Modelo matemático no lineal en un sistema de temperatura para un recinto cerrado
Abstract
In this article the mathematical model is explained for a didactic control module where the temperature variable is analyzed. The model being used is necessary to simulate the dynamics of the process and develop some control strategies that can be applied in a real system. With this purpose in mind, it is important that the model, which is not the only one, is a trustworthy representation of the purpose of analysis. To obtain the mathematical model, the gray box system is carried out. Here, the mathematical equations that rule the behavior of the process are known in terms of dynamic parameters of the system applied; this is why that the obtaining of the mathematical model is divided into two parts. The first one has to do with the physical equations of the system in terms of some unknown parameters. The second one deals with the way these parameters are found by using minimum squares. Once the mathematical model was done, its worthiness was confirmed. For such a purpose, the validity of the model was proved and it was found to be adequate. This system identification technique can be applied in other process with known physical equations in terms of unknown parameters.
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References
[2] A. Bula, A. Márquez, “Modelación matemática y simulación de un sistema de acondicionamiento de aire en estado transitorio”, Ingeniería y desarrollo, No.11, 2002.
[3] L.E. Barajas, “Identificación de parámetros de un modelo matemático mediante un algoritmo basado en cuasi-linearización y mínimos cuadrados”. Disponible en: http://biee.epn.edu.ec/ dspace/handle/123456789/377, 2004.
[4] M. Campbell, S. Brunke, “Nonlinear Estimation of Aircraft Models for On-line Control Customization”. Aerospace Conference IEEE Proceedings, Vol.2, pp: 2/621 - 2/628, 2001.
[5] D. Bravo, M. López, “Modelo Matemático de un Tubo Intercambiador de Calor”, Revista de la Sociedad Colombiana de Física, Vol. 41, No. 2, pp. 520-523, 2009.
[6] D. Mihai, “Digital Equipment for the Temperature Control Inside an Enclosure. The System Modelling”. ICATE 2010, Craiova, University of Craiova, Romania, 2010.
[7] D. Mihai, C. Caramida, “Digital equipment for the temperature ontrol inside an enclosure. The hardware and some experimental results”, ICMET, Craiova, Romania, 2010.
[8] D. Álvarez de los Corrales Melgar, “Modelización de calderas de recuperación de calor (soplado)”, Ingeniería química, No.417, pp.73-84, 2004.
[9] Engineering ToolBox. “Tools and Basic Information for Design, Engineering and Construction of Technical Applications”, 2005. http://www.engineeringtoolbox.com/air-temperature-pressuredensity-d_771.html Consulta: Marzo, 2009.
[10] J. Evans, S. Elkaim, B. Parkinson, “System Identification of an Autonomus Aircraft using GPS” Stanford Universtity, 2001.
[11] F. Cortés, F. Chejne, J. Zartha, C. Isaza. “Modelo Matemático de un refrigerador por adsorción de metanol en carbón activo”, Revista Biotecnología en el Sector Agropecuario y Agroindustrial, Vol.8, No.2, 2010.
[12] G.V. Kuznetsov, M.A., Sheremet, “Mathematical modelling of complex heat transfer in a rectangular enclosure”, Thermophysics and Aeromechanics, Vol.16, No.1, pp.119-128, DOI: 10.1007/ s11510-009-0012-z, 2009.
[13] S. Lyashevskiy, Y. Chen, “Nonlinear Identification of Aircraft Indianapolis. Control Applications”, Proceedings of the 1996 IEEE International Conference, 1996.
[14] N. Durango, A. Bula, L. Donaldo, “Modelo matemático para secador de alimentos de flujo radial”. Ingeniería y desarrollo, No. 15, pp.1-8, 2004.
[15] NI USB-622x/625x OEM. USER GUIDE. M Series USB-6221/6225/6229/6251/6255/6259 OEM Devices. http://www.ni.com/pdf/products/us/371910a.pdf, Consultado el 26 de Marzo de 2009.
[16] NS, LM34/LM35 Precision Monolithic Temperature Sensors. National Semiconductor.Application Note 460. October 1986.
[17] Manual NI USB-6259. http://sine.ni.com/ds/ app/doc/p/id/ds-20/lang/en, Consultado el 26 de Marzo de 2009.
[18] P. Ortiz, A. Arias, “Simulink aplicado a sistemas de control”. Fondo editorial ITM, Medellín, 2010.
[19] M. Pramparo, P. Rossi, “Balances de energía”, Universidad Nacional de Rio Cuatro http://www.ing.unrc.edu.ar/materias/balances_de_ masa_y_energia/archivos/teoricos/08-balances_de_energia.pdf Consulta octubre de 2010.
[20] L.C. Ríos, N. Toro, “Estimación de parámetros en modelos arma por el criterio de mínimos cuadrados” Scientia et Technica, Año XII, No.31, UTP, 2006.
[21] Power Control with Thyristors and Triacs. Power Semiconductor Applications Philips Semiconductors. 1994.
[22] Tools and Basic Information for Design, Engineering and Construction of Technical Applications”, 2005.Engieneering Toolbox, http://www.engineeringtoolbox.com/air-temperature-pressuredensity-d_771.html Consulta: Marzo, 2010.
[23] Triacs BT138 series.Philips Semiconductors Product specification.June 2001.
[24] A. Zabaleta, M. Larrayoz, “Computational Fluid Dynamics Studies in Heat and Mass Transfer Phenomena in Packed Bed Extraction and Reaction Equipment”, Universitdad Politécnica de Catalunya (España), 2007.
