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
{"title":"Optimal Control of Lipid Extraction Model on Microalgae Using Linear Quadratic Regulator (LQR) and Pontryagin Maximum Principle (PMP) Methods","authors":"M. Mardlijah, Nur Ilmayasinta, L. Hanafi, Suharmadi Sanjaya","doi":"10.11113/MATEMATIKA.V34.N3.1145","DOIUrl":null,"url":null,"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.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1145","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Matematika
Matematika MATHEMATICS-
自引率
25.00%
发文量
0
审稿时长
24 weeks
期刊最新文献
An Almost Unbiased Regression Estimator: Theoretical Comparison and Numerical Comparison in Portland Cement Data Neutrosophic Bicubic Bezier Surface ApproximationModel for Uncertainty Data Using the ARIMA/SARIMA Model for Afghanistan's Drought Forecasting Based on Standardized Precipitation Index Heat Transfer Enhancement of Convective Casson Nanofluid Flow by CNTs over Exponentially Accelerated Plate Biclustering Models Under Collinearity in Simulated Biological Experiments
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1