Stability Assessment of Microalgal Photobioreactors for Carbon Dioxide Capture under Dilution Rate Constraints

Algal cultivation is a sustainable approach which can be used not only for carbon dioxide sequestration but also for making useful products in many industries. To facilitate the widespread adoption of this approach, the current research studies the stable control of closed photobioreactors (PBRs) cultivating microalgae. More specifically, a proportional-integral (PI) controller is employed for the tracking of the microalgal concentration to a desired reference corresponding to a required amount of sequestrated carbon dioxide. In the presence of the practically positive and bounded constraints of the dilution rate, the stability and reference tracking of the closed-loop PBR system needs to be assessed. This work then derives conditions under which a unique equilibrium point exists and the closed-loop PBR system is asymptotically stable around such an equilibrium point. The derived theoretical results are validated and illustrated through numerical simulations for PBRs of the microalgae Chlorella vulgaris.