Dynamic Analysis and Control for a Bioreactor in Fractional Order

Abstract

In this paper, a mathematical model was developed to describe the dynamic behavior of a bioreactor in which a fermentation process takes place. The analysis took into account the bioreactor temperature controlled by the refrigerant fluid flow through the reactor jacket. An optimal LQR control acting in the water flow through a jacket was used in order to maintain the reactor temperature during the process. For the control design, a reduced-order model of the system was considered. Given the heat transfer asymmetry observed in reactors, a model considering the fractional order heat exchange between the reactor and the jacket using the Riemann–Liouville differential operators was proposed. The numerical simulation demonstrated that the proposed control was efficient in maintaining the temperature at the desired levels and was robust for disturbances in the inlet temperature reactor. Additionally, the proposed control proved to be easy to apply in real life, bypassing the singularity problem and the difficulty of initial conditions for real applications that can be observed when considering Riemann–Liouville differential operators.