Nonlinear productivity control using a multi-staged cell population balance model

Cell growth processes are inherently nonlinear and as such are difficult to control. Moreover, due to the operation of the cell cycle, cell properties are distributed among the cells of a population. The only type of mathematical models that account for this heterogeneous nature of cell growth consists of the so-called cell population balance models. In this paper, we address the problem of controlling the productivity of a desired product using such a cell population balance model for the process description. It is assumed that cells grow in a continuous bioreactor, in two cell cycle stages. We further assume that the product is only being produced during the second stage of the cell cycle. We develop a cell population balance model consisting of a system of two partial differential equations, each describing the dynamics of cell growth during each of the two stages of the cell cycle, and two ordinary differential equations, describing the dynamics of the limiting substrate and product concentrations. The feed substrate concentration is considered as the manipulated input for achieving the control objective. Nonlinear and linear feedback laws that use measurements of the mass distributions of the two stages and the substrate and product concentrations, to induce a pre-specified output response are synthesized and are tested and compared through numerical simulations.