Parameter Identi cation and Robust State Estimation of Microalgae Cultures

Microalgae cultivation is increasingly applied in view of their various applications, ranging from renewable energy to comestics, food and wastewater treatment. At the industrial level, microalgae are usually cultivated in bioreactors, speci cally designed to ensure an optimal distribution of light and nutrients, and called photobiorecators (PBR). To improve the PBR operation, it is of interest to develop monitoring and control techniques. However, the on-line instrumentation remains relatively limited, due to the costs of the probes, and the fact that probes are not commercially available to follow all the variables of interest. This is particularly true for intracellular concentrations. To alleviate this problem, the solution of choice is the use of state estimation techniques, or software sensors, which fuse the information from a predictive process model and readily available probes. These software sensors allow the on-line reconstruction of non-measured variables, and provide important dynamic information that can be exploited for monitoring and control purposes. However, the performance of these software sensors is dependent, on the dynamic model quality (robustness issue), and the available sensors (at minimum observability has to be satis ed, and beyond, the information content has an important impact on the estimator convergence). In this thesis, a at-pannel laboratory-scale PBR is considered for the cultivation of the marine microalgae Dunaliella Tertiolecta, which are selected as a representative case study. The on-line and o -line instrumentation and the collection of experimental data are described. Special attention is paid to the question of the availability of a ordable sensors for key variables, and a low-cost RGB sensor is proposed to monitor the biomass. On the basis of the experimental set-up, data can be collected to study the cultures of microalgae and to estimate the parameters of dynamic models. One of the most accepted models is the one proposed by Droop in 1968, and it is adopted in this study to develop several software sensors. Before embarking in model identi cation, structural identi cation is investigated using di erential algebra. Then, practical identi ability is assessed and optimal experiment design (OED) is used to propose informative experiments. The identi ed dynamic model can be used to design software sensors. The main contribution of this thesis is the proposal of several software sensors based on the concept of the extended Luenberger observer. These observers use either the on-line measurement of the biomass only, or the measurement of the biomass and extracellular nutrient concentrations, and are designed based on Lyapunov arguments to ensure the stability of the error dynamic. The Lyapunov arguments are reduced to a convex optimization problem expressed in terms of linear matrix inequalities (LMIs). To deal with the nonlinearities and uncertainties of the model, linear di erential inclusion (LDI) and quasi-Linear Parameter Varying (quasiLPV) representation are used. The observers are tested both in simulation and with experimental data.