Optimal Control of Lipid Extraction Model on Microalgae Using Linear Quadratic Regulator (LQR) and Pontryagin Maximum Principle (PMP) Methods

Algae are good plants as raw materials for biodiesel. Chlorella Vulgaris is one of the most economical algae to produce biodiesel since it is rich in carbohydrates, require no special care, and easy to grow. Algae oil for biodiesel production is obtained through fairly long processes, one of which is the lipid extraction. Mathematical model can be used to obtain optimal results. The optimal control theory itself is concerned with the analysis of controlled dynamic systems, in which a system is directed from configurations given to some desire target by minimizing or maximizing some criteria. In this study, LQR formulation has the advantages of easy to analyze and implementation. In comparison, optimum control is performed using the PMP method, to obtain the best control of the dynamic system from the initial state to the end, i.e by maximizing the objective function. This method is a better method than the LQR method. Optimal control is performed in order to optimize the yield of lipid concentration in the solvent flow (C-s), in the microalgae particles (C-p), and minimizing the volume of solvent (v). From the simulation, it is found that the PMP method is more optimal in this system compared to the LQR method.