Estimation of plasmid concentration in batch culture of Escherichia coli DH5α via simple state observer

The aim of this paper is to present an alternative state observer structure for online estimation purposes of the key dynamical variables in a class of batch culture for plasmid production; the latter has been extremely attractive to be used as DNA vaccines or gene therapy. A mathematical model for culture of Escherichia coli DH5α-harboring plasmid was considered a benchmark system for the application of the proposed estimation methodology. Local observability analysis revealed that the system is partially observable for plasmid concentration considering only the biomass concentration in the batch culture as the measured variable. The proposed observer is designed with a simple proportional–integral feedback of the measured biomass concentration, where under the proposed design, the observer gain´s array can compensate the main nonlinearities of the estimation error dynamics. The convergence of estimated variables to the real ones is mathematically analyzed, reaching an asymptotic behavior. Numerical experiments were performed, where a comparison with a standard extended Luenberger observer was done and the proposed estimation methodology revealed a satisfactory performance.