Optimal control of nutrition restricted dynamics model of Microalgae biomass growth model

The biomass of the microalgae is very potential to be proposed as an alternative renewable energy resources because it could be extracted into lipid. Afterward, the lipid could be processed to get the biodiesel or bioethanol. The extraction of the biomass on lipid synthesis process is very important to be studied because the process just gives some amount of lipid. A mathematical model of restricted microalgae biomass growth just gives 1/3 proportion of lipid with respect to the biomass in the synthesis process. An optimal control is designed to raise the ratio between the number of lipid formation and the microalgae biomass to be used in synthesis process. The minimum/ Pontryagin maximum principle is used to get the optimal lipid production. The simulation shows that the optimal lipid formation could be reach by simultaneously controlling the carbon dioxide, in the respiration and photosynthesis the process, and intake nutrition rates of liquid waste and urea substrate. The production of controlled microalgae lipid could be increase 6.5 times comparing to the uncontrolled one.