Dinámica de un sistema lineal en R2 conmutado por histéresis
Main Article Content
Keywords
histéresis, órbita periódica, sistemas dinámicos suaves a trozos, dominios de atracción.
Resumen
En este artículo se analiza el comportamiento local y global de un sistema dinámico suave a trozos en dos variables, estudiando el flujo de dos sistemas dinámicos lineales no homogéneos que conmutan con las fronteras de una banda de histéresis. Analíticamente se determinan las soluciones de equilibrio y los dominios paramétricos que garantizan la existencia de órbitas periódicas entre la banda. Se realizan simulaciones numéricas para obtener los retratos de fases y los dominios de atracción con diferentes valores de los parámetros. Los resultados muestran la coexistencia de múltiples estados estacionarios de diferente tipo para determinados valores de los parámetros.
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2006. [Online]. Available: http://www.sciencedirect.com/science/article/pii/B9780124808744500002
K. J. Å ström, G. C. Goodwin, and P. R. Kumar, Adaptive Control, Filtering, and Signal Processing, ser. The IMA Volumes in Mathematics and its Applications. New York, NY: Springer New York, The IMA Volumes in Mathematics and Its Applications Series., 1995, vol. 74. [Online]. Available: http://link.springer.com/10.1007/978-1-4419-8568-2
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M. Dawande, V. Kanetkar, and G. Dubey, “Three-phase switch mode rectifier with hysteresis current control,” IEEE Transactions on Power Electronics, vol. 11, no. 3, pp. 466–471, May 1996. [Online]. Available: http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=491640
H. Lee and V. I. Utkin, “Chattering suppression methods in sliding mode control systems,” Annual Reviews in Control, vol. 31, no. 2, pp. 179–188, jan 2007. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S1367578807000363
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J. N. Hincapié, A. Trejos, M. E. Moncada, and A. Escobar, “Electrónica de potencia para el calentamiento por inducción doméstico: revisión del estado del arte,” Ingeniería y ciencia, vol. 9, no. 18, pp. 237–262, 2013.
M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, ser. Applied Mathematical Sciences. New York, NY: Springer New York, 1996, vol. 121. [Online]. Available: http://link.springer.com/10.1007/978-1-4612-4048-8
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F. Han, X. Yu, Y. Feng, and J. Hu, “On multiscroll chaotic attractors in hysteresis-based piecewise-linear systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 11, pp. 1004–1008, Nov 2007.
M. D. Bernardo, K. H. Johansson, and F. Vasca, “Self-Oscillations and Sliding in Relay Feedback Systems: Symetry and Bifurcations,” International Journal of Bifurcation and Chaos, vol. 11, no. 04, pp. 1121–1140, Apr. 2001. [Online]. Available: http://www.worldscientific.com/doi/abs/10.1142/ S0218127401002584
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L. Perko, Differential Equations and Dynamical Systems, ser. Texts in Applied Mathematics. New York, NY: Springer-Verlag New York, 2001, vol. 7.
H. Minkowski, Geometrie der zahlen. Leipzig-Berlin: R. G. Teubner, 1910. [Online]. Available: https://archive.org/details/geometriederzahl00minkrich
U. Moreno, P. Peres, and I. Bonatti, “Analysis of piecewise-linear oscillators with hysteresis,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 8, pp. 1120–1124, Aug. 2003. [Online]. Available: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.
htm?arnumber=1219573
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M. Spivak, Calculus on Manifolds: a Modern Approach to Classical Theorems of Advanced Calculus. Benjamin-Cummings, 1965. [Online]. Available: http://en.wikipedia.org/wiki/Calculus_on_Manifolds_(book)
Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, ser. Texts in Applied Mathematics. New York: Springer-Verlag, Texts in Applied Mathematics Volume 2., 2003, vol. 2. [Online]. Available: http://link.springer.com/10.1007/b97481
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