LAUSR

Abstract The multiple-input, multiple-output nature of microbial fermentation processes are most often described by nonlinear state space models. In order to apply these models for control purposes, they require the fitting of a set of model parameters so they can provide an accurate description of the fermentation system. In order to prevent overfitting of the experimental data, the parameter estimation procedures should produce unique estimates with small confidence intervals. This is facilitated by dimensional analysis, a tool that provides proper scaling of the dynamic model, removing its dimensional units. However, it is surprising that fermentation models seldom employ dimensional analysis, although it is recognized as a tool that can reduce the number of parameters and thus facilitate a comparison between different sets of data. In this tutorial review, we develop a systematic approach for dimensionless reformulation applied to fermentation systems. The approach is demonstrated on parameter estimation studies for a non-isothermal CSTR model and two common microbial fermentation state space models. It is shown that the analysis reduces the number of parameters in the models to yield identifiable reparameterizations, increases the accuracy of the parameter estimation, facilitates sensitivity analysis, and it can be stated that model identification and dimensional analysis as two concepts/approaches are complementary to each other. These benefits are relevant for the next stage of process optimization and control implementation. This review demonstrates the benefits of the dimensional analysis procedure, especially as an essential model development step for bioreactor systems, and together with a structural identifiability analysis it corresponds to methodologies for model reparameterization and parameter reduction.