Optimal control strategies combined with PSO and control vector parameterization for batchwise chemical process

doi:10.11949/j.issn.0438-1157.20181140

Abstract

Abstract:

As a gradient search algorithm for dynamic optimization of chemical process, the efficiency of control vector parameterization depends on the initial given trajectory deeply. At present, the initial trajectory is usually set at the boundary value or the intermediate value, which does not have enough scientific reason and it affects the convergence speed of the algorithm. To solve this problem, a hybrid strategy combined with particle swarm optimization and control vector parameterization method is proposed in this paper, it uses particle swarm optimization to achieve the value of control variables before employing the method of control vector parameterization to reoptimize the process. The two-layer optimization hybrid strategy improves the convergence speed of the control vector parameterization method and the precision of the particle swarm optimization. The hybrid strategy is applied to two examples of batch chemical process optimization control, and the simulation results show that the algorithm is feasible and effective for solving dynamic optimization problems of chemical process.

Key words: batchwise, process control, control vector parameterization, optimal control, optimization

摘要：

控制变量参数化方法作为一种化工过程动态优化的梯度搜索算法，其求解效率过于依赖初始给定轨迹。目前初始轨迹一般都是设定在边界值或中间值，缺乏科学依据，从而大大影响了算法的收敛速度。针对这一问题，提出了一种粒子群优化(PSO)与控制变量参数化方法混合的策略，首先利用粒子群优化对间歇化工过程最优控制量进行求解，结果作为控制变量参数化方法初始给定轨迹，进行二次优化。双层优化的混合策略提高了控制变量参数化方法的收敛速度和粒子群优化算法的求解精度。将混合策略应用于两个间歇化工过程优化控制实例，仿真结果表明了该算法对求解化工过程动态优化问题具有可行性和有效性。

关键词: 间歇式, 过程控制, 控制变量参数化, 最优控制, 优化

CLC Number:

TQ 021.8

Bowen SHI, Yanyan YIN, Fei LIU. Optimal control strategies combined with PSO and control vector parameterization for batchwise chemical process[J]. CIESC Journal, 2019, 70(3): 979-986.

石博文, 尹燕燕, 刘飞. 基于PSO-控制变量参数化混合策略的间歇化工过程优化控制[J]. 化工学报, 2019, 70(3): 979-986.

Figures/Tables 14

Fig.1 Piecewise constant parameterization

Fig.2 Flowchart of PSO-CVP algorithms

Fig.3 Optimal temperature control trajectory

Fig.4 Optimal state variable trajectory

Table 1 Setting parameters of PSO-CVP algorithm

Parameter	Value
quantity of swarm	100
dimension of particle	25
maximum number of iterations	100
accelerated factor c1	2
accelerated factor c2	2
inertia weight	0.8

Ref.	Method	Optimum
[14]	SQP	0.610775
[15]	ACSO	0.61045
[16]	OC	0.61
[17]	IACA(N=10)	0.61
[17]	IACA(N=20)	0.6104
this work	PSO-CVP	0.6105359

Fig.5 Lee-Ramirez biochemical reactor

Table 3 Lee-Ramirez reactor parameters

Parameter	Meaning	Value
$C n f$ /(g/L)	nutrients feed	100
k _s/(g²/L²)	matrix inhibition	111.5
Y	increased quantities of yield	0.51
k _CN/(g/L)	constant	14.35
f _IO/(g/L)	constant	0.005
k ₁₁/h^-1	constant	0.09
μ _max/h^-1	maximum growth rate	1.0
f _max/h^-1	maximum protein yield	0.233
k _cr/(g/L)	constant	0.22
k ₁ _x /(g/L)	constant	0.034
k_I /(g/L)	constant	0.022

Table 3 Lee-Ramirez reactor parameters

Parameter	Meaning	Value
$C n f$ /(g/L)	nutrients feed	100
k _s/(g²/L²)	matrix inhibition	111.5
Y	increased quantities of yield	0.51
k _CN/(g/L)	constant	14.35
f _IO/(g/L)	constant	0.005
k ₁₁/h^-1	constant	0.09
μ _max/h^-1	maximum growth rate	1.0
f _max/h^-1	maximum protein yield	0.233
k _cr/(g/L)	constant	0.22
k ₁ _x /(g/L)	constant	0.034
k_I /(g/L)	constant	0.022

Fig.6 Optimal control trajectory

Fig.7 Optimal state variable trajectory

Fig.8 Substrate state variable trajectory of x 3(t)

Fig.9 Mass of foreign protein

Table 4 Setting parameters of PSO-CVP algorithm

Parameter	Value
quantity of swarm	200
dimension of particle	30
maximum number of iterations	500
accelerated factor c1	2
accelerated factor c2	2
inertia weight	0.8

Ref.	Method	Optimum
[19]	FIDP	6.16
[20]	GA	6.1504
[21]	biogeographic algorithm	6.15
[22]	CVP	6.15123355
[23]	multiple shooting	6.15153759
this work	PSO-CVP	6.15154923

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