ESTIMATION OF FERMENTATION PARAMETERS USING PARTIAL DATA

Frequently state variables in fermentation processes cannot be measured for the lack of sensors or interference. For example, in complex medium fermentations it is nearly impossible to obtain reliable estimates of the cell concentration. Absence of such data makes it difficult to model the fermentation process accurately. In such situations a mathematical technique called external differential representation (EDR) can be used to identify the system model by estimating the parameters in the absence of part of the data. The objective of this method is to rewrite the system equations in terms of the higher order differential equations in the input and output variables. This reduces the number of state variables needed to estimate the parameters. Additionally, relationships between the measured variables and the measured outputs and known inputs can also be developed which can be used to predict the unmeasured states. The reconstructibility of the system with the selected output is central to this analysis. This method is demonstrated on two systems-gibberellin and gramicidin S fermentations. The external differential representation in each case is used to identify the system parameters using only partial data, and the accuracy in predicting the unmeasured variables is checked with the complete data.