Optimal control for extraction lipid model of microalgae Chlorella Vulgaris using PMP method

Abstract

Microalgae is one of the energy to be used as biodiesel. Chlorella Vulgaris is one of the most economical algae to produce biodiesel, because these green algae are rich in carbohydrates, require no special care, and easy to grow. Algae oil obtained for biodiesel production is obtained through a fairly long process, one of which is the process of lipid extraction. In the study of lipid extraction process using solid-liquid or leaching extraction is the transfer of dissolved dissolved components from solids into the solvent. In the study used CO2-expended methanol (CXM). Soxhlet Extraction Method is a method for lipid extraction using hexane, in the process of extraction with Soxhlet tool there is a process of lipid mass transfer contained in Chlorella Vulgaris to flow CXM. This process of displacement has created a diferential equation which can be viewed as a system by Sriati Monalisa Siahaan(2016) to be used as a mathematical model to predict extractable lipid results for subsequent use as the main ingredient of biodiesel production. In her research, Sriati refers to a research conducted by Yi-Hung Yang(2015). In this research aims to perform optimal control with Pontryagin Maximum Principle (PMP) method to produce maximum lipid extraction result. This method is used to obtain the best control of the dynamic system from the initial state to the last by maximizing the objective function and more modern than other methods such as Linear Quadratic Regulator (LQR). Using the PMP method to optimal control in this systems, can increase the value of lipid concentration.