| Title:
|
Optimal control from inoculation on a continuous microalgae culture (English) |
| Author:
|
Torres-Muñoz, Jorge Antonio |
| Author:
|
Gutierrez-Carmona, Irandi |
| Author:
|
Dominguez-Bocanegra, Alma Rosa |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
224-240 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present work is centred on the problem of biomass productivity optimization of a culture of microalgae Spirulina maxima. The mathematical tools consisted of necessary and sufficient conditions for optimal control coming from the celebrated Pontryagin's Maximum Principle (PMP) as well as the Bellman's Principle of Optimality, respectively. It is shown that the optimal dilution rate turns to be a bang-singular-bang control. It turns out that, the experimental results are in accordance to the optimal mathematical findings. (English) |
| Keyword:
|
optimal control |
| Keyword:
|
microalgae |
| Keyword:
|
singular arc |
| Keyword:
|
dilution rate |
| MSC:
|
90C46 |
| MSC:
|
93C95 |
| idZBL:
|
Zbl 06587896 |
| idMR:
|
MR3501159 |
| DOI:
|
10.14736/kyb-2016-2-0224 |
| . |
| Date available:
|
2016-07-17T12:02:33Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145772 |
| . |
| Reference:
|
[1] Asenjo, J. A.: Bioreactor System Design..CRC Press, 1994. |
| Reference:
|
[2] Bertsekas, D. P., Bertsekas, D. P.: Dynamic Programming and Optimal Control. Vol. 1. No. 2..Athena Scientific, Belmont 1995. |
| Reference:
|
[3] Cañizares, R. O., Dominguez, A. R.: Growth of Spirulina maxima on swine waste..Bioresource technology 45 (1993), 1, 73-75. 10.1016/0960-8524(93)90148-5 |
| Reference:
|
[4] Cañizares, R. O.: Aerated swine-wastewater treatment with K-carrageenan-immobilized Spirulina maxima..Bioresource technology 47 (1994), 1, 89-91. 10.1016/0960-8524(94)90035-3 |
| Reference:
|
[5] Čelikovský, S., Cervantes-Herrera, Al., Ruiz-León, J.: Singular perturbation based solution to optimal microalgal growth problem and its infinite time horizon analysis..IEEE Trans. Automat. Control 55 (2010), 3, 767-772. MR 2654847, 10.1109/tac.2010.2040498 |
| Reference:
|
[6] Costa, J. A. V., Colla, L. M., Filho, P. F. Duarte: Improving Spirulina platensis biomass yield using a fed-batch process..Bioresource Technol. 92 (2004), 3, 237-241. 10.1016/j.biortech.2003.09.013 |
| Reference:
|
[7] Domínguez-Bocanegra, A. R.: Biosorption of Cadmium (II), Lead (II) and Nickel (II) by Spirulina Maxima..Int. J. Sci. 2.2013-10 (2013), 45-55. |
| Reference:
|
[8] al., M. C. García-Malea et: Modelling of growth and accumulation of carotenoids in Haematococcus pluvialis as a function of irradiance and nutrients supply..Biochem. Engrg. J. 26 (2005), 2, 107-114. 10.1016/j.bej.2005.04.007 |
| Reference:
|
[9] Goh, B. J.: Optimal control of a fish resource..Malayan Scientist 5.65-70 (1969), 1970. |
| Reference:
|
[10] al., M. J. Griffiths et: Interference by pigment in the estimation of microalgal biomass concentration by optical density..J. Microbiol. Methods 85 (2011), 2, 119-123. 10.1016/j.mimet.2011.02.005 |
| Reference:
|
[11] Johnson, C. D., Gibson, J.: Singular solutions in problems of optimal control..IEEE Trans. Automat. Control 8 (1963), 1, 4-15. MR 0151341, 10.1109/tac.1963.1105505 |
| Reference:
|
[12] Kirk, D. E.: Optimal Control Theory: An Introduction..Courier Corporation, 2012. |
| Reference:
|
[13] Kopp, R. E., Moyer, H. G.: Necessary conditions for singular extremals..AIAA J. 3 (1965), 8, 1439-1444. Zbl 0142.23303, 10.2514/3.3165 |
| Reference:
|
[14] Lee, Y. K., Low, Ch.-S.: Productivity of outdoor algal cultures in enclosed tubular photobioreactor..Biotechnol. and Bioengrg. 40 (1992), 9, 1119-1122. 10.1002/bit.260400917 |
| Reference:
|
[15] Lee, J. M.: Biochemical Engineering..Englewood Cliffs, Prentice Hall, NJ 1992. |
| Reference:
|
[16] Liberzon, D.: Calculus of Variations and Optimal Control Theory: A Concise Introduction..Princeton University Press, 2012. Zbl 1239.49001, MR 2895149 |
| Reference:
|
[17] Moreno, J.: Optimal time control of bioreactors for the wastewater treatment..Optimal Control Appl. Methods 20 (1999), 3, 145-164. MR 1710689, 10.1002/(sici)1099-1514(199905/06)20:3<145::aid-oca651>3.0.co;2-j |
| Reference:
|
[18] Pontryagin, L. S.: Mathematical Theory of Optimal Processes..CRC Press, 1987. Zbl 0882.01027 |
| Reference:
|
[19] Rehák, B., Čelikovský, S., Papáček, Š.: Model for photosynthesis and photoinhibition: parameter identification based on the harmonic irradiation O 2 response measurement..IEEE Trans. Automat. Control 53 Special Issue (2008), 101-108. MR 2492555, 10.1109/tac.2007.911345 |
| Reference:
|
[20] Zhang, X-W., Zhang, Y-M., Chen, F.: Application of mathematical models to the determination optimal glucose concentration and light intensity for mixotrophic culture of Spirulina platensis..Process Biochemistry 34 (1999), 5, 477-481. 10.1016/s0032-9592(98)00114-9 |
| . |
