Modeling And Identification Of Nonlinear Hybrid Dynamical S System In Batch Anaerobic Culture

The batch anaerobic culture of glycerol bio-conversion to1.3-propanediol(1.3-PD) by Klebsiella Pneumoniae(K. Pneumoniae) isinvestigated in this paper. Considering separately unclear transportmechanism of both extracellular glycerol and intracellular1.3-PD acrosscell membrane, and the inhibitions of3-hydroxypropionaldehyde(3-HPA)to the growth of biomass, the consumption of glycerol and the productionof extracellular substances, nonlinear hybrid dynamical S systems areproposed to simulate the batch anaerobic culture process. Then takingthe minimal error between calculated data and experimental results asobjective function, a nonlinear hybrid dynamical S system identificationmodel is set up. Finally, an improved particle swarm optimization (PSO)algorithm with the inertia weight is used to solve the identificationproblem, aiming to infer the most reasonable transport mechanisms ofglycerol and1.3-PD across cell membrane, and the inhibitions of3-HPAto biomass, substrate and extracellular products.This research can not only enrich the theory and application ofnonlinear hybrid dynamical system, S system, system identification, butalso be helpful for deeply understanding metabolism pathways ofglycerol bio-conversion to1.3-PD by Klebsiella Pneumoniae.Subsequently, it can provide some reference for the industrial productionof1.3-PD. Therefore, this research is interesting and meaningful in batchtheoretical guide and productive practice.The main results obtained in this dissertation may be summarized asfollows:(1) In this dissertation, firstly, based on the batch anaerobic culture of glycerol bio-conversion to1.3-PD by Klebsiella Pneumoniae, andwithout considering the inhibitions of3-HPA to the growth of biomass,the consumption of glycerol and the production of products(1.3-PD,acetic, ethanol), the corresponding nonlinear hybrid dynamical S systemwhich is accordance with nine possible transport mechanismcombinations of glycerol and1.3-PD across cell membrane, is developedto describe the batch culture. Subsequently, the Lipschitz and lineargrowth conditions of functions of S system are proved. The existence,uniqueness, continuity and differential of solutions to S system are alsodiscussed. Secondly, taking the minimal error between calculated dataand experimental results as objective function, the parameteridentification model is set up, and the identification of model containingdiscrete and continuous parameters is also proved. Finally, an improvedparticle swarm optimization (PSO) algorithm with the inertia weight isused to solve the identification problem. Numerical results show that it ismost reasonable that both glycerol and1.3-PD pass cell membrane byboth passive diffusion and active transport, and the nonlinear hybriddynamical S system can simulate the batch culture process better.(2)On the basis of the above nonlinear hybrid dynamical S system,and supposing that glycerol and1.3-PD pass cell membrane by bothpassive diffusion and active transport, nonlinear hybrid dynamical Ssystem is developed in order to deduce the inhibitions of3-HPA tobiomass, substrate and extracellular products. Then, applying PSOalgorithm with inertia weight to solve the identification model, theinhibitions of3-HPA to biomass, substrate and products are deducedaccording to the minimal values of objective function.(3)Due to the difficulty to solve the identification model, in whichdiscrete and continuous parameter variables are contained, the original problem can be divided into identification sub-problem about continuousparameters and identification sub-problem about discrete variables inaccordance with the independence of the two kinds of identificationparameters. Because the objective function and constraint conditions ofthe above two nonlinear hybrid dynamical S systems arenonlinear-functional in terms of parameters, analytic solutions can not beobtained so far. Secondly, numerical simulations are given by softwareC++and Matlab. Finally, the more satisfactory numerical solution isobtained, so the most reasonable S system is identified.