Parameter identification and steady-state optimization of microbial continuous fermentation based on two-stage and interior point methods

Abstract

In this paper, a mathematical model of the GMA(Generalized Mass Action) system for a class of microbial continuous fermentation processes is proposed, and the mathematical properties of the GMA system are discussed. A two-stage method is proposed to determine the parameter values of the GMA system. First, the GMA system is rewritten. In the first stage, the logarithmic transformation and linear least square method are used to solve the parameter identification problem of the rewritten system. In the second stage, a system of linear equations is solved. The parameters in the original GMA system are then identified by the two-stage method. Compared with the error results of existing literature [5,6,10,20,22,25], smaller error values have been achieved. This shows that our proposed GMA system can better describe the microbial continuous fermentation process. To determine the optimal operating condition of the microbial continuous fermentation process, a steady-state optimization model is established by maximizing the volume yield of 1,3-propanediol. Considering the power function structure of the steadystate optimization model, we further transform it into a problem with a linear objective and multiple linear constraints. The transformed problem can be easily solved by the presented interior point algorithm. The optimization results show that the maximum volume yield of 1,3-propanediol has increased to 403.4028 mmol/(L • h). This result can provide a theory guide for the practical production of 1,3-propanediol.