Optimal control of microalgae growth using linear quadratic regulator method with firefly algorithm optimization

Microalgae is an important potential resource for various industrial applications. In the industry, there are a variety of processed products from algae biomass. Lipids from microalgae used for biofuell, humans and animals in food supplements while in the pharmaceutical, lipids used as a vitamin or protein. The other application of microalgae captures CO ₂ and wastewater treatment. This research discusses the optimal control of microalgae growth with variable control are carbon dioxide and nutrients. In this case, the methodology is the Linear Quadratic Regulator method. In the Linear Quadratic Regulator method, there are weights in which the value is determined by trial and error in the matrices Q and R. The method of optimizing the weight value is required to optimize the weight. In this paper, the firefly algorithm is used to optimize the matrix values for Q and R. Application of firefly algorithm is able to optimally increase microalgae growth, so that the biomass produced is also abundant. The using of Firefly Algorithms optimization in the LQR method can increase algal concentration by 63.3% of the initial concentration.