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

doi:10.11949/0438-1157.20220454

Abstract

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

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

CLC Number:

TP 3

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.

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.

Figures/Tables 11

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	$P n * + P m * → k t D m + n$

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	$P n * + P m * → k t D m + n$

Fig.1 Schematic diagram of control vector independent parameterization

Fig.2 Schematic diagram of the boundary constraint processing

Fig.3 Flowchart of optimization and control

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

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

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

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

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

Fig.7 Comparison of coolant control input

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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