Observer design for lactic-acid bacteria population balances with non-uniformly delayed measurements

The paper addresses the problem estimating the cell-mass distribution density, glucose and lactate concentration, as well as of the total biomass concentration in lactic-acid fermentation. The estimate is based on the combination of a cell population balance model with the available measurements. The model shows a cascade structure of a nonlinear finite-dimensional subsystem and a linear infinite-dimensional subsystem. The measurements are available on different time scales. On a quasi-continuous time scale optical density and conductivity are measured. The cell-size distribution is measured with a considerably lower frequency and is furthermore subject to non-uniform delays. The proposed estimation strategy exploits the cascade structure and consists of two cascaded discrete-time extended Kalman filters (EKFs). The performance of the proposed approach is demonstrated using experimental data from batch experiments with Streptococcus thermophilus . The estimation strategy improves the mean normalized root mean squared error of the distribution by approximately 41.6 % compared to a pure simulation.