Cell population balance modeling and control in continuous bioreactors

In this work we address the problem of controlling different moments of the cell mass distribution using cell population balance modeling for the derivation of appropriate nonlinear feedback control laws. The mathematical model used for dynamic simulation and controller synthesis consists of a partial integro-differential equation describing the dynamics of the cell mass distribution and an ordinary integro-differential equation accounting for substrate consumption. Nonlinear feedback laws that induce a desired closed-loop response for the biomass concentration (first moment), the cell density (zeroth moment) and the second moment of the cell mass distribution are developed and their performance and robustness to parameter uncertainties are tested via numerical simulations.