MULTISTAGE OPTIMAL CONTROL FOR MICROBIAL FED-BATCH FERMENTATION PROCESS

In this paper, we consider multistage optimal control of biocon-version glycerol to 1,3-propanediol(1,3-PD) in fed-batch fermentation process. To maximize the productivity of 1,3-PD, the whole fermentation process is divided into three stages according to the characteristics of microbial growth. Stages 2 and 3 are discussed mainly. The main aim of stage 2 is to restrict accumulation of 3-hydroxypropionaldehyde and maximize the biomass in the shortest time, and the purpose of stage 3 is to get high productivity of 1,3-PD. With these different objectives, multi-objective optimal control problems are proposed in stages 2 and 3. In order to solve the above optimal control problems, the multi-objective problems are transformed to the corresponding single-objective problems using the mass balance equation of biomass and nor-malization of the objective. Furthermore, the single-objective optimal control problems are transformed to two-level optimization problems by the control parametrization technique. Finally, numerical solution methods combined an improved Particle Swarm Optimization with penalty function method are de-veloped to solve the resulting optimization problems. Numerical results show that the productivity of 1,3-PD is higher than the reported results.