Optimal control of photobioreactor accounting for photoinhibition and photoacclimation

The industrial cultivation of microalgae has increased substantially over the past two decades. These microorganisms have the ability to adapt their photosynthetic pigments in response to the amount of light they experience. Herein, we investigate a dynamic model that describes pigment adaptation and its effect on microalgal productivity in a photobioreactor where light is shone onto the surface and attenuated as it traverses the culture medium. We consider two controls – the light irradiance and the dilution rate of the photobioreactor under continuous operation and constant volume – and analyze strategies for maximal production of microalgal biomass using Pontryagin’s maximum principle. We also conduct a numerical investigation of turnpike properties in this context and discuss how self-shading within the culture could be exploited to increase productivity.