Observability analysis of nonlinear tubular (bio)reactor models: A case study

This paper deals with the observability analysis of nonlinear tubular bioreactor models. Due to the lack of tools for the observability analysis of nonlinear infinite-dimensional systems, the analysis is performed on a linearized version of the model around some steady-state profile, in which coefficients can be functions of the spatial variable. The study starts from an example of tubular bioreactor that will serve as a case study in the present paper. It is shown that such linear models with coefficients dependent on the spatial variable are Sturm–Liouville systems and that the associated linear infinite-dimensional system dynamics are described by a Riesz-spectral operator that generates a C0 (strongly continuous)-semigroup. The observability analysis based on infinite-dimensional system theory shows that any finite number of dominant modes of the system can be made observable by an approximate point measurement.