Técnica ZAD Aplicada a un Convertidor Buck: Análisis de Estabilidad y de Transición al Caos

Fabiola Angulo, Enric Fossas, Gerard Olivar

Resumen

En este trabajo se presentan algunos resultados obtenidos al analizar el convertidor buck controlado mediante un modulador de anchura de pulsos (PWM) centrado. El ciclo de trabajo se calcula obligando a que una salida, definida como una ecuación diferencial de primer orden en el error en tensión, tenga promedio cero en cada ciclo. Los resultados obtenidos han mostrado que la técnica garantiza frecuencia de conmutación fija y una variedad de fenómenos no lineales como bifurcaciones y caos, en la medida en que el parámetro asociado a la dinámica de primer orden, varía. Estos fenómenos han sido estudiados en el presente trabajo de forma analítica y numérica. Finalmente a nivel de simulación se ha hecho uso de la técnica Time Delay Auto-Synchronization para controlar el sistema.

Palabras clave

frecuencia de conmutación fija; bifurcaciones; caos; control de caos; convertidor buck

Texto completo:

PDF

Referencias

Baillieul, J., R.W. Brockett and R.B. Washburn (1980). Chaotic motion in nonlinear feedback systems. IEEE Transcations on Circuits and Systems 27, No. 11, 990–997.

Banerjee, S. and G.C. Verghese (2001). Eds. Non-linear phenomena in power electronics. IEEE Press. Piscataway.

Baranovski, A.L., A. Mögel, W. Schwarz and O. Woywode (2000). Chaotic control of a dc-dc-converter. In Proceedings of the IEEE International Symposium on Circiuts and Systems 2, 108–111.

Batlle, C., E. Fossas and G. Olivar (1997). Time delay stabilization of the buck converter. In Proceedings of the IEEE International Conference in Control of Oscillations and Chaos 3, 590–593.

Batlle, C., I. Massana and A. Miralles (2003). Lyapunov exponents for bilinear systems. application to the buck converter. International Journal of Bifurcations and Chaos 13, 713–722.

Biel, D., E. Fossas, R. Ramos and F. Guinjoan (2002). Implementación de controles "pseudo-sliding"en sistemas conmutados. Congreso Latinoamericano de Control Automático

Bilalović, F., O. Mušić and A. Šabanović (1983). Buck converter regulator operating in the sliding mode. Proceedings VII International PCI pp. 331–340.

Borle, L.J. and N. Chemmangot (1995). Zero averge current error controlled power flow for ac-dc power converters. IEEE Transactions on Power Electronics 10, No. 6, 725–732.

Carpita, M., M. Marchesoni, M. Oberti and L. Puguisi (1988). Power conditioning system using slide mode control. In Proceedings of the IEEE Power Electronics Specialist Conference pp. 623–633.

Deane, J.H.B. and D.C. Hamill (1990). Analysis, simulation and experimental study of chaos in the buck converter. In Proceedings IEEE Power Electronics Specialists Conference II, 491–498.

di Bernardo, M., C.J. Budd and A.R. Champneys (2001). Corner collision implies border-collision bifurcation. Physica D 154, 171–194.

di Bernardo, M., F. Garofalo, L. Glielmo and F. Vasca (1996). Quasi-periodic behaviors in dc/dc converters. In Proceedings IEEE Power Electronics Specialists Conference pp. 1376–1381.

di Bernardo, M., F. Garofalo, L. Glielmo and F. Vasca (1997). Analysis of chaotic buck, boost and buck-boost converters through switching maps. In Proceedings of the IEEE Power Electronics Specialists Conference pp. 754–760.

Fliess, M. and H. Sira-Ramírez (1993). Régimes glissants structures variables linéaries et modules. C. R. Acd. Sci. París I, 703–706.

Fossas, E. and G. Olivar (1996). Study of chaos in the buck converter. Transcations on Circuits and Systems-I: Fundamental Theory and Applications 43, No 1, 13–25.

Fossas, E., R. Griñó and D. Biel (2001). Quasi-Sliding control based on pulse width modulation, zero averaged dynamics and the L2 norm, In Advances in Variable Structure System, Analysis, Integration and Applications. pp. 335–344. World Scientific. Singapur.

Janaki, T.M., G. Rangarajan, S. Habib and R.D. Ryne (1999). Computation of the lyapunov spectrum for continuos-time dynamical systems and discrete maps. Physics Reviews E 60, 6614–6626.

Kuznetsov, Y. (1998). Elements of Applied Bifurcation Theory. Springer Verlag. New York.

Lim, Y.H. and D.C. Hamill (1999). Problems of computing lyapunov exponents in power electronics. In proceedings IEEE International Symposium on Circuits and systems 5, 297–301.

Ott, E., C. Grebogi and J. Yorke (1990). Controlling chaos. Physics Review Letter 64, 1196–1199.

Parker, T.S. and L.O. Chua (1989). Practical numerical algorithms for chaotic systems. Springer Verlag. New York.

Poddar, G., K. Chakrabarty and S. Banerjee (1995). Control of chaos in the boost converter. Electronics letters 31, No. 11, 841–842.

Pyragas, K. (1992). Continuos control of chaos by self-controlling feedback. Physics Letter A 170, 421–428.

Ramos, R., D. Biel, E. Fossas and F. Guinjoan (2003). A fixed-frequency quasi-sliding control algorithm: Application to power inverters design by means of fpga implementation. IEEE Transcations on Power Electronics

Rodríguez, J.L., R. Santos and G.C. Verghese (1999). Analysis and control of chaotic dc-dc switching power converters. In Proceedings of the IEEE International Symposium on Circuits and Systems 5, 287–292.

Santos, R. and J.L. Rodríguez (1998). Control of dc-dc converters in the chaotic regime. In Proceedings of the IEEE International Conference on Control Applications pp. 832–837.

Venkataramanan, R., A. Sabanović and S. Ćuk (1985). Sliding mode control of dc-to-dc converters. Proceedings IECON 1985 pp. 251–258.

Abstract Views

368
Metrics Loading ...

Metrics powered by PLOS ALM




Creative Commons License

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

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

e-ISSN: 1697-7920     ISSN: 1697-7912