Toward Optimal Control of Flat Plate Photobioreactors: the Greenhouse Analogy?

The cultivation of algae in photo-bioreactors shows similarities to crop cultivation in greenhouses, especially when the reactors are driven by sun light. Advanced methodologies for dynamic optimization and optimal control for greenhouses are known from earlier research. The aim here is to extend these methodologies to microalgae cultivated in a flat plate photo-bioreactor. A one-state space model for the algal biomass in the reactor is presented. The growth rate vs. light curve is parameterized on the basis of experimental evidence. Spatial distribution of light and growth rate between the plates is also considered. The control variable is the dilution rate. Dynamic optimal control trajectories are presented for various choices of goal function and external solar irradiation trajectories over a horizon of 3 days. It was found that the algae present in the reactor at final time represent a value for the future. Numerical and theoretical results suggest that the control is bang-(singular-)bang, with a strong dependence on the weather. The optimal biomass also depends on the available light, and achieving it to reach a new optimal steady cycle after a prolonged change in weather may take several days. A preliminary theoretical analysis suggests a control law that maximizes the effective growth rate. The analysis shows that like in the greenhouse case, the co-state of the algal biomass plays a pivot role in developing on-line controllers.