期刊
APPLIED MATHEMATICAL MODELLING
卷 37, 期 3, 页码 695-706出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.02.044
关键词
Nonlinear dynamical system; Optimal control; Control parametrization enhancing transform; Constraint transcription; Fed-batch fermentation
资金
- Natural Science Foundation for the Youth of China [11001153]
- TianYuan Special Funds of the National Natural Science Foundation of China [11126077]
- Shandong Province Natural Science Foundation of China [ZR2010AQ016]
- National Natural Science Foundation of China [11171050]
The main control goal in fed-batch fermentation is to get a high concentration of production. In this paper, a new nonlinear dynamical system, in which the feed rate of glycerol is the control function and the switching instants between the batch and feed processes are the variables, is proposed to formulate the fed-batch fermentation process of glycerol bio-conversion to 1,3-propanediol (1,3-PD). To maximize the concentration of 1.3-PD at the terminal time, an optimal control model involving the nonlinear system and subject to the continuous state constraints and the control constraint is presented. To seek the optimal solution of the constrained optimal control problem, the control parametrization enhancing transform together with the constraint transcription technique is first used to convert the constrained optimal control problem into a sequence of mathematical programming problems. An improved Particle Swarm Optimization is subsequently constructed to solve the resultant mathematical programming problem. Numerical results show that, by employing the obtained optimal strategy, 1,3-PD concentration at the terminal time can be increased considerably. (C) 2012 Elsevier Inc. All rights reserved.
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