Optimal Control For Nonlinear Dynamical System Of Microbial Continuous Culture

Based on the microbial conversion of glycerol to 1,3-propanediol,we study the optimal control problem of continuous fermentation.This study provides a reference for large-scale production of 1,3-PD,and is also conducive to the study of optimal control direction.The main research results of this paper can be summarized as follows.1.In the process of continuous culture about glycerol bioconversion to 1,3-propanediol,taking into account the microbial growth rate is dependent not only on the concentration of current moment but also on the concentraton of the moment before.So we introduce a time-delay variable in the concentration of microorganism and establish a nonlinear time-delay dynamic system for continuous fermentation.And some important properties are discussed.2.Taking the concentration of 1,3-PD at terminal time as the objective function,using the dilution rate and the feeding glycerol concentration as continuous functions about time t,and taking these functions as control variables,we propose an optimal control model governed by the time-delay system and continuous state inequality constraints.The aim is to maximize the concentration of 1,3-PD at the terminal time by controlling the dilution rate and the feeding glycerol concentration.3.The optimal control problem is an optimization problem with constraints.In order to solve this problem,first,we use a constraint transcript technology.Then,we use control parametrization method to solve this problem,the whole time-based process control is transformed into a multi-stage control,an optimal control problem is approximated by a corresponding optimal parameter selection problem.4.Based on the control vector parametrization approach,we developed a sensitivity-based adaptive refinement method to find the optimal control parameter,in which he number of stages and the length of each stage's interval are both self-adapted.Moreover,in order to avoid falling into local optimum,we combined improved particle swarm with sensitivity-based adaptive refinement optimization algorithm to solve the problem.The numerical results illustrate the validity of the optimization algorithm and indicate that the concentration of 1,3-PD at the terminal time is increased significantly by the obtained optimal control strategy,proves the effectiveness and the validity of this algorithm.5.Considering the mode of transmemberane transport between substrate and product and the inhibition of 3-HPA to the growth of cells,we use a eight dimensional dynamical system to describe the reaction process of continuous fermentation.The optimal control model is established and the optimal control strategy is obtained by numerical calculation.