The piecewise-affine model of buck converter suitable for practical stability analysis

摘要

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.