Subharmonic ripple analysis of an interleaved buck converter based on the Filippov method
Abstract
In many papers, the averaged model of power switching converters is used to design the control system due to its simple manipulation, which can be approximated by linear transfer functions. Therefore, the power converter commutation causes a state variable ripple that is not considered on the averaged model. The component frequency of the state variables is composed by a power spectrum with a unique peak at the DC level (average variable), a unique peak at the switching frequency (ripple component) and a finite number of peaks in each sub-harmonic (instabilities). The Filippov method is used for instability predictions due to fast dynamics, this method predicts the parameters range that avoids the first bifurcation of the fast dynamics. In this paper a stable space of parameters (Kp, Ti) for a PI controller is presented, it estimated with the Filippov method, for a buck converter with voltage regulation. Finally, the presented results are validated using both Matlab and Psim simulations.References
R. W. Erickson and D. Maksimović, Fundamentals of Power Electronics. Boston, MA: Springer US, 2001.
D. Biel, E. Fossas, and R. Ramos, “Sliding mode control multiphase Buck converter implementation issues,” in 2010 11th International Workshop on Variable Structure Systems (VSS), 2010, pp. 434–439.
C.-M. L. C.-M. Liaw, Y.-M. L. Y.-M. Lin, and K.-H. C. K.-H. Chao, “A VSS speed controller with model reference response for inductionnmotor drive,” IEEE Trans. Ind. Electron., vol. 48, no. 6, pp. 1136–1147, 2001.
H. J. Zhang, “Basic Concepts of Linear Regulator and Switching Mode Power Supplies,” Milpitas, CA, 2013.
M. Orabi and A. Shawky, “Proposed Switching Losses Model for Integrated Point-of-Load Synchronous Buck Converters,” IEEE Trans. Power Electron., vol. 30, no. 9, pp. 5136–5150, Sep. 2015.
V. Bist and B. Singh, “A reduced sensor PFC BL-Zeta converter based VSI fed BLDC motor drive,” Electr. Power Syst. Res., vol. 98, pp. 11–18, May 2013.
A. Mansour, B. Faouzi, G. Jamel, and E. Ismahen, “Design and analysis of a high frequency DC–DC converters for fuel cell and super-capacitor used in electrical vehicle,” Int. J. Hydrogen Energy, vol. 39, no. 3, pp. 1580–1592, Jan. 2014.
Z. Wang, B. Liu, Y. Zhang, M. Cheng, K. Chu, and L. Xu, “The Chaotic-Based Control of Three-Port Isolated Bidirectional DC/DC Converters for Electric and Hybrid Vehicles,” Energies, vol. 9, no. 2, p. 83, Jan. 2016.
A. D. Martin, J. M. Cano, J. F. A. Silva, and J. R. Vázquez, “Backstepping Control of Smart Grid-Connected Distributed Photovoltaic Power Supplies for Telecom Equipment,” IEEE Trans. Energy Convers., vol. 30, no. 4, pp. 1496–1504, Dec. 2015.
R. Priewasser, M. Agostinelli, C. Unterrieder, S. Marsili, and M. Huemer, “Modeling, Control, and Implementation of DC - DC Converters for Variable Frequency Operation,” IEEE Trans. Power Electron., vol. 29, no. 1, pp. 287–301, Jan. 2014.
L. Guo, J. Y. Hung, and R. M. Nelms, “Comparative evaluation of sliding mode fuzzy controller and PID controller for a boost converter,” Electr. Power Syst. Res., vol. 81, no. 1, pp. 99–106, Jan. 2011.
Yanfeng Chen, C. K. Tse, Shui-Sheng Qiu, L. Lindenmuller, and W. Schwarz, “Coexisting Fast-Scale and Slow-Scale Instability in Current-Mode Controlled DC/DC Converters: Analysis, Simulation and Experimental Results,” IEEE Trans. Circuits Syst. I Regul. Pap., vol. 55, no. 10, pp. 3335–3348, Nov. 2008.
