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http://dx.doi.org/10.6113/JPE.2017.17.5.1298

Reduced-order Mapping and Design-oriented Instability for Constant On-time Current-mode Controlled Buck Converters with a PI Compensator  

Zhang, Xi (Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University)
Xu, Jianping (Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University)
Wu, Jiahui (Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University)
Bao, Bocheng (School of Information Science and Engineering, Changzhou University)
Zhou, Guohua (Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University)
Zhang, Kaitun (Key Laboratory of Magnetic Suspension Technology and Maglev Vehicle, Ministry of Education, School of Electrical Engineering, Southwest Jiaotong University)
Publication Information
Journal of Power Electronics / v.17, no.5, 2017 , pp. 1298-1307 More about this Journal
Abstract
The constant on-time current-mode controlled (COT-CMC) switching dc-dc converter is stable, with no subharmonic oscillation in its current loop when a voltage ripple in its outer voltage loop is ignored. However, when its output capacitance is small or its feedback gain is high, subharmonic oscillation may occur in a COT-CMC buck converter with a proportional-integral (PI) compensator. To investigate the subharmonic instability of COT-CMC buck converters with a PI compensator, an accurate reduced-order asynchronous-switching map model of a COT-CMC buck converter with a PI compensator is established. Based on this, the instability behaviors caused by output capacitance and feedback gain are investigated. Furthermore, an approximate instability condition is obtained and design-oriented stability boundaries in different circuit parameter spaces are yielded. The analysis results show that the instability of COT-CMC buck converters with a PI compensator is mainly affected by the output capacitance, output capacitor equivalent series resistance (ESR), feedback gain, current-sensing gain and constant on-time. The study results of this paper are helpful for the circuit parameter design of COT-CMC switching dc-dc converters. Experimental results are provided to verify the analysis results.
Keywords
Buck converter; Constant on-time current-mode control (COT-CMC); Proportional-integral (PI) compensator; Reduced-order mapping; instability;
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1 C. C. Fang, "Critical conditions for a class of switched linear systems based on harmonic balance: applications to DC-DC converters," Nonlinear Dynamics, Vol. 70, No. 3, pp. 1767-1789, Nov. 2012   DOI
2 C. W. Deisch, "Switching control method changes power converter into a current source," in Proc. IEEE Power Electron. Sepc. Conf., pp. 300-306, 1978.
3 R. Redl and N. O. Sokal, "Current-mode control, five different types, used with the three basic classes of power converters: small-signal ac and large-signal dc characterization, stability requirements, and implementation of practical circuits," in Proc. IEEE Power Electron. Spec. Conf., pp. 771-785, 1985.
4 Texas Instruments, LM3409 datasheet. http://www.ti.com/lit/ds/symlink/lm3409.pdf, 2016.
5 Linear Technology, LTC3869 datasheet. http://cds.linear.com/docs/en/datasheet/38692fb.pdf, 2011.
6 Analog Devices, ADP1882 datasheet. http://www.analog.com/media/en/technical-documentation/data-sheets/ADP1882_1883.pdf, 2010.
7 Maxim, MAX17512 datasheet. https://datasheets.maximintegrated.com/en/ds/MAX17512.pdf, 2011.
8 C. P. Basso, Switch-Mode Power Supplies: SPICE Simulations And Practical Designs, 2nd ed., New York, NY, USA: McGraw-Hill, pp. 258-262, 2015.
9 J. Sun, "Small-signal modeling of variable-frequency pulsewidth modulators," IEEE Trans. Aerosp. Electron. Syst., Vol. 38, No. 3, pp. 1104-1108, Jul. 2002.   DOI
10 R. Redl and I. Novak, "Instability in current-mode controlled switching voltage regulators," in Proc. IEEE Power Electron. Spec. Conf., pp. 17-28, 1981.
11 D. J. Packard, "Discrete modeling and analysis of switching regulators," Ph. D. dissertation, California Institute Technology, CA, May, 1976.
12 C. K. Tse and Y. M. Lai, "Controlling bifurcations in power electronics: a conventional practice re-visited," Latin American Applied Research, Vol. 31, No. 3, pp. 177-184, 2001.
13 A. R. Brown and R. D. Middlebrook, "Sampled-data modeling of switched regulators," in Proc. IEEE Power Electron. Spec. Conf., pp. 349-369, 1981.
