Modeling and multi-objective optimal state-dependent control of a continuous double-bioreactor in series fermentation

Abstract

This paper models a continuous double-bioreactor in series fermentation of glycerol to 1,3-propanediol by a nonlinear dynamic system and formulates its process control by a multi-objective optimal control problem formulating the dilution rates as varying-coefficient state-dependent controls. Control parameterization and time scale transformation are firstly applied to transform the proposed optimal control problem into a large-scale parameter optimization problem, which is then solved by a novel numerical algorithm based on an improved dynamic neighborhood learning strategy and a classified pairwise competition mechanism. Numerical results suggest that the proposed algorithm has good diversity of solutions and convergence to the Pareto optimal front for complex multi-objective problems. Numerical comparisons indicate that the proposed control has the characters of shorter computation time, higher calculation accuracy, and poorer stability when compared to two closed-loop controls, and is better in system stability and improving mean productivity compared to two other open-loop controls. Simulation curves also show the potential application of double-bioreactor in series fermentation.