Parameter identification and optimization algorithm in microbial continuous culture

In this study, a novelty mathematical model is established to formulate the continuous culture of glycerol to 1,3-Propanediol (1,3-PD) by Klebsiella pneumoniae, in which the inhibition of 3-hydroxypropionaldehyde (3-HPA) to cells growth and activity of some enzymes (such as glycerol dehydratase (GDHt) and 1,3-PD oxidoreductase (PDOR)), and the passive diffusion and active transport of glycerol and 1,3-PD across cell membrane are all taken into consideration. Taking the mean relative error between the experimental data and calculated values as the performance index, a parameter identification model involving multiple nonlinear dynamic systems is presented. The identifiability of the parameter identification model is also proved. Finally, an improved particle swarm optimization (PSO) algorithm is constructed to find the optimal parameters for the systems under substrate limitation and excess conditions, respectively. Numerical results not only show that the established model can be used to describe the continuous fermentation reasonably, but also the improved PSO algorithm is valid.