Application of an extended Kalman filter for state estimation of a yeast fermentation

The development of a Kalman filter for state and parameter estimation of a biotechnical process is discussed. Because of the large complexity of biotechnical processes, mathematical models for online estimation are based on extensive simplifications. Therefore model errors in the structure and parameters cannot be avoided. In such situations, simulations of the process in combination with the estimator are very helpful during the design phase: these permit fast examinations of the different behaviour of linear filters compared to nonlinear algorithms and also investigations of the influence of sampling interval and initial values of state and filter variables on the estimation. By the use of such simulations, the suitability of process models with various degrees of simplifications can also be easily tested. Based on the simulations, an extended Kalman filter with iteration of the output equations was chosen. Besides the states, two parameters of a third order process model are estimated online. The filter algorithm was tested during batch processes and worked well after a slight modification. The filter behaviour observed in the experiments was very similar to the simulations.