Influence of the sensor location on the practical observability of distributed parameter bioreactors

In this paper, the practical observability of a fixed bed bioreactor with two biochemical reactions (microorganisms growth and death) and two components (biomass and a limiting substrate), and where dispersion is assumed to be negligible, is analyzed. The substrate is assumed to be measured by one, two or three sensors, either at one position in the reactor (one sensor), or at the reactor output and somewhere (one (two sensors) or two (three sensors) positions) along the reactor. The optimal location of the internal sensor(s) is analyzed by considering the conditioning number of the observability matrix of the linearized tangent model of the discretized model of the fixed bed bioreactor. The sensitivity analysis with respect to the model parameters and the discretization method (orthogonal collocation) parameters is carried out. The results are illustrated via simulation of an extended Luenberger observer.