Control fraccionario: fundamentos y guía de uso

Blas M. Vinagre, Vicente Feliu Batlle, Inés Tejado

Resumen

El objetivo del presente tutorial de control fraccionario es presentar los fundamentos de esta disciplina y las principales herramientas computacionales disponibles para su uso y aplicación por parte del ingeniero de control. El enfoque escogido pretende hacer accesible desde el primer momento su ubicación en el control clásico y las bases para entender cómo cualquier estrategia de control que haga uso de los operadores derivada y/o integral (es decir, casi todas) puede generalizarse al considerar la posibilidad de utilizar dichos operadores con un orden no necesariamente entero. Los casos de estudio considerados (el doble integrador y el servomecanismo de posición) han sido elegidos no para exponer las bondades del control fraccionario, sino para mostrar la amplitud de posibilidades que proporciona su utilización incluso considerando sistemas extraordinariamente comunes en la literatura de control.

Palabras clave

Control fraccionario; Sistemas fraccionarios; Control robusto

Texto completo:

PDF

Referencias

Astrom, ¨ K. J., Murray, R. M., 2008. Feedback Systems. An Introduction for Scientists and Engineers. Princeton University Press, Princeton.

Bennett, S., 1993. A History of Control Engineering 1930–1955. Peter Peregrinus (IEE), London.

Bode, H., 1940. Relations between attenuation and phase in feedback amplifier design. Bell System Technical Journal 19, 421–454.

Bode, H., 1945. Network Analysis and Feedback Amplifier Design. Van Nostrand.

Carlson, G. E., Halijak, C., 1961. Simulation of the fractional derivative operator (s) and the fractional integral operator (1/s). In: Proceedings of the Central States Simulation Council Meeting on Extrapolation of Analog Computation Methods. Kansas, USA, pp. 1–22.

Chen, Y. Q., Petras, ´ I., Xue, D., 2009. Fractional order control - A tutorial. In: Proceedings of the American Control Conference (ACC’09). pp. 1397–1411.

CRONE Group, 2010b. Crone toolbox. URL: http://archive.ims-bordeaux.fr/CRONE/toolbox

CRONE Group, 2010b. Brief Presentation of the Object Oriented CRONE Toolbox. Version Beta 1.

CRONE Group, 2010c. CRONE Control Design Module User’s Guide. Version 4.0.

Dormido, S., Pisoni, E., Visioli, A., 2012. Interactive tools for designing fractional-order PID controllers. International Journal of Innovative Computing, Information and Control 8, 7(A), 4570–4590.

Dugowson, S., 1994. Les differentielles metaphysiques: Histoire et philosophie de la generalisation ´ de l’ordre de derivation. Ph.D. thesis, University of Paris.

Edwards, C., Spurgeon, S. K., 1998. Sliding Mode Control. Theory and Applications. Taylor & Francis Ltd.

Horowitz, I., 1963. Synthesis of Feedback Systems. Academic Press.

Horowitz, I., Sidi, M., 1972. Synthesis of feedback systems with large plant ignorance for prescribed time domain tolerances. International Journal of Control 16 (2), 287–309.

HosseinNia, S. H., Sierociuk, D., Calderon, ´ A. J., Vinagre, B. M., 2010. Augmented system approach for fractional order SMC of a DC-DC Buck converter. In: Proceedings of the 4th IFAC Workshop Fractional Differentiation and its Applications (FDA’10).

HosseinNia, S. H., Tejado, I., Vinagre, B. M., 2013. Fractional-order reset control: Application to a servomotor. Mechatronics 23 (7), 781–788.

Li, Z., 2015. Fractional order root locus. URL: http://www.mathworks.com/matlabcentral/fileexchange/50458- fractional-order-root-locus

Li, Z., Liu, L., Dehghan, S., Chen, Y. Q., Xue, D., 2016. A review and evaluation of numerical tools for fractional calculus and fractional order controls. International Journal of Control. DOI:10.1080/00207179.2015.1124290.

Manabe, S., 1961. The non-integer integral and its application to control systems. Japanese Institute of Electrical Engineers Journal 6 (3-4), 83– 87.

Miller, K., Ross, B., 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons, New York.

Monje, C. A., Chen, Y. Q., Vinagre, B. M., Xue, D., Feliu, V., 2010. Fractional-order Systems and Controls. Fundamentals and Applications. Springer.

