Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production

Chunjin Wei,Lansun Chen,Shuwen Zhang

doi:10.1155/2013/354095

Abstract

The work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate, and the initial concentrate of microorganism and substrate. For some special cases, it is also shown that the system may exist in order-2 periodic solution. Furthermore, our findings are confirmed by means of numerical simulations.

Highlights

Single-cell protein (SCP) is the protein extracted from cultivated microbial biomass
Kurbanoglu and Algur [6] studied single-cell protein production from ram horm hydrolysate by bacteria, and El-Saadany et al [7] studied the production of single cell protein from agricultural wastes by fungi
According to different reactions and differential control technologies, many dynamic models concerning the culture of microorganisms in the continuous bioreactor have been established [9,10,11,12,13]

Summary

Introduction

Single-cell protein (SCP) is the protein extracted from cultivated microbial biomass. In order to obtain the optimal conditions for microorganism growth and decrease the inhibition of the microorganism concentration or other negative effects, many authors introduced the state-dependent impulsion into the microorganism culture process and analyzed the system’s dynamic behavior [16,17,18]. No papers have discussed the mathematical model of cheese whey fermentation for single-cell protein production with impulsive feedback control. This paper aims to propose a mathematical model of cheese whey fermentation for single-cell protein production with feedback control.

Model Formulation

Numerical Analysis and Discussion