Identificación de procesos y sintonización de controladores PID mediante una prueba de relé usando un algoritmo genético simple

Autores/as

  • José Rubén F. Lagunas-Jiménez Facultad de Ingeniería, Universidad Autonoma de Campeche Campus V Predio s/n por Av. Humberto Lanz Cardenas y Fracc. Ecologico Ambiental Siglo XXIII, col Ex Hacienda Kala. San Francisco de Campeche, Campeche. CP 24085
  • Benjamín Ortiz-Moctezuma Universidad Politécnica de Victoria Av. Nuevas Tecnologias 5902, Parque Cientifico y Tecnologico de Tamaulipas, Carretera Victoria-Soto La Marina Km. 5.5. Ciudad Victoria, Tamaulipas. CP 87138
  • Victor Moo-Yam Facultad de Ingeniería, Universidad Autonoma de Campeche Campus V Predio s/n por Av. Humberto Lanz Cardenas y Fracc. Ecologico Ambiental Siglo XXIII, col Ex Hacienda Kala. San Francisco de Campeche, Campeche. CP 24085
  • Alonzo E. González Aguilar Facultad de Ingeniería, Universidad Autonoma de Campeche Campus V Predio s/n por Av. Humberto Lanz Cardenas y Fracc. Ecologico Ambiental Siglo XXIII, col Ex Hacienda Kala. San Francisco de Campeche, Campeche. CP 24085

DOI:

https://doi.org/10.30973/progmat/2015.7.3/4

Palabras clave:

FFT, modelado, optimización no lineal, mínimos cuadrados, controlador PID

Resumen

En este trabajo se presentan dos problemas de control a partir de la identificación de múltiples puntos de la respuesta en frecuencia de sistemas lineales, mediante la técnica de relevador en lazo cerrado. En un caso, los puntos identificados son usados para la sintonización de controladores PID. La otra aplicación es hacia la obtención del modelo matemático mediante función de transferencia. Ambas dificultades son planteadas como un problema de minimización no lineal de mínimos cuadrados sin restricciones. El problema de optimización es resuelto con un algoritmo genético simple.

Biografía del autor/a

José Rubén F. Lagunas-Jiménez, Facultad de Ingeniería, Universidad Autonoma de Campeche Campus V Predio s/n por Av. Humberto Lanz Cardenas y Fracc. Ecologico Ambiental Siglo XXIII, col Ex Hacienda Kala. San Francisco de Campeche, Campeche. CP 24085

José Rubén F. Lagunas-Jiménez received a diploma engineering degree in Communications and Electronics Engineering from ESIME-IPN and a PhD in automatic control from Cinvestav-IPN, México D.F. He is researcher and teacher at University of Campeche, México. His research includes multiobjective optimization using genetic algorithms and fuzzy control.

Benjamín Ortiz-Moctezuma, Universidad Politécnica de Victoria Av. Nuevas Tecnologias 5902, Parque Cientifico y Tecnologico de Tamaulipas, Carretera Victoria-Soto La Marina Km. 5.5. Ciudad Victoria, Tamaulipas. CP 87138

Benjamín Ortiz-Moctezuma received a diploma engineering degree in Mechanical Engineering from ESIME-IPN and a PhD in Automatic Control from Cinvestav-IPN, México, D.F. He is researcher and teacher at Polytechnic University of Victoria, Tamaulipas. Mexico. His research includes delay systems in automatic control.

Victor Moo-Yam, Facultad de Ingeniería, Universidad Autonoma de Campeche Campus V Predio s/n por Av. Humberto Lanz Cardenas y Fracc. Ecologico Ambiental Siglo XXIII, col Ex Hacienda Kala. San Francisco de Campeche, Campeche. CP 24085

Victor Moo-Yam received a diploma engineering degree in Electronics Engineering from University of Campeche and a PhD degree in Bioelectronics from Cinvestav-IPN, México D.F. He is researcher and teacher at University of Campeche, México. His research includes instrumentation and chemical sensors.

Alonzo E. González Aguilar, Facultad de Ingeniería, Universidad Autonoma de Campeche Campus V Predio s/n por Av. Humberto Lanz Cardenas y Fracc. Ecologico Ambiental Siglo XXIII, col Ex Hacienda Kala. San Francisco de Campeche, Campeche. CP 24085

Alonzo E. González Aguilar is a senior student of Engineering in Mechatronics at University of Campeche, México.

Citas

Åström, K.J., Hägglund, T. PID Controllers: Theory, Design, and Tuning. Instrument Society of America, Research Triangle Park, NC, 1995.