J. D. Morcillo-Bastidas, “Analysis and bifurcations of a dc-dc buck converter controlled by sine wave,” Universidad Nacional de Colombia - Sede Manizales, 2012.
C. Yfoulis, D. Giaouris, F. Stergiopoulos, C. Ziogou, S. Voutetakis, and S. Papadopoulou, “Robust constrained stabilization of boost DC–DC converters through bifurcation analysis,” Control Eng. Pract., vol. 35, pp. 67–82, Feb. 2015.
J. K. Hunter, Introduction to Dynamical Systems, 1st ed. Davis, CA 95616: Department of Mathematics, University of California at Davis, 2011.
J. H. B. Deane and D. C. Hamill, “Instability, subharmonics, and chaos in power electronic systems,” IEEE Trans. Power Electron., vol. 5, no. 3, pp. 260–268, Jul. 1990.
L. Wei-Guo, X. Ping-Ye, Z. Luo-Wei, and L. Quan-Ming, “Bifurcation Control of Current-Mode Buck Converter via TDFC,” Chinese Phys. Lett., vol. 27, no. 3, p. 30501, Mar. 2010.
M. Kamyar, “Modeling and stability analysis of closed loop current-mode controlled Cuk converter using Takagi-Sugeno fuzzy approach,” in 2nd IFAC Conference on Analysis and Control of Chaotic Systems, 2009, pp. 223–228.
S. I. Serna-Garcés, R. E. Jiménez, and C. A. Ramos-Paja, “Sliding-Mode Control of a Dc/Dc Postfilter for Ripple Reduction and Efficiency Improvement in POL Applications,” J. Appl. Math., vol. 2013, no. Article ID 915146, p. 10 pages, 2013.
D. Giaouris, S. Banerjee, B. Zahawi, and V. Pickert, “Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov’s Method,” IEEE Trans. Circuits Syst. I Regul. Pap., vol. 55, no. 4, pp. 1084–1096, May 2008.
D. Giaouris, S. Maity, S. Banerjee, V. Pickert, and B. Zahawi, “Application of Filippov Method For The Analisys Of Subharmonic Instability in DC-DC Converters,” Int. J. Circuit Theory Appl., no. 37, pp. 899–919, 2008.
I. Daho, D. Giaouris, B. Zahawi, V. Picker, and S. Banerjee, “Stability analysis and bifurcation control of hysteresis current controlled CUK converter using Filippov’s method,” in 4th IET International Conference on Power Electronics, Machines and Drives (PEMD 2008), 2008, pp. 381–385.
O. Imrayed, I. Daho, and H. M. Amreiz, “Controlling Nonlinear Behavior in Current Mode Controlled Boost Converter Based on the Monodromy Matrix,” Conf. Pap. Eng., vol. 2013, pp. 1–7, 2013.
B. Zahawi, N. C. Okafor, S. Banerjee, and D. Giaouris, “Analysis of fast-scale instability in dc drives with full-bridge converter using Filippov’s method,” in 5th IET International Conference on Power Electronics, Machines and Drives (PEMD 2010), 2010, pp. 235–235.
R. A. A. Lopez and G. O. Londono, “Stability analysis of a photovoltaic system with DC/DC flyback converter using Filippov’s method,” in Alternative Energies and Energy Quality (SIFAE), 2012 IEEE International Symposium on, 2012, pp. 1–4.
R. Giral Castrillon, “Sintesis de Estructuras Multiplicadoras de Tesión Basadas en Células Convertidoras Continua-Continua de Tipo Conmutado,” Universitat Politécnica de Calaluña, 1999.
K. Kaoubaâ, J. Pelaez-Restrepo, M. Feki, B. G. M. Robert, and A. El Aroudi, “Improved static and dynamic performances of a two-cell DC-DC buck converter using a digital dynamic time-delayed control,” Int. J. Circuit Theory Appl., vol. 40, no. 4, pp. 395–407, Apr. 2012.
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