Gain scheduled luenberger observers for microalgal cultures

Monitoring of microalgal processes is delicate due to the lack of on-line sensors, except for a few variables such as biovolume. In this study, software sensors are designed to reconstruct variables such as the internal nitrogen quota, whose follow-up is important when considering the production of lipids. The proposed software sensor makes use of a Droop model (one of the simplest available models in the literature) and it is based on a extended Luenberger observer. In the design procedure, uncertain parameters and model nonlinearities are formulated as time varying parameters, resulting into a quasi-Linear Parameter Varying (quasi-LPV) system. Lyapunov arguments and linear matrix inequalities (LMI) are used to design the proposed software sensors. A case study is considered to illustrate the observer demonstrating the potentials of the proposed approach.