Unfixed terminal economic optimization and control for fed-batch reaction process

doi:10.11949/0438-1157.20210019

Abstract

Abstract:

Aiming at the uncertainty of operating condition in the batch process, an unfixed terminal time economic optimization method is proposed. Firstly, the economic model predictive control method is adopted, with terminal constraints replaced by economical maximum item in objective function, and add the batch length of the batch process into the optimization degree of freedom. Duration of batch production is included in optimized variables to establish a dynamic economic optimization problem. Through the different parameterization of each control variable which is updated with time, the dynamic optimization problem is transformed into an NLP problem. Then the interior point penalty function method is used to solve the optimization problem with nonlinear constraints, the obtained optimal control sequence and optimal batch production cycle can minimize the loss caused by uncertain disturbances. The control structure adopts the receding horizon control method, which not only improves the cooperative control ability of the multivariable system, but also adjusts the control curve according to the real-time forecast of the terminal product output, which flexibly optimize trajectory of manipulated variables and operating time. Finally, this method has been tested on the batch optimized control for the aniline hydrogenation process, and the performance is significantly better than that controlled by complex PI method based on selection-splitting. The test results show that the economic optimized control of unfixed terminals optimizes the operating conditions of each batch production from the perspective of the total production efficiency, and realizes the optimal management of the production time and economic efficiency of the batch reaction process.

Key words: fed-batch reaction, economic optimization and control, receding horizon control, unfixed terminals, interior point optimizer

摘要：

针对批次生产周期不确定问题，提出一种非固定终端的经济优化控制方法。首先采用经济模型预测控制方法，用收益最大化的经济型目标函数代替终端约束，并将批次生产周期纳入被优化变量，建立动态经济优化问题，并通过对每个控制变量进行有差异的参数化，将动态优化问题转化为非线性规划（NLP）问题；然后使用内点罚函数法求解含非线性约束的优化问题，得到的最优控制序列和最佳批次生产周期，可将不确定扰动带来的损失降低到最小。其次采用非固定预测时域的滚动时域控制方法，不仅提高多变量系统的协同控制能力，而且根据实时预测终端产品产量不断优化更新关键操纵变量的控制分段函数的分割数及控制序列，从而可灵活优化操纵变量和操作时间的轨迹。最后在苯胺加氢过程上进行了批次优化控制性能测试，测试结果表明，非固定终端的经济优化控制从批次的总生产效益角度来优化每个批次生产的操作条件，实现批次反应过程生产时间与经济效益的最优化管理。

关键词: 分批补料反应, 经济优化控制, 滚动时域控制, 非固定终端, 内点最优化法

CLC Number:

TQ 021.8

Shuqi TANG, Cuimei BO, Hui YU, Jun LI, Dengfeng ZHANG, Quanling ZHANG, Xiaoming JIN. Unfixed terminal economic optimization and control for fed-batch reaction process[J]. CIESC Journal, 2021, 72(8): 4215-4226.

汤舒淇, 薄翠梅, 俞辉, 李俊, 张登峰, 张泉灵, 金晓明. 分批补料反应过程的非固定终端经济优化控制[J]. 化工学报, 2021, 72(8): 4215-4226.

Figures/Tables 12

Fig.1 Schematic diagram of control vectors respectively parameterized

Fig.2 Flow chart of economic optimization control with unfixed terminal

Fig.3 Schematic diagram of fed-batch reactor

Table 1 Process， initial and boundary conditions， reactor structure data， and economic value of components

