Model predictive control of continuous yeast bioreactors using cell population balance models

Continuous cultures of budding yeast are known to exhibit autonomous oscill ations that adversely affect bioreactor stability and productivity. We demo nstrate that this phenomenon can be modeled by coupling the population bala nce equation (PBE) for the cell mass distribution to the mass balance of th e rate limiting substrate. An efficient and robust numerical solution proce dure using orthogonal collocation on finite elements is developed to approx imate the PBE model by a coupled set of nonlinear ordinary differential equ ations (ODEs). A controller design model is obtained by linearizing and tem porally discretizing the ODEs derived from spatial discretization of the PB E model. The resulting linear state-space model is used to develop model pr edictive control (MPC) strategies that regulate the discretized cell number distribution by manipulating the dilution rate and the feed substrate conc entration. Two choices of the controlled output Vector are considered: (i) the entire discretized distribution; and (ii) a subset of the discretized d istribution. The ability of the MPC controllers to stabilize steady-state a nd periodic solutions is evaluated via simulation. We show that superior cl osed-loop performance is obtained when a subset of the distribution is empl oyed as controlled outputs. (C) 2000 Elsevier Science Ltd. All rights reser ved.