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

Saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations duringthe 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 unstructuredsegregatedmodel is used for dynamic simulation and controller synthesis. the mathematical modelconsists of a partial integro-differential equation describing the dynamics of the cell massdistribution (pbe) and an ordinary integro-differential equation accounting for substrateconsumption. in order to solve the mathematical model, three methods, finite difference, orthogonalcollocation on finite elements and galerkin finite element are used to approximate the pbe modelby a coupled set of nonlinear ordinary differential equations (odes). then the resulted odes aresolved by 4th order rung-kutta method. the results indicated that the orthogonal collocation onfinite element not only is able to predict the oscillating behavior of the cell culture but also needsmuch little time for calculations. therefore this method is preferred in comparison with othermethods. in the next step two controllers, a globally linearizing control (glc) and a conventionalproportional-integral (pi) controller are designed for controlling the total cell mass per unitvolume, and performances of these controllers are compared through simulation. the resultsshowed that although the pi controller has simpler structure, the glc has better performance.