Monje, C. A., Vinagre, B. M., Feliu, V., Chen, Y. Q., 2008. Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice 16 (7), 798–812.

Oldham, K., Spanier, J., 2006. The Fractional Calculus. Theory and Applications of Differentiation and Integration of Arbitrary Order. Dover, New York.

Opdycke, R. R., 1967. An Investigation of the Strait servo. Master Thesis, Kansas State University, Kansas, USA.

Oustaloup, A., 1991. La Commade CRONE: Commande Robuste d’Ordre Non Entier. Hermes, Paris.

Petras, I., 2011a. Discrete fractional-order PID controller. URL: http://www.mathworks.com/matlabcentral/fileexchange/33761- discrete-fractional-order-pid-controller

Petras, I., 2011b. Engineering Education and Research Using MATLAB. InTech, Ch. Fractional Derivatives, Fractional Integrals, and Fractional Differential Equations in Matlab, pp. 239–264.

Petras, I., 2015. Non-linear fractional-order PID controller. URL: http://www.mathworks.com/matlabcentral/fileexchange/51190- non-linear-fractional-order-pid-controller

Podlubny, I., 1999a. Fractional Differential Equations. Vol. 198 of Mathematics in Science and Engineering. Academic Press, San Diego.

Podlubny, I., 1999b. Fractional order systems and PI-lambda-D-mu controllers. IEEE Transactions on Automatic Control 44 (1), 208–214.

Podlubny, I., Petras, ´ I., Vinagre, B. M., O’Leary, P., Dorcak, ´ L., 2002. Analogue realizations of fractional-order controllers. Nonlinear Dynamics 29, 281–296.

Rao, V. G., Bernstein, D. S., 2001. Naive control of the double integrator. IEEE Control Systems Magazine October, 86–97.

Sierociuk, D., 2003. Fractional states-space toolkit (FSST). URL: http://www.ee.pw.edu.pl/ dsieroci/fsst/fsst.htm

Stein, G., Athans, M., 1987. The LQR/LTR procedure for multivariable feedback control design. IEEE Transactions on Automatic Control 32, 105–114.

Tenreiro Machado, J. A., 2011. Communications in nonlinear science and numerical simulation. Root locus of fractional linear systems 16 (10), 3855–3862.

Tepljakov, A., 2015. FOMCON toolbox reference manual. URL: http://docs.fomcon.net/

Tepljakov, A., 2016. FOMCON: Fractional-order modeling and control. (Fecha de consulta: 21/03/16). URL: http://fomcon.net/

Tejado, I., HosseinNia, S. H., Vinagre, B. M., 2014. Adaptive gain-order fractional control for network-based applications. Fractional Calculus and Applied Analysis 17 (2), 462–482.

Tricaud, C., 2008. Solution of fractional optimal control problems. URL: http://www.mathworks.com/matlabcentral/fileexchange/22196- solution-of-fractional-optimal-control-problems

Tustin, A., Allanson, J. T., Layton, J. M., Jakeways, R. J., 1958. The design of systems for automatic control of the position of massive objects. The Proceedings of the Institution of Electrical Engineers 105.

Valerio, D., 2005a. Ninteger: Fractional control toolbox for MatLab. URL: http://www.mathworks.com/matlabcentral/fileexchange/8312- ninteger

Valerio, D., 2005b. Ninteger: Fractional control toolbox for MatLab. URL: http://web.ist.utl.pt/duarte.valerio/ninteger/ninteger.htm

Valerio, D., 2005c. Ninteger v. 2.3 – fractional control toolbox for MatLab. URL: http://web.ist.utl.pt/duarte.valerio/ninteger/Manual.pdf

Vilanova, R., Visioli, A., (Eds.), 2012. PID Control in the Third Millennium. Springer, London.

Vinagre, B. M., Monje, C. A., 2006. Introduccion al control fraccionario.

Abstract Views

536
Metrics Loading ...

Metrics powered by PLOS ALM


 

Citado por (artículos incluidos en Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Back to Basics: Meaning of the Parameters of Fractional Order PID Controllers
Inés Tejado, Blas Vinagre, José Traver, Javier Prieto-Arranz, Cristina Nuevo-Gallardo
Mathematics  vol: 7  num.: 6  primera página: 530  año: 2019  
doi: 10.3390/math7060530



Creative Commons License

Esta revista se publica bajo una Licencia Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Universitat Politècnica de València     https://doi.org/10.4995/riai

e-ISSN: 1697-7920     ISSN: 1697-7912