Abstract
Continuous cultures of budding yeast are known to exhibit autonomous oscillations that adversely affect bioreactor stability and productivity. This phenomenon is modeled by coupling the population balance equation (PBE) for the cell mass distribution to the mass balance for the rate limiting substrate. An efficient and robust numerical solution technique is developed using orthogonal collocation on finite elements. The controller design model is obtained by linearizing and temporally discretizing the ordinary differential equations resulting from spatial discretization of the PBE model. The resulting linear state-space model is used to design model predictive controllers that regulate the cell number distribution by manipulating the dilution rate and the feed substrate concentration. The ability of the controllers to stabilize steady-state and periodic solutions is evaluated via simulation.
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