Dynamic Simulation and Control of a Continuous Bioreactor Based on Cell Population Balance Model

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Saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance equation (PBE) can be used to capture the dynamic behavior of such cultures. In this work, an unstructured-segregated model is used for dynamic simulation and controller synthesis. The mathematical model consists of a partial integro-differential equation describing the dynamics of the cell mass distribution (PBE) and an ordinary integro-differential equation accounting for substrate consumption. In order to solve the mathematical model, three methods, finite difference, orthogonal collocation on finite elements and Galerkin finite element are used to approximate the PBE model by a coupled set of nonlinear ordinary differential equations (ODEs). Then the resulted ODEs are solved by 4th order Rung-Kutta method. The results indicated that the orthogonal collocation on finite element not only is able to predict the oscillating behavior of the cell culture but also needs much little time for calculations. Therefore this method is preferred in comparison with other methods. In the next step two controllers, a globally linearizing control (GLC) and a conventional proportional-integral (PI) controller are designed for controlling the total cell mass per unit volume, and performances of these controllers are compared through simulation. The results showed that although the PI controller has simpler structure, the GLC has better performance.