CIESC Journal ›› 2019, Vol. 70 ›› Issue (3): 979-986.doi: 10.11949/j.issn.0438-1157.20181140

• Process system engineering • Previous Articles     Next Articles

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

Bowen SHI1(),Yanyan YIN2,Fei LIU1()   

  1. 1. Key Laboratory of Advanced Control for Light Industry Process, Ministry of Education, Jiangnan University, Wuxi 214122, Jiangsu, China
    2. Department of Mathematics and Statistics, Curtin University, Perth 6102, Australia
  • Received:2018-10-08 Revised:2018-12-18 Online:2019-03-05 Published:2018-12-19
  • Contact: Fei LIU;


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

CLC Number: 

  • TQ 021.8


Piecewise constant parameterization"


Flowchart of PSO-CVP algorithms"


Optimal temperature control trajectory"


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


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
kI /(g/L) constant 0.022


Optimal control trajectory"


Optimal state variable trajectory"


Substrate state variable trajectory of x 3(t)"


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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LI Qingzhao;ZHAO Changsui;CHEN Xiaoping;WU Weifang;LI Yingjie


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