变量	数值	单位	变量	数值	单位
k₀	4×10⁴	m³/(s?kmol)	$C a 0$	8.01	kmol/m³
F^in,0	0	m³/s	$C b 0$	0	kmol/m³
Tⁱⁿ	350	K	$C c 0$	0	kmol/m³
$C a i n$	8.01	kmol/m³	$V R 0$	11.3097	m³
$C b i n$	0	kmol/m³	$T R 0$	350	K
$C c i n$	0	kmol/m³	$T j o u t, 0$	350	K
$F j 0$	0	m³/s	θ_a	0.558	CNY/mol
$T j i n$	350	K	θ_b	0.066	CNY/mol
D_R	2	m	θ_c	1.075	CNY/mol
V_j	2.5133	m³	θ_j	5×10^-3	CNY/kg
$V R m a x$	12.56	m³	$C p a$	0.23	kJ/(kmol?K)
$V R m i n$	0	m³	$C p b$	0.102	kJ/(kmol?K)
$T R m a x$	475	K	$C p c$	181.67	kJ/(kmol?K)
$T R m i n$	350	K	$C p j$	4.183	kJ/(kg?K)
F_j^max	0.005	m³/s	ρ_j	1000	kg/m³
F_j^min	0	m³/s	?H_R	46.49×10³	kJ/kmol
F^in,max	8.739×10^-5	m³/s	U_trans	0.851	kW/(m²?K)
F^in,min	0	m³/s

Table 1 Process， initial and boundary conditions， reactor structure data， and economic value of components

变量	数值	单位	变量	数值	单位
k₀	4×10⁴	m³/(s?kmol)	$C a 0$	8.01	kmol/m³
F^in,0	0	m³/s	$C b 0$	0	kmol/m³
Tⁱⁿ	350	K	$C c 0$	0	kmol/m³
$C a i n$	8.01	kmol/m³	$V R 0$	11.3097	m³
$C b i n$	0	kmol/m³	$T R 0$	350	K
$C c i n$	0	kmol/m³	$T j o u t, 0$	350	K
$F j 0$	0	m³/s	θ_a	0.558	CNY/mol
$T j i n$	350	K	θ_b	0.066	CNY/mol
D_R	2	m	θ_c	1.075	CNY/mol
V_j	2.5133	m³	θ_j	5×10^-3	CNY/kg
$V R m a x$	12.56	m³	$C p a$	0.23	kJ/(kmol?K)
$V R m i n$	0	m³	$C p b$	0.102	kJ/(kmol?K)
$T R m a x$	475	K	$C p c$	181.67	kJ/(kmol?K)
$T R m i n$	350	K	$C p j$	4.183	kJ/(kg?K)
F_j^max	0.005	m³/s	ρ_j	1000	kg/m³
F_j^min	0	m³/s	?H_R	46.49×10³	kJ/kmol
F^in,max	8.739×10^-5	m³/s	U_trans	0.851	kW/(m²?K)
F^in,min	0	m³/s

Table 2 Tuning parameter settings of the optimized control

参数	对应变量
	F_j			Fⁱⁿ
β	1.12564×10⁷			2.12×10¹¹
N_u	4			6
ΔT_u	60 s			50 s
	C_a	C_b	C_c	V_R	$T j o u t$	T_R
α	0	0	0	0	0	2.3125×10^-5

Table 2 Tuning parameter settings of the optimized control

参数	对应变量
	F_j			Fⁱⁿ
β	1.12564×10⁷			2.12×10¹¹
N_u	4			6
ΔT_u	60 s			50 s
	C_a	C_b	C_c	V_R	$T j o u t$	T_R
α	0	0	0	0	0	2.3125×10^-5

Fig.4 Comparison of coolant flow with disturbance

Fig.5 Comparison of feed flow with disturbance

Fig.6 Anti-disturbance comparison of temperature control

Fig.7 Anti-disturbance comparison of pressure control

Fig.8 Changes of aniline concentration

Fig.9 Changes of cyclohexylamine concentration

Table 3 Economic profitability of two kinds of control

参数	无扰动		有扰动
参数	Optimized control	PI control	Optimized control	PI control
T_f/min	123.87	145.17	164.68	190.97
净收入/CNY	2.47×10⁴	2.84×10⁴	1.84×10⁴	1.56×10⁴
平均收益/(CNY/min)	199.40	195.63	111.73	81.69

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