方程式
引发剂分解	$I → k d 2 R *$
链引发	$R * + M → k i P 1 *$
链增长	$P n * + M → k p P n + 1 *$
向单体转移	$P n * + M → k t r, M D n + P 1 *$
向溶剂转移	$P n * + S k → k t r, S D n + R *$
向链转移剂转移	$P n * + A k → k t r, A D n + R *$
链终止	$P n * + P m * → k t D m + n$

表1 PTFE聚合反应中存在的反应

Table 1 The existing reactions of PTFE polymerization reaction

反应类型	反应方程式
引发剂分解	$I → k d 2 R *$
链引发	$R * + M → k i P 1 *$
链增长	$P n * + M → k p P n + 1 *$
向单体转移	$P n * + M → k t r, M D n + P 1 *$
向溶剂转移	$P n * + S k → k t r, S D n + R *$
向链转移剂转移	$P n * + A k → k t r, A D n + R *$
链终止	$P n * + P m * → k t D m + n$

图1 控制向量独立参数化示意图

Fig.1 Schematic diagram of control vector independent parameterization

图2 边界约束处理过程示意图

Fig.2 Schematic diagram of the boundary constraint processing

图3 优化控制算法结构图

Fig.3 Flowchart of optimization and control

表2 聚合反应优化控制状态变量定义

Table 2 State variables of polymerization reaction optimization control

状态变量名称	含义	单位
T_cIN	冷却水进口温度	K
T_c0	冷却水平均温度	K
T_bat	反应釜内部温度	K
C_I	引发剂浓度	mol/L
C_R	初级自由基浓度	mol/L
C_M	单体浓度	mol/L
C_Sk	溶剂浓度	mol/L
C_Ak	链转移剂浓度	mol/L
A₀、A₁、A₂	活性链的0、1、2次矩	—
B₀、B₁、B₂	死聚物的0、1、2次矩	—
m_PT	产品总质量	kg

表3 聚合反应过程控制器参数设定

Table 3 Tuning parameter settings of polymerization process controller

参数	数值
Dv	[0, 0, 1.5×10^-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
Oscl	1.2×10^-2
N_u	5
ΔT_u	300 s
θ_c	0.05 CNY/kg
θ_PT	150 CNY/kg

图4 PTFE聚合过程自由终端经济优化集成控制结构图

Fig.4 Structure diagram for economic optimization control of PTFE polymerization process with free terminals

图5 PTFE聚合过程反应器温度响应比较

Fig.5 Comparison of reactor temperature response for PTFE polymerization process

图6 PTFE聚合过程冷却剂出口温度响应比较

Fig.6 Comparison of coolant outlet temperature response for PTFE polymerization process

图7 冷却剂控制输入对比

Fig.7 Comparison of coolant control input

表4 经济参数对比

Table 4 Comparison of economic parameters

参数	无扰动			有扰动
参数	EO控制	PI控制	NMPC	EO控制	PI控制	NMPC
生产周期/min	84.2	95.7	95.1	103.8	120.9	117.3
产品质量/kg	409.4	430.1	441.7	469.7	514.9	518.7
净收益/CNY	5752.9	5861.6	6079.2	5125.5	3432.7	4683.2
平均收益/(CNY/min)	68.3	61.3	63.9	49.4	28.4	39.9

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PTFE间歇聚合反应过程变周期动态经济优化控制

Dynamic economic optimal control for PTFE batch polymerization process with free terminal

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