Observability analysis of a nonlinear tubular bioreactor

In this paper an observability analysis is performed for an axial dispersion tubular bioreactor that involves one nonlinear growth reaction. The process is described by a semilinear parabolic Partial Differential Equation (PDE). More precisely, the analysis is performed on a tangent linearized model, that is described by a linear PDE with a spatial-dependent coefficient. It is reported that the associated linear infinitedimensional operator is a Riesz-spectral operator and generates a C0-semigroup. Then it is shown that a finite number of dominant modes of the system are observable when the substrate concentration is measured at the reactor output by an appropriate sensor. This result is confirmed by a numerical simulation.