14 R. B. Ridley, "A new, continuous-time model for current-mode control," IEEE Trans. Power Electron., Vol. 6, No. 2, pp. 271-280, Apr. 1991.   DOI
15 W. H. Ki, "Analysis of subharmonic oscillation of fixed-frequency current-programming switch mode power converters," IEEE Trans. Circuits Syst. I, Fundam. Theory and Appl., Vol. 45, No. 1, pp. 104-108, Jan. 1998.   DOI
16 G. H. Zhou, B. C. Bao, and J. P. Xu, "Complex dynamics and fast-slow scale instability in current-mode controlled buck converter with constant current load," Int. J. Bifurc. Chaos, Vol. 23, No. 4, pp. 1350062, Apr. 2013.   DOI
17 J. H. B. Deane, "Chaos in a current-mode controlled boost dc-dc converter," IEEE Trans. Circuits Syst. I, Fundamental Theory and Applications, Vol. 39, No. 8, pp. 680-683, Aug. 1992.   DOI
18 C. K. Tse, S. C. Fung, and M. W. Kwan, "Experimental confirmation of chaos in a current-programmed Cuk converter," IEEE Trans. Circuits Syst. I, Fundam. Theory and Appl., Vol. 43, No. 7, pp. 605-608, Jul. 1996.   DOI
19 Y. F. Chen, C. K. Tse, S. S. 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, Reg. Papers, Vol. 55, No. 10, pp. 3335-3348, Nov. 2008.   DOI
20 S. Banerjee, S. Parui, and A. Gupta, "Dynamical effects of missed switching in current-mode controlled dc-dc converters," IEEE Trans. Circuits Syst. II, Express Briefs, Vol. 51, No. 12, pp. 649-654, Dec. 2004.   DOI
21 C. C. Fang and R. Redl, "Subharmonic instability limits for the peak-current-controlled buck converter with closed voltage feedback loop," IEEE Trans. Power Electron., Vol. 30, No. 2, pp. 1085-1092, Feb. 2015.   DOI
22 G. H. Zhou, J. P. Xu, and B. C. Bao, "Symmetrical dynamics of current-mode controlled switching dc-dc converters," Int. J. Bifurc. Chaos, Vol. 22, No. 1, pp. 1250008, Jan. 2012.   DOI
23 B. C. Bao, G. H. Zhou, J. P. 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
24 C. C. Fang, "Asymmetric instability conditions for peak and valley current programmed converters at light loading," IEEE Trans. Circuits Syst. I, Reg. Papers, Vol. 61, No. 3, pp. 922-929, Mar. 2014.   DOI
25 A. E. Aroudi, J. Calvente, R. Giral, M. Al-Numay, and L. Martinez-Salamero, "Boundaries of subharmonic oscillations associated to filtering effects of controllers and current sensors in switched converters under CMC," IEEE Trans. Ind. Electron., Vol. 63, No. 8, pp. 4826-4837, Aug. 2016.   DOI
26 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
27 C. C. Fang and R. Redl, "Subharmonic instability limits for the peak-current-controlled boost, buck-boost, flyback, and SEPIC converters with closed voltage feedback loop," IEEE Trans. Power Electron., Vol. 32, No. 5, pp. 4048-4055, May 2017.   DOI
28 J. Li and F. C. Lee, "New modeling approach and equivalent circuit representation for current-mode control," IEEE Trans. Power Electron., Vol. 25, No. 5, pp. 1218-1230, May 2010.   DOI
29 X. M. Duan and A. Q. Huang, "Current-mode variable-frequency control architecture for high-current low-voltage DC-DC converters," IEEE Trans. Power Electron., Vol. 21, No. 4, pp. 1133-1137, Jul. 2006.   DOI
30 C. C. Fang, "Closed-form critical conditions of instabilities for constant on-time controlled buck converters," IEEE Trans. Circuits Syst. I, Reg. Papers, Vol. 59, No. 12, pp. 3090-3097, Dec. 2012.   DOI
31 J. P. Wang, B. C. Bao, J. P. Xu, G. H. Zhou, and W. Hu, "Dynamical effects of equivalent series resistance of output capacitor in constant on-time controlled buck converter," IEEE Trans. Ind. Electron., Vol. 60, No. 5, pp. 1759-1768, May 2013.   DOI
32 Y. Y. Yan, F. C. Lee, and P. Mattavelli, "Unified three-terminal switch model for current mode controls," IEEE Trans. Power Electron., Vol. 27, No. 9, pp. 4060-4070, Sep. 2012.   DOI
33 S. L. Tian, F. C. Lee, J. Li, Q. Li, and P. H. Liu, "Three-terminal switch model of constant on-time current mode with external ramp compensation," IEEE Trans. Power Electron., Vol. 31, No. 10, pp. 7311-7319, May 2016.   DOI
34 J. Cortes, V. Svikovic, P. Alou, J. A. Oliver, J. A. Cobos, and R. Wisniewski. "Accurate analysis of subharmonic oscillations of $V^2$ and $V^2I_c$ controls applied to buck converter," IEEE Trans. Power Electron., Vol. 30, No. 2, pp. 1005-1018, Feb. 2015.   DOI
35 X. Zhang, J. P. Xu, B. C. Bao, and G. H. Zhou, "Asynchronous-switching map based stability effects of circuit parameters in fixed off-time controlled buck converter," IEEE Trans. Power Electron., Vol. 31, No. 9, pp. 6686-6697, Sep. 2016.   DOI
36 J. P. Wang, J. P. Xu, and B. C. Bao, "Analysis of pulse bursting phenomenon in constant on-time-controlled buck converter," IEEE Trans. Ind. Electron., Vol. 58, No. 12, pp. 5406-5410, Dec. 2011.   DOI