Optimal Control for Multistage Nonlinear Dynamic System of Microbial Bioconversion in Batch Culture

Lei Wang,Enmin Feng,Zhilong Xiu,Yuduo Zhang

doi:10.1155/2011/624516

Abstract

In batch culture of glycerol biodissimilation to 1,3‐propanediol (1,3‐PD), the aim of adding glycerol is to obtain as much 1,3‐PD as possible. Taking the yield intensity of 1,3‐PD as the performance index and the initial concentration of biomass, glycerol, and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. A computational approach is constructed to seek the solution of the above model. Firstly, we transform the optimal control problem into the one with fixed terminal time. Secondly, we transcribe the optimal control model into an unconstrained one based on the penalty functions and an extension of the state space. Finally, by approximating the control function with simple functions, we transform the unconstrained optimal control problem into a sequence of nonlinear programming problems, which can be solved using gradient‐based optimization techniques. The convergence analysis and optimality function of the algorithm are also investigated. Numerical results show that, by employing the optimal control, the concentration of 1,3‐PD at the terminal time can be increased, compared with the previous results.

Highlights

The bioconversion of glycerol to 1,3-propanediol 1,3-PD has recently received more and more attention throughout the world due to its environmental safety, high region specificity, cheaply available feedstock, and relatively high theoretical molar yield 1
Nonlinear dynamical systems in this culture have been extensively considered in recent years 13–15
In this paper, based on the previous model in 16, taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state

Summary

Introduction

The bioconversion of glycerol to 1,3-propanediol 1,3-PD has recently received more and more attention throughout the world due to its environmental safety, high region specificity, cheaply available feedstock, and relatively high theoretical molar yield 1. 8 for the models of the continuous cultures, feeding strategy of glycerol 9 , and optimal control and optimality condition in fed-batch culture. Compared with continuous and feed-batch cultures, glycerol fermentation in batch culture can obtain the highest production concentration and molar yield 1,3-PD to glycerol 12. In this paper, based on the previous model in 16 , taking the yield intensity of 1,3-PD as the performance index and the initial concentration of biomass, glycerol and terminal time as the control vector, we propose an optimal control model subject to a multistage nonlinear dynamical system and constraints of continuous state. By employing the optimal control, the concentration of 1,3-PD at the terminal time can be increased, compared with the previous results

Objectives

Results

Conclusion