The Theory of LQ Optimization of Fermentation

Abstract

Linear-quadratic (LQ) optimal control theory is applied to the problem of optimizing the time-dependent process conditions affecting the fed-batch production of blomass. Two linear models are derived which are suitable for model-based optimization. Neither model assumes a particular time behaviour of the specific growth rate. The minimization of three different quadratic cost criteria is solved.The first optimization problem is to maximize the blomass production. This results in a undesirable specific growth rate trajectory, so that In the second optimization problem an additional constraint to minimize the specific growth rate Is incorporated, leading to an exponential substrate feed rate trajectory. The third problem considered is when the specific growth rate must follow a predetermined trajectory while at the same time the blomass production must be maximized. The result of this optimization gives useful insight into how competing requirements can be met In an optimal fashion.Finally, the problem of on-line parameter estimation is addressed and a solution proposed in the form of a (standard) Kalman Filter.