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Abstract
This research applies a modeling approach known as Tendency Modeling and couples it with a Kalman filter to provide state estimates of a fed-batch fermentation process, the penicillin fermentation. The effect of building Kalman filters based on tendency models with the ultimate objective of updating tendency models on-line was the subject of the research.
The penicillin process was represented by an augmented version of the Bajpai and Reu$\beta$ model. This model was modified to include mass transfer limitations, gas phase equations, and precursor and carbon dioxide equations. Data collected from the simulated process had errors incorporated as noisy parameters, inputs, and measurements. In order to account for these errors, the data was pretreated during the tendency modeling step. Traditional methods for data pretreatment are non-linear and cannot be used for the linear stoichiometric modeling procedure employed by tendency modeling. Alternatively, a method was developed by applying a technique known as weighted factor analysis in conjunction with a linearized standard deviation model.
Because data is typically collected at various rates during a fermentation, a technique known as sequential measurement updating was applied so that the Kalman filter estimates could be updated as data became available. In addition, a parameter adaptive Kalman filter was developed so that a model for the mass transfer coefficient, $k\sb{\rm L}a$ would not be required.
In general, errors in the model structure affect estimation performance more than errors in the model parameters. Among the model parameters, however, the yield and maintenance coefficients had the largest effect on estimation accuracy. A comparison of Kalman filters based on different tendency models revealed that the accuracy of the stoichiometry was more important than the accuracy of the kinetic parameters. The focus of the modeling effort, therefore, must be on accurately identifying the process stoichiometry and revealing key phenomena such as maintenance.
