Differential algebraic estimator for the monitoring of a class of partially known bioreactor models

The problem of monitoring in a common class of partially known bioreactor models is addressed. A reduced order observer namely differential algebraic estimator is proposed. The biomass is estimated by means of substrate concentration measurements. The estimation methodology is based on a suitable change of variable which allows generating artificial variables to infer the remaining mass concentrations constructing a differential-algebraic structure. The proposed methodology is applied to a class of Haldane unstructured kinetic model with success. Stability analysis in a Lyapunov sense for the estimation error is performed. Some remarks about the convergence characteristics of the proposed estimator are given and numerical simulations show its satisfactory performance. Finally, for comparison purposes, a high gain observer is presented: the convergence is possible only when the model is perfectly known.