Robust Luenberger observers for microalgal cultures

The advanced control of microalgal cultures usually requires the knowledge of several component concentrations, which are however not always measurable on-line. In this context, state estimation plays an important role, and software sensors should be robust to model uncertainties and measurement noise. In this study, two software sensors are designed in the form of extended Luenberger observers, using Lyapunov arguments and linear matrix inequalities (LMI). These observers are based on Droop model and a few available on-line sensors. The first observer design estimates the intracellular quota and substrate concentrations considering a linear differential inclusion modeling technique and a constant observer gain. On the other hand, the second one estimates only the intracellular quota concentration assuming uncertainties in the model parameters and a quasi-Linear Parameter Varying (quasi-LPV) representation of the nonlinear system. The results are presented considering simulated and experimental data from Dunaliella tertiolecta culture.