Vol. 17 No. 1 (2013), Articles
Vol. 17 No. 1 (2013)

Control in a system of non-linear interacting tanks from the perspective of dynamic hybrid systems

Articles
Published 2013-05-10
Christian Felipe Ramirez-Acosta, MSc
Pontificia Universidad Javeriana
Diego Alegandro Patiño-Guevara, PhD
Pontificia Universidad Javeriana
https://orcid.org/0000-0001-6181-6175
Carlos Eduardo Cotrino, MSc
Pontificia Universidad Javeriana
PDF (Spanish)

Keywords

Dynamic hybrid systems
identification
non-linear systems
multiple Lyapunov functions

How to Cite

Control in a system of non-linear interacting tanks from the perspective of dynamic hybrid systems. (2013). Ingenieria Y Universidad, 17(1), 143-166. https://doi.org/10.11144/Javeriana.iyu17-1.csni
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Abstract

This paper presents a methodology for identifying a system of interacting tanks that follows a non-linear behavior as a dynamic hybrid system (DHS) based on the method for identifying non-linear systems known as bounded error approach. Having identified this tank system as a DHS, it is represented through state variables to apply a commuted state feedback control law in order to find a multiple Lyapunov function, which would allow us to guarantee the stability of the identified commuted system.

PDF (Spanish)

ANTSAKLIS, P.; STIVER, J. y LEMMON, M. Hybrid system modeling and autonomous control systems. Lecture Notes in Computer Science. 1993, vol. 736, pp. 366-392.
BEMPORAD, A.; FERRARI-TRECATA, G. y MORARI, M. Observability and controllability of piecewise affine and hybrid systems. Proceedings of the 38th IEEE Conference on Decision and Control. 1999, vol. 4, núm. 1, pp. 3966-3971.
BEMPORAD, A. et al. Bounded error approach to piecewise affine system identification. IEEE Transactions On Automatic Control. 2005, vol. 50, núm. 10, pp. 1567-1580.
BENNET, K. P. y MANGASARIAN, O. L. Robust linear programming discrimination of two linearly inseparable sets. Optimization Methods and Software. 1995, vol. 1, núm. 1, pp. 23-34.
CORTÉS, C. y VAPNIK, V. Support-vector networks. 1st ed. Berlin: Springer-Verlag, 1995.
DAAFOUZ, J.; RIEDINGER, P. e IUNG, C. Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach. IEEE Transactions on Automatic Control. 2002, vol. 47, núm. 11, pp. 1883-1887.
DUDA, R.; HART, O. y STORK, D. Pattern classification. 2nd ed. New York: Wiley-Interscience, 2000.
DUQUE, M. et al. Control de sistemas híbridos usando el acercamiento MLD. Parte I: modelamiento. Congreso Nacional de la Asociación Colombiana de Automática, 2004.
FERRARI-TRECATA, G.; BEMPORAD, A. y MORARI, M. Observability and controllability of piecewise affine and hybrid systems. Proceedings of the 38th IEEE Conference on Decision and Control. 1999, vol. 4, núm. 1, pp. 3966-3971.
FLIELLER, D.; RIEDINGER, P. y LOUIS, J.P. Computation and stability of limit cycles in hybrid systems. Nonlinear Analysis. 2006, vol. 64, núm. 2, pp. 352-367.
GOEBEL, R.; SANFELICE, R. y TEEL, A. Hybrid dynamical systems. IEEE Control Systems Magazine. 2009, vol. 29, núm. 2, pp. 28-93.
GROSSMAN, R. L. et al. Hybrid systems. Berlin: Springer-Verlag, 1993.
HEEMELS, M.; SCHUTTER, B. y BEMPORAD, A. Equivalence of hybrid dynamical models. Automatica. 2001, vol. 37, núm. 7, pp. 1085-1091.
HESPANHA, J. P. y MORSE, A. S. Stability of switched systems with average dwell time. Proceedings of the 38th IEEE Conference on Decision and Control. 1999, vol. 3, núm. 1, pp. 2655-2660.
LIBERZON, D. Switching in systems and control. 1st ed. Boston: Birkhäuser, 2003.
MCGRATH, B. et al. Predictive control of a flying capacitor converter. American Control Conference. 2007, vol. 1, pp. 3763-3768.
PATINO, D. Control of limit cycles in hybrid dynamical systems: An introduction to cyclic switched systems. Application to power converters. Berlin: LAP Publishing, 2009.
VILLA, J. L. et al. Modelamiento y control de sistemas híbridos. Revista de Ingeniería. 2004, vol. 19, núm. 1, pp. 177-182.
ZACCARIAN, L. y TEEL, A. The L2 (l2) Bumpless transfer problem for linear plants: Its definition and solution. Automatica. 2005, vol. 41, núm. 7, pp. 1273-1280.

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