Singular Perturbation Theory for DC–DC Converters and Application to PFC Converters

Many control schemes for DC-DC converters begin with the assertion that inductor currents are ldquofastrdquo states and capacitor voltages are ldquoslowrdquo states. This assertion must be true for power factor correction (PFC) converters to allow independent control of current and voltage, and is important for many other applications. In the present study, singular perturbation theory is applied to two-state switching-power converters to provide rigorous justification of the timescale separation. Krylov-Bogoliubov-Mitropolsky averaging is used to include switching ripple effects. A relationship between inductance, capacitance, load resistance, and loss resistances derives from an analysis of the off-manifold dynamics of an approximate model. Similar results hold for boost, buck, and buck-boost converters. Experimental boost converters validate the results. Discrete-time analysis is also shown. Simulated PFC converters demonstrate a simple, sensorless control technique that requires timescale separation.

[1]  P. Kokotovic.  A Riccati equation for block-diagonalization of ill-conditioned systems , 1975 .

[2]  Slobodan Cuk,et al.  A general unified approach to modelling switching-converter power stages , 1976, 1970 IEEE Power Electronics Specialists Conference.

[3]  W. Miranker,et al.  Multitime Methods for Systems of Difference Equations , 1977 .

[4]  Slobodan Cuk,et al.  A general unified approach to modelling switching DC-tO-DC converters in discontinuous conduction mode , 1977, 1977 IEEE Power Electronics Specialists Conference.

[5]  R. Phillips.  Reduced order modelling and control of two-time-scale discrete systems† , 1980 .

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

[8]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[9]  A General Approach to Sampled-Data Modeling for Power Electronic Circuits , 1986, IEEE Transactions on Power Electronics.

[10]  R. D. Middlebrook.  Small-signal modeling of pulse-width modulated switched-mode power converters , 1988 .

[11]  R. M. Bass,et al.  On the use of averaging for the analysis of power electronic systems , 1989, 20th Annual IEEE Power Electronics Specialists Conference.

[12]  J. M. Noworolski,et al.  Generalized averaging method for power conversion circuits , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[13]  P.T. Krein,et al.  A new approach to fast simulation of periodically switching power converters , 1990, Conference Record of the 1990 IEEE Industry Applications Society Annual Meeting.

[14]  R. M. Bass,et al.  Switching frequency dependent averaged models for PWM DC-DC converters , 1995, Proceedings of PESC '95 - Power Electronics Specialist Conference.

[15]  Donald Grahame Holmes,et al.  Implementation of a direct digital predictive current controller for single and three phase voltage source inverters , 1996, IAS '96. Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting.

[16]  Frede Blaabjerg,et al.  Improved digital current control methods in switched reluctance motor drives , 1999 .

[17]  Stéphane Bibian,et al.  High performance predictive dead-beat digital controller for DC power supplies , 2001, APEC 2001. Sixteenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No.01CH37181).

[18]  Stéphane Bibian,et al.  High performance predictive dead-beat digital controller for DC power supplies , 2002 .

[19]  Aleksandar Prodic,et al.  Predictive digital current programmed control , 2003 .

[20]  Oscar Garcia,et al.  Single phase power factor correction: a survey , 2003 .

[21]  V. Jayashankar,et al.  A predictive switching modulator for current mode control of high power factor boost rectifier , 2003 .

[22]  P. Mattavelli.  Digital control of DC-DC boost converters with inductor current estimation , 2004, Nineteenth Annual IEEE Applied Power Electronics Conference and Exposition, 2004. APEC '04..

[23]  Ching-Tsai Pan,et al.  An error bounded current controller with constant sampling frequency , 2004 .

[24]  D. Maksimovic,et al.  Variable-frequency predictive digital current mode control , 2004, IEEE Power Electronics Letters.

[25]  D. Maksimovic,et al.  A digital current mode control technique for DC-DC converters , 2005, Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005..

[26]  D. Maksimovic,et al.  Digital current-mode controller for DC-DC converters , 2005, Twentieth Annual IEEE Applied Power Electronics Conference and Exposition, 2005. APEC 2005..

[27]  Y.-S. Jung.  Small-signal model-based design of digital current-mode control , 2005 .

[28]  S. Chattopadhyay,et al.  A Digital Current-Mode Control Technique for DC–DC Converters , 2006, IEEE Transactions on Power Electronics.

[29]  P.T. Krein,et al.  Singular Perturbation Theory for DC-DC Converters and Application to PFC Converters , 2007, 2007 IEEE Power Electronics Specialists Conference.

[30]  Jonathan W. Kimball,et al.  Digital control techniques for switching power converters , 2007 .