R. Aguilar–Lopez *1, V. Peña–Caballero2, M. I. Neria–Gonzalez3
1,2 Departamento de Biotecnología y Bioingeniería CINVESTAV–IPN, 2508 I.P.N. Av., San Pedro Zacatenco, Mexico City, Mexico, 07360 *E–mail: raguilar@cinvestav.mx
3 División de Ingeniería Química y Bioquímica, Tecnológico de Estudios Superiores de Ecatepec, Tecnológico Av., Ecatepec, Mexico, 53210
ABSTRACT
The main goal of this work is to present a new class of feedback controller which contains on its structure a polynomial form of the named control error, the proposed controller is applied to a class of sulfate–reducing chemostat in order to control the sulfate concentration, which would be useful for several biotechnological issues, as heavy metal removal in wastewater. The closed–loop behavior of the chemostat is theoretically analyzed and a practical convergence to the selected optimum trajectory is proved. The proposed methodology is applied to an experimentally corroborated kinetic model of a sulfate–reducing bacterium and further numerical experiments show the satisfactory closed–loop performance of the process in comparison with other controllers.
Keywords: Sulfate reducing chemostat, polynomial feedback, closed–loop stability.
]]>RESUMEN
El principal objetivo de este trabajo es el presentar una nueva clase de controlador de tipo retroalimentado, el cual contiene en su estructura una forma polinomial del llamado error de control, el controlador propuesto es aplicado a un quimiostato sulfato–reductor, el cual pudiera ser usado para varios fines biotecnológicos, como la remoción de metales pesados en aguas residuales. El comportamiento a lazo cerrado del quimiostato considerado es teóricamente analizado y se prueba convergencia práctica a la trayectoria óptima seleccionada. La metodología propuesta es aplicada a un modelo cinético de una bacteria sulfato–reductora experimentalmente validado y experimentos numéricos complementarios muestran un comportamiento a lazo cerrado satisfactorio en comparación con otros controladores.
DESCARGAR ARTÍCULO EN FORMATO PDF
References
[1] Alford JS, Bioprocess control: Advances and challenges. Computers and Chemical Engineering 30: 1464–1475 (2006). [ Links ]
[2] Aguilar R, Martínez SA, Rodríguez MG and Soto G, Process analysis for treatment of industrial plating wastewater: simulation and control approach. Chemical Engineering Journal 105: 139–145 (2005). [ Links ]
[3] Aguilar–López R, Neria–González MI, Domínguez–Bocanegra AR and Acevedo R, Robust generic model feedback under model uncertainties: Application to tubular reactor for treatment of industrial plating wastewater. Journal of Applied Research and Technology 3: 147–158 (2008). [ Links ]
[4] Baeza JA, Ferreira EC and Lafuente J, Knowledge–Based Supervision and Control of Wastewater Treatment Plant: a Real–Time Implementation, Water Science and Technology 12: 129–137 (2000). [ Links ]
[5] Bastin G and Dochain D, On–line Estimation and Adaptive Control of Bioreactors, Process Measurement and Control, Vol. 1. Elsevier: Amsterdam, (1990). [ Links ]
[6] Bailey JE and Ollis DF, Biochemical Engineering Fundamentals, Mc Graw Hill, Singapore (1986). [ Links ]
[7] Betancur MJ, Moreno JA, Moreno–Andrade I, Buitrón G, Practical optimal control of fed–batch bioreactors for the waste water treatment. International Journal of Robust and Nonlinear Control 3: 173 – 190 (2006). [ Links ]
[8] Chidambaram M and See RPA, Simple method of tuning PID controllers for integrator/dead–time processes. Computer & Chemical Engineering 27: 211-215 (2002). [ Links ]
[9] Cord–Ruwisch R (1985) A quick method for determination of dissolved and precipitated sulfides in cultures of sulfate–reducing bacteria. J Microbiol Methods 4:33–6. [ Links ]
[10] Fordyce AP, Rawlings JB, Edgar TF, In Computer Control of Fermentation Processes D. Omstead, Eds. CRC Press, Inc., Florida, (1987). [ Links ] Jorgensen BB, Mineralization of organic matter in a sea bed –the role of sulfate reduction–, Nature 296: 643–645 (1982). [ Links ]
[11] Hungate RE. A roll tube method for cultivation of strict anaerobes In: Norris JR, Ribbons DW, editors. Methods in Microbiology, Vol. 3B. London: Academic Press; (1969) p 117–32. [ Links ]
]]>[12] Kalafatis AD, Wang L and Cluett WR, Linearizing feed forward–feedback control of pH process based on Wiener model. Journal of Process Control 15: 103 –112 (2005). [ Links ]
[13] Kolmert Å, Wikström P, Hallberg K (2000) A fast and simple turbidimetric method for the determination of sulfate in sulfate–reducing bacterial cultures. J. Microbiol. Meth. 41:179–184. [ Links ]
[14] Neria–González I, Wang ET, Ramírez V, Romero JM, Hernández–Rodríguez E (2006) Characterization of Bacterial Community Associated to Biofilms of Corroded Oil Pipelines from the Southeast of Mexico. Anaerobe 12: 122–133. [ Links ]
[15] Neria.González MI and Aguilar–López R, Tracking Trajectories in a Continuous Anaerobic Bioreactor employing a Nonlinear Proportional Controller. Int. Journal of Chemical Reactor Engineering. 5 A73 (2007). [ Links ]
[16] Ogunnaike, B.A. & Ray, W.H. Process, Dynamics, Modeling and Control. Oxford University Press. New York, 1994. [ Links ]
]]>[17] Rivera ED, Morari M and Skogestad S, Internal model control 4. PID controller design. Industrial & Engineering Chemistry Process Design and Development 1: 252–265 (1986). [ Links ]
[18] Schugerl K, Bioreaction Engineering, vol. 1. Wiley: Chichester (1987). [ Links ]
[19] Smets IYM, Versyck KJE and Van Impe JFM, Optimal control theory: a generic tool for identification and control of (bio–) chemical reactors. Annual Reviews in Control 26: 57–73 (2002). [ Links ]
[20] Spear M, Time to turn up the speed? Process control developments continue to outrun their uptake by industry. Chemical Processing (2005), 23, 5, 345–349. [ Links ]
[21] Widdel F, In biology of anaerobic organism, ed Zehnder, AJB, Jhon Wiley, New York, pp 569–586 (1988). [ Links ]
]]>[22] Ziegler JG and Nichols NB, Optimum settings for automatic controllers, Trans. ASME, 64: 759 – 765 (1942). [ Links ]
]]>