Stability aspects of a multifrequency model of a PWM converter

In this paper the stability of a multifrequency model of a PWM converter is investigated. A multifrequency model is a model based on Fourier series that contains as a special case the so-called state space average model. In contrast to a state space average model a multifrequency model may also include so-called higher order harmonics, where the zeroth order harmonic corresponds to the ( moving) average. This paper focuses on a specific PWM converter, namely a Cuk converter, and it is proved that a multifrequency model of a Cuk converter with fixed duty ratio is asymptotically stable. This result generalizes the known corresponding result for a state space average model of a Cuk converter with fixed duty ratio. Taking all the harmonics into account the result also illustrates the well-known fact that a Cuk converter with a fixed duty ratio and a finite switching frequency is asymptotically stable in the following sense. If the signals in a Cuk converter do not correspond with a periodic behaviour, they will however do so in the limit, i.e. as time goes to infinity the signals will become periodic, and this limiting periodic behaviour is unique. Although the paper mainly deals with the stability issues fora Cuk converter, it is possible to use the ideas of the paper to derive similar results for other types of PWM converters.