Browse > Article
http://dx.doi.org/10.6113/JPE.2014.14.6.1208

Stability Analysis and Control of Nonlinear Behavior in V2 Switching Buck Converter  

Hu, Wei (Lab Center, Guangzhou University)
Zhang, Fangying (Lab Center, Guangzhou University)
Long, Xiaoli (Lab Center, Guangzhou University)
Chen, Xinbing (Lab Center, Guangzhou University)
Deng, Wenting (Lab Center, Guangzhou University)
Publication Information
Journal of Power Electronics / v.14, no.6, 2014 , pp. 1208-1216 More about this Journal
Abstract
Mismatch between switching frequency and circuit parameters often occurs in industrial applications, which would lead to instability phenomena. The bifurcation behavior of $V^2$ controlled buck converter is investigated as the pulse width modulation period is varied. Nonlinear behavior is analyzed based on the monodromy matrix of the system. We observed that the stable period-1 orbit was first transformed to the period-2 bifurcation, which subsequently changed to chaos. The mechanism of the series of period-2 bifurcations shows that the characteristic eigenvalue of the monodromy matrix passes through the unit circle along the negative real axis. Resonant parametric perturbation technique has been applied to prevent the onset of instability. Meanwhile, the extended stability region of the converter is obtained. Simulation and experimental prototypes are built, and the corresponding results verify the theoretical analysis.
Keywords
Bifurcation; Buck converter; Chaos; Monodromy matrix; $V^2$ switching;
Citations & Related Records
연도 인용수 순위
  • Reference
1 G. H. Zhou, J. P. Xu, and J. P. Wang, "Constant-frequency peak-ripple-based control of buck converter in CCM: review, unification and duality," IEEE Trans. Ind. Electron., Vol. 61, No. 3, pp. 1280-1291, Mar. 2014.   DOI   ScienceOn
2 J. Li and F. C. Lee, "Modeling of $V^2$ Current-Mode Control," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 57, no. 9, pp. 2552-2563, Sept. 2010.   DOI   ScienceOn
3 D. Gorder and W. R. Pelletier, "$V^2$ architecture provides ultra fast transient response in switch mode power supplies," in Proc. HFPC Conf., pp. 19-23, 1996.
4 D. Gorder, "Switching regulators," U.S. Patent 5 770 940, 1998.
5 S. Qu, "Modeling and design considerations of $V^2$ controlled buck regulator," in Proc. IEEE Apply Power Electron. Conf. Expo., pp. 507-513, 2001.
6 F. Wang, J. Xu, and J. Xu, "Small-signal model of $V^2$ control technique with compensation," in Proc. IEEE Int. Conf. Commun. Circuits Syst., Vol. 2, pp. 27-29, 2004.
7 C. Tsai, S.-M. Lin, and C.-S. Huang, "A fast-transient quasi-$V^2$ switching buck regulator using AOT control with a load current correction (LCC) technique," IEEE Trans. Power Electron., Vol. 28, No. 8, pp. 3949-3957, Aug. 2013.   DOI   ScienceOn
8 S. Maity, "Dynamics and stability issues of a discretized sliding-mode controlled DC-DC buck converter governed by fixed-event-time switching," IEEE Trans. Circuits Syst. I, Reg. Papers, Vol. 60, No. 6, pp. 1657-1669, Dec. 2013.   DOI   ScienceOn
9 K. Y. Cheng, F. Yu, F. C. Lee, and P. Mattavelli, "Digital enhanced $V^2$-type constant on-time control using inductor current ramp estimation for a buck converter with low-ESR capacitors," IEEE Trans. Power Electron., Vol. 28, No. 3, pp. 1241-1252, Mar. 2013.   DOI   ScienceOn
10 C. K. Tse, "Flip bifurcation and chaos in three-state boost switching regulators," IEEE Trans. Circuits Syst. I Fundam. Theory Appl., Vol. 41, No. 1, pp. 16-23, Jan. 1994.   DOI   ScienceOn
11 A. El Aroudi, L. Benadero, E. Toribio, and G. Olivar, "Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC-DC boost converter," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., Vol. 46, No. 11, pp. 1374-1382, Nov. 1999.   DOI   ScienceOn
12 J. Sun, "Characterization and performance comparison of ripple-based control for voltage regulator modules," IEEE Trans. Power Electron., Vol. 21, No. 2, pp. 346-353, Mar. 2006.   DOI   ScienceOn
13 C. C. Fang, "Bifurcation boundary conditions for current programmed PWM DC-DC converters at light loading," Int. J. Electron., Vol. 99, No. 10, pp. 1365-1393, Apr. 2012.   DOI
14 P. Deivasundari, G. Uma, and K. Murali, "Chaotic dynamics of voltage-mode controlled buck converter with periodic interference signals," Int. J. Bifurcat. Chaos, Vol. 23, No. 6, Jun. 2013.
15 G. H. Zhou, J. P. Xu, Y. Y. Jin, and J. Sha, "Stability analysis of $V^2$ controlled buck converter operating in CCM and DCM," in Int. Conf. Commun., Circuits. Syst., pp. 551-555, 2010.
16 J. Cortes, "Modelling, analysis and optimization of analog controls for a Buck converter," Master Thesis, Universidad Politecnica de Madrid, chap. 3, 2013.
17 F. Zhang, R. Yang, X. Long, C. Y. Xie, and H. Chen, "Mechanism of instability behaviors and stabilization on $V^2$ controlled buck converter," Acta Phys. Sin., Vol. 62, No. 21, Dec. 2013.
18 E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos," Phys. Rev. Lett., Vol. 64, No. 11, pp. 1196-1199, Mar. 1990.   DOI   ScienceOn
19 C. Fuh and H. Tsai, "Control of discrete-time chaotic systems via feedback linearization," Chaos Soliton. Fract., Vol. 13, pp. 285-294, Feb. 2002.   DOI   ScienceOn
20 S. Samanta, S. Mukhopadhyay, and R. Sheehan, "Discrete-time simulation of a peak current controlled DC/DC buck converter using modal decomposition," IET Power Electron., Vol. 4, No. 6, pp. 642-650, Jul. 2011.   DOI   ScienceOn
21 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, Reg. Papers, Vol. 55, No. 4, pp. 1084-1096, May 2008.   DOI   ScienceOn
22 Y. Zhou, C. K. Tse, S.-S. Qiu, and F. C. M. Lau, "Applying resonant parametric perturbation to control chaos in the buck DC/DC converter with phase shift and frequency mismatch considerations," Int. J. Bifurcat. Chaos, Vol. 13, No. 11, pp. 3459-3471, Nov. 2003.   DOI   ScienceOn
23 B. Bao, G. Zhou, J. Xu, and Z. Liu, "Unified classification of operation-state regions for switching converters with ramp compensation," IEEE Trans. Power Electron., Vol. 26, No. 7, pp. 1968-1975, Jul. 2011.   DOI   ScienceOn
24 G. Chen and X. Dong, "On feedback control of chaotic continuous-time systems," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., Vol. 40, No. 9, pp. 591-601, Sep. 1993.   DOI   ScienceOn
25 R. I. Leine, D. H. Van Campen, and B. L. Van de Vrande, "Bifurcations in nonlinear discontinuous systems," Nonlinear Dynam., Vol. 23, No. 2, pp. 105-164, Oct. 2000.   DOI
26 A. F. Filippov, "Differential equations with discontinuous right-hand side," American Mathematical Society Translations, Vol. 42, No. 2, pp. 199-231, 1964.