Optimal 1,3-propanediol production: Exploring the trade-off between process yield and feeding rate variation

• We consider the optimal control of a microbial fed-batch process.
• The control scheme is designed to minimize control changes.
• Minimizing control changes results in high-quality controls that are cheap to implement.

This paper proposes a new optimal control model for the production of 1,3-propanediol (1,3-PD) via microbial fed-batch fermentation. The proposed model is governed by a nonlinear multistage dynamic system with two modes: feeding mode, in which glycerol and alkali substrates are added continuously to the fermentor; and batch mode, in which no substrates are added to the fermentor. The non-standard objective function incorporates both the final 1,3-PD yield and the cost of changing the input feeding rate, which is the control variable for the fed-batch fermentation process. Continuous state inequality constraints are imposed to ensure that the concentrations of biomass, glycerol, and reaction products lie within specified limits. Using the constraint transcription method, we approximate the continuous state inequality constraints by a conventional inequality constraint to yield an approximate parameter optimization problem. We then develop a combined particle swarm and gradient-based optimization algorithm to solve this approximate problem. The paper concludes with simulation results.