Journal of Power Electronics

The Korean Institute of Power Electronics (전력전자학회)
권호 표지
DOI QR코드

DOI QR Code

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)
  • Received : 2016.10.23
  • Accepted : 2017.06.28
  • Published : 2017.09.20
Download PDF
⟨ Previous Next ⟩

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

References

  1. C. W. Deisch, "Switching control method changes power converter into a current source," in Proc. IEEE Power Electron. Sepc. Conf., pp. 300-306, 1978.
  2. 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.
  3. Texas Instruments, LM3409 datasheet. http://www.ti.com/lit/ds/symlink/lm3409.pdf, 2016.
  4. Linear Technology, LTC3869 datasheet. http://cds.linear.com/docs/en/datasheet/38692fb.pdf, 2011.
  5. Analog Devices, ADP1882 datasheet. http://www.analog.com/media/en/technical-documentation/data-sheets/ADP1882_1883.pdf, 2010.
  6. Maxim, MAX17512 datasheet. https://datasheets.maximintegrated.com/en/ds/MAX17512.pdf, 2011.
  7. C. P. Basso, Switch-Mode Power Supplies: SPICE Simulations And Practical Designs, 2nd ed., New York, NY, USA: McGraw-Hill, pp. 258-262, 2015.
  8. J. Sun, "Small-signal modeling of variable-frequency pulsewidth modulators," IEEE Trans. Aerosp. Electron. Syst., Vol. 38, No. 3, pp. 1104-1108, Jul. 2002. https://doi.org/10.1109/TAES.2002.1039428
  9. R. Redl and I. Novak, "Instability in current-mode controlled switching voltage regulators," in Proc. IEEE Power Electron. Spec. Conf., pp. 17-28, 1981.
  10. D. J. Packard, "Discrete modeling and analysis of switching regulators," Ph. D. dissertation, California Institute Technology, CA, May, 1976.
  11. A. R. Brown and R. D. Middlebrook, "Sampled-data modeling of switched regulators," in Proc. IEEE Power Electron. Spec. Conf., pp. 349-369, 1981.
  12. 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. https://doi.org/10.1109/63.76813
  13. 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. https://doi.org/10.1109/81.660771
  14. 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.
  15. 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. https://doi.org/10.1109/81.168922
  16. 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. https://doi.org/10.1109/81.508184
  17. 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. https://doi.org/10.1109/TCSI.2008.923282
  18. 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. https://doi.org/10.1142/S0218127413500624
  19. 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. https://doi.org/10.1109/TCSII.2004.838438
  20. 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. https://doi.org/10.1142/S0218127412500083
  21. 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. https://doi.org/10.1109/TPEL.2010.2098421
  22. 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. https://doi.org/10.1109/TCSI.2013.2284178
  23. 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. https://doi.org/10.1109/TIE.2015.2458966
  24. 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. https://doi.org/10.1109/TIE.2013.2257143
  25. 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. https://doi.org/10.1109/TPEL.2014.2312354
  26. 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. https://doi.org/10.1109/TPEL.2016.2587827
  27. 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. https://doi.org/10.1109/TPEL.2010.2040123
  28. 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. https://doi.org/10.1109/TCSI.2012.2206445
  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. https://doi.org/10.1109/TPEL.2006.878031
  30. 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. https://doi.org/10.1109/TPEL.2012.2188841
  31. 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. https://doi.org/10.1109/TPEL.2015.2508037
  32. 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. https://doi.org/10.1109/TPEL.2014.2308015
  33. 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. https://doi.org/10.1109/TIE.2012.2190956
  34. 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. https://doi.org/10.1109/TPEL.2015.2501367
  35. 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. https://doi.org/10.1109/TIE.2011.2123861
  36. 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 https://doi.org/10.1007/s11071-012-0572-2