On limit cycles and the describing function method in periodically switched circuits

Examines existence, uniqueness, and stability of limit cycles in periodically switched circuits. The motivation comes from the field of power electronics where switched circuit models composed of passive elements, independent sources, and ideal switches are studied. The paper then studies the describing function method for computation of limit cycles in these switched circuits. Typical power circuit models have nonlinear elements with characteristics that do not satisfy a Lipschitz continuity condition. As a result of these nonsmooth characteristics, previously developed justifications for the describing function method are not applicable. The present paper develops a justification for the describing function method that relies on the incrementally passive characteristics of the network elements comprising typical power electronic circuit models. This justification holds for nonsmooth circuit nonlinearities, and takes the form of a set of asymptotically convergent bounds on the errors incurred with the describing function method. In particular, the developed bounds become arbitrarily tight as the number of harmonics included in the analysis increases. >

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

[2]  George C. Verghese,et al.  Synthesis of averaged circuit models for switched power converters , 1991 .

[3]  R.D. Middlebrook,et al.  Low-Frequency Characterization of Switched dc-dc Converters , 1972, IEEE Transactions on Aerospace and Electronic Systems.

[4]  D. C. Hamill,et al.  Instability, subharmonics and chaos in power electronic systems , 1989 .

[5]  Felix F. Wu,et al.  NONLINEAR MONOTONE NETWORKS , 1974 .

[6]  A. I. Mees,et al.  Limit Cycle Stability , 1973 .

[7]  L. Chua,et al.  A qualitative analysis of the behavior of dynamic nonlinear networks: Steady-state solutions of nonautonomous networks , 1976 .

[8]  Philip T. Krein,et al.  Multiple limit cycle phenomena in switching power converters , 1989, Proceedings, Fourth Annual IEEE Applied Power Electronics Conference and Exposition.

[9]  Arthur Gelb,et al.  Multiple-Input Describing Functions and Nonlinear System Design , 1968 .

[10]  A. I. Mees,et al.  The Describing Function Matrix , 1972 .

[11]  Slobodan Cuk,et al.  A general unified approach to modelling switching-converter power stages , 1977 .

[12]  Dariusz Czarkowski,et al.  Linear circuit models of PWM flyback and buck/boost converters , 1992 .

[13]  J. M. Noworolski,et al.  Generalized in-plane circuit averaging , 1991, [Proceedings] APEC '91: Sixth Annual Applied Power Electronics Conference and Exhibition.

[14]  Roger W. Brockett,et al.  Electrical networks containing controlled switches , 1974 .

[15]  A. R. Bergen,et al.  Justification of the Describing Function Method , 1971 .

[16]  R. Steigerwald,et al.  A comparison of half-bridge resonant converter topologies , 1987, 1987 IEEE Applied Power Electronics conference and Exposition.

[17]  Martin Hasler,et al.  Nonlinear Circuits , 1986 .

[18]  C. Desoer,et al.  Feedback Systems: Input-Output Properties , 1975 .

[19]  R. Redl,et al.  Dynamic analysis of switching-mode DC/DC converters , 1991 .

[20]  F. Verhulst,et al.  Averaging Methods in Nonlinear Dynamical Systems , 1985 .

[21]  George C. Verghese,et al.  Principles of Power Electronics , 2023 .

[22]  Marian K. Kazimierczuk,et al.  Frequency-domain analysis of series resonant converter for continuous conduction mode , 1992 .

[23]  J.H.B. Deane,et al.  Analysis, simulation and experimental study of chaos in the buck converter , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[24]  Seth R. Sanders,et al.  Nonlinear control of switching power converters , 1989 .

[25]  Philip T. Krein,et al.  On the use of averaging for the analysis of power electronic systems , 1989 .