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

IF 0.3 Q4 MATHEMATICS Matematika Pub Date : 2018-12-31 DOI:10.11113/MATEMATIKA.V34.N3.1145
M. Mardlijah, Nur Ilmayasinta, L. Hanafi, Suharmadi Sanjaya
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引用次数: 4

Abstract

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 (Cs), in the microalgae particles (Cp), 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.
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线性二次调节器(LQR)和庞特里亚金最大值原理(PMP)对微藻脂质提取模型的优化控制
藻类是作为生物柴油原料的好植物。小球藻是生产生物柴油最经济的藻类之一,因为它富含碳水化合物,不需要特别护理,而且易于种植。用于生产生物柴油的藻类油是通过相当长的过程获得的,其中之一是脂质提取。数学模型可以用来获得最佳结果。最优控制理论本身涉及受控动态系统的分析,其中通过最小化或最大化一些标准,将系统从给定的配置引导到某个期望目标。在本研究中,LQR公式具有易于分析和实现的优点。相比之下,使用PMP方法进行最佳控制,以获得从初始状态到结束的动态系统的最佳控制,即通过最大化目标函数。这种方法比LQR方法更好。进行最佳控制以优化溶剂流(Cs)、微藻颗粒(Cp)中脂质浓度的产率,并最小化溶剂体积(v)。仿真结果表明,与LQR方法相比,PMP方法在该系统中更为优化。
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来源期刊
Matematika
Matematika MATHEMATICS-
自引率
25.00%
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0
审稿时长
24 weeks
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