Jamshidi, M., Coelho, L., Dos Santos, R.A. Krohling, R.R., Fleming P.J. Robust Control Systems with Genetic Algorithms. CRC Press LLC, 2003.

Ziegler,G., Nichols, N.B. Optimum Settings for Automatic Controllers. Trans. ASME. 1942, 64(11), 759-768. https://doi.org/10.1115/1.2899060

Hang, C.C., Åström, K.J., Wang, Q.G. Relay feedback auto-tuning of process controllers—a tutorial review. IFAC, Journal of Process Control. 2002, 12(1), 143– 162. https://doi.org/10.1016/S0959-1524(01)00025-7

Åström, K.J., Hägglund, T. Automatic Tuning of simple controllers with specification on phase and amplitude margins. Automatica. 1984, 20(5), 645-651. https://doi.org/10.1016/0005-1098(84)90014-1

Wang, Q. G. Process Frequency Response Estimation from Relay Feedback. Control Eng. Practice.1997, 5(9), 1293-1302. https://doi.org/10.1016/S0967-0661(97)84368-7

Doyle, J., Francis, B.A., Tannenbaum, A.R., Feedback Control Theory. Macmillan Publishing Company, 1992.

Wang, Q.G., Chieh, C.C., Bi, Q. A Frequency domain controller design method. Chemical Engineering Research and Design. 1997, 75, 64-72. https://doi.org/10.1205/026387697523228

Gavin, H. P. The Levenberg-Marquardt method for nonlinear least squares curve-fitting problems. Department of Civil and Environmental Engineering Duke University, 2013.

Griva, I., Nash, S.G., Ariela, S. Linear and Nonlinear Optimization, Second Edition. Society for Industrial Mathematics, 2009.

Transtrum, B., Sethna, J.P. Improvements to the Levenberg-Marquardt algorithm for nonlinear leastsquares minimization, Preprint submitted to Journal of Computational Physics. 2012. https://doi.org/10.48550/arXiv.1201.5885

Liu, T., Wang, Q. G., Huang, H. P. A tutorial review on process identification from step or relay feedback test. Journal of Process Control. 2013, 23, 1597–1623. https://doi.org/10.1016/j.jprocont.2013.08.003

Levy, S., Korotkin, S., Hadad, K., Ellenbogen, A., Arad, M., Kadmon, Y. PID autotuning using relay feedback. Electrical & Electronics Engineers in Israel (IEEE), 2012, 1-4. https://doi.org/10.1109/EEEI.2012.6377118

Majhi, S. Relay based identification of processes with time delay. Journal of Process Control. 2007, 17(2), 93-101. https://doi.org/10.1016/j.jprocont.2006.09.005

Padhy, P. K., Majhi, S. Relay based PI_PID design for stable and unstable FOPDT processes. Computer & Chemical Engendering. 2006, 30(5), 790-796.

Coello-Coello, C. A., Van Veldhuizen, D. A., Lamont, G.B. Evolutionary Algorithms for Solving MultiObjective Problems. Springer, 2007. https://doi.org/10.1007/978-0-387-36797-2

Fleming, P. J., Purshouse, R.C. Genetic Algorithms in Control Systems Engineering. Department of Automatic Control Systems Engineering University of Sheffield, SI 3JD, Research Report No. 789, May 2001.

Goldberg, D. E. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison Wesley, 1989.

Holland, J.H. Adaptation in Natural and Artificial Systems. Ann Arbor: University of Michigan Press, 1975.

Kristiansson, B., Lennartson, B. Robust tuning of PI and PID Controllers. IEEE Control Systems Magazine. 2006, 26(1), 55-69. https://doi.org/10.1109/MCS.2006.1580154

Lennartson, B., Kristiansson, B. Pass Band and High frequency Robustness for PID Control. Proceeding of the 36th Conference on Decision & Control. San Diego: 1997, 2666-2671. https://doi.org/10.1109/CDC.1997.657783

Panagopoulos, H., Åström, K. J., Hägglund, T. Design of PID Controllers based on Constrained Optimization. Proceedings of the American Control conference. San Diego: 1999, 6(1), 3858-3862. https://doi.org/10.1109/CDC.1997.657783

Zhou, K., Doyle, J.C. Essentials of Robust Control. Prentice Hall, 1998.

Descargas

Publicado

30-10-2015

Cómo citar

Lagunas-Jiménez, J. R. F., Ortiz-Moctezuma, M. B., Moo-Yam, V., & González Aguilar, A. E. . (2015). Identificación de procesos y sintonización de controladores PID mediante una prueba de relé usando un algoritmo genético simple. Programación matemática Y Software, 7(3), 27–35. https://doi.org/10.30973/progmat/2015.7.3/4

Número

Sección

Artículos