Using Nyquist or Nyquist-Like Plot to Predict Three Typical Instabilities in DC-DC Converters

Abstract By transforming an exact stability condition, a new Nyquist-like plot is proposed to predict occurrences of three typical instabilities in DC–DC converters. The three instabilities are saddle-node bifurcation (coexistence of multiple solutions), period-doubling bifurcation (subharmonic oscillation), and Neimark bifurcation (quasi-periodic oscillation). In a single plot, it accurately predicts whether an instability occurs and what type the instability is. The plot is equivalent to the Nyquist plot, and it is a useful design tool to avoid these instabilities. Four examples are used to illustrate the accuracy of this new plot to predict instabilities in the buck or boost converter with fixed or variable switching frequency.

[1]  Chung-Chieh Fang,et al.  Critical conditions of saddle-node bifurcations in switching DC–DC converters , 2013 .

[2]  D. C. Hamill,et al.  Modeling of chaotic DC-DC converters by iterated nonlinear mappings , 1992 .

[3]  Eyad H. Abed,et al.  Limit cycle stabilization in PWM DC-DC converters , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[4]  Benjamin C. Kuo,et al.  AUTOMATIC CONTROL SYSTEMS , 1962, Universum:Technical sciences.

[5]  James A. Yorke,et al.  Border-collision bifurcations in the buck converter , 1998 .

[6]  M. Kazimierczuk.  Transfer function of current modulator in PWM converters with current-mode control , 2000 .

[7]  Doug Mattingly.  Designing Stable Compensation Networks for Single Phase Voltage Mode Buck Regulators TB 417 , 2003 .

[8]  Chung-Chieh Fang.  Sampled-data poles, zeros, and modeling for current-mode control , 2013, Int. J. Circuit Theory Appl..

[9]  Eduard Alarcón,et al.  A Design-Oriented Combined Approach for Bifurcation Prediction in Switched-Mode Power Converters , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Malik Elbuluk,et al.  Fundamentals of Power Electronics , 2013 .

[11]  Eyad H. Abed,et al.  Sampled-data modelling and analysis of the power stage of PWM DC-DC converters , 2001 .

[12]  D. Maksimovic,et al.  Small-Signal Discrete-Time Modeling of Digitally Controlled PWM Converters , 2007, IEEE Transactions on Power Electronics.

[13]  Eyad H. Abed,et al.  Sampled-data modeling and analysis of closed-loop PWM DC-DC converters , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[14]  Damian Giaouris,et al.  Stability Analysis of the Continuous-Conduction-Mode Buck Converter Via Filippov's Method , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Chung-Chieh Fang.  Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control , 2012, ArXiv.

[16]  Chung-Chieh Fang,et al.  Saddle-node bifurcation in the buck converter with constant current load , 2012 .

[17]  Chung-Chieh Fang.  Unified Discrete-Time Modeling of Buck Converter in Discontinuous Mode , 2011, IEEE Transactions on Power Electronics.

[18]  Jian Sun,et al.  Ripple-Based Control of Switching Regulators—An Overview , 2009, IEEE Transactions on Power Electronics.

[19]  Francis Labrique,et al.  Switch-Mode Power Supplies , 1993 .

[20]  Eyad H. Abed,et al.  Local Bifurcations in DC-DC Converters , 2012, ArXiv.

[21]  R. B. Ridley,et al.  A new, continuous-time model for current-mode control (power convertors) , 1991 .

[22]  Chung-Chieh Fang.  Bifurcation boundary conditions for current programmed PWM DC–DC converters at light loading , 2012 .

[23]  Chung-Chieh Fang.  Sampled-Data and Harmonic Balance Analyses of Average Current-Mode Controlled Buck Converter , 2012, ArXiv.

[24]  Eyad H. Abed,et al.  Robust Feedback Stabilization of Limit Cycles in PWM DC-DC Converters , 2002 .

[25]  M. R. D. Al-Mothafar.  Small-signal modelling of current-programmed N-connected parallel-input/series-output bridge-based buck dc-dc converters , 2012, J. Frankl. Inst..

[26]  Yuan Yu,et al.  Generalized Computer-Aided Discrete Time-Domain Modeling and Analysis of DC-DC Converters , 1979, IEEE Transactions on Industrial Electronics and Control Instrumentation.

[27]  Chung-Chieh Fang.  Unified model of voltage/current mode control to predict saddle-node bifurcation , 2012, ArXiv.

[28]  Chung-Chieh Fang.  Unified model of voltage/current mode control to predict subharmonic oscillation , 2012, ArXiv.

[29]  Chung-Chieh Fang.  Modeling and Instability of Average Current Control , 2012, ArXiv.

[30]  Seth R. Sanders,et al.  Bifurcation of power electronic circuits , 1994 .

[31]  Chi K. Tse,et al.  Complex behavior in switching power converters , 2002, Proc. IEEE.

[32]  R.D. Middlebrook,et al.  Sampled-data modeling of switching regulators , 1981, 1981 IEEE Power Electronics Specialists Conference.

[33]  Chung-Chieh Fang,et al.  Closed-Form Critical Conditions of Subharmonic Oscillations for Buck Converters , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[34]  Fred C. Lee,et al.  Small-signal modeling of average current-mode control , 1992, [Proceedings] APEC '92 Seventh Annual Applied Power Electronics Conference and Exposition.

[35]  W. L. De Koning,et al.  On the periodic behavior of PWM DC-DC converters , 2002 .

[36]  R. M. Bass,et al.  Switching frequency dependent averaged models for PWM DC-DC converters , 1995 .

[37]  F. D. Tan,et al.  A unified model for current-programmed converters , 1995 .

[38]  C. Fang.  Critical conditions for a class of switched linear systems based on harmonic balance: applications to DC-DC converters , 2012 .

[39]  J. A. Kuznecov.  Elements of applied bifurcation theory , 1998 .

[40]  Chung-Chieh Fang,et al.  Sampled-Data Modeling and Analysis of the Power Stage of PWM DC-DC Converters , 1999 .

[41]  Chung-Chieh Fang,et al.  Subharmonic Stability Limits for the Buck Converter With Ripple-Based Constant On-Time Control and Feedback Filter , 2014, IEEE Transactions on Power Electronics.

[42]  Chung-Chieh Fang.  Sampled-Data Analysis and Control of DC-DC Switching Converters , 1997 .