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The piecewise‐affine model of buck converter suitable for practical stability analysis
Author(s) -
Siewniak Piotr,
Grzesik Bogusław
Publication year - 2015
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.1915
Subject(s) - commutation , piecewise , control theory (sociology) , stability (learning theory) , mathematics , affine transformation , buck converter , pulse width modulation , lyapunov function , realization (probability) , lyapunov stability , ideal (ethics) , power (physics) , computer science , voltage , control (management) , mathematical analysis , nonlinear system , engineering , physics , pure mathematics , statistics , philosophy , epistemology , quantum mechanics , artificial intelligence , machine learning , electrical engineering
A generalized geometrical piecewise‐affine continuous‐time model (GMD) of buck converter under pulse‐width modulated (PWM) voltage‐mode control is presented in this paper. In general, such a model can be applied to any DC‐DC power electronic converter (PEC) in which the valves are modelled as ideal switches. The GMD is suitable and convenient to analyse PEC practical stability which is a completely different concept in relation to the notion of its stability in the classical Lyapunov sense. The PEC GMD is based on its commutation structure which is a general geometrical model of its commutation. The general idea of this model consists in determining the local dynamic behaviour of PEC trajectories on the faces of its commutation structure and/or their sections. These faces and sections are treated as geometrical objects with generalized local dynamics. The analysis of buck converter practical stability is carried out using a new method based directly on the definition of this term but not Lyapunov‐like functions as in the direct method. It has been shown that PEC Lyapunov stability does not imply its practical stability. These two concepts are complementary to each other. Copyright © 2013 John Wiley & Sons, Ltd.