Optimal control of nonlinear switched system in an uncoupled microbial fed-batch fermentation process |
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Authors: | Teng Niu Jingang Zhai Hongchao Yin Enmin Feng |
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Institution: | 1. School of Energy and Power Engineering, Dalian University of Technology, Dalian, Liaoning 116024, PR China;2. School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, PR China;3. School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, PR China |
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Abstract: | The bio-dissimilation of glycerol to 1,3-propanediol (1,3-PD) is a complex bioprocess due to the multiple inhibitions of substrate and products onto the cell growth. In consideration of both the inhibition mechanisms of 3-hydroxypropionaldehyde (3-HPA) and the transport modes of glycerol and 1,3-PD across the cell membrane, we establish a novel switched system which is represented by a ten-dimensional nonlinear dynamical equation containing both extracellular and intracellular environments. The uncoupled microbial fed-batch fermentation process are modeled using the switched system which the glycerol and alkali are respectively poured into. Taking the feeding rates of glycerol and alkali, the switching times and the mode sequence as the control variables, an optimal control model is proposed with the concentration of the terminal time 1,3-PD as performance index. In order to maximize the yield of 1,3-PD, the control parameterization technique and the exact penalty function method are used to solve the considered problem. Numerical results show that under the obtained optimal feeding rates of glycerol and alkali, switching times and mode sequence, the productivity of 1,3-PD at the terminal time is increased significantly compared with previous results. |
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Keywords: | Corresponding author |
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