Two types of limit cycles of a resonant converter modelled by a three-dimensional system

A complementarity approach for the computation of periodic oscillations in piecewise linear systems

“…The model (5) includes the representation of many typical PWL functions such as minimum, maximum, relay, deadzone and PWL characteristics obtained by linear combinations of these ones.…”

“…We can mention electrical circuits where the current-voltage characteristics of some devices can be considered as piecewise linear, such as nonlinear resistors [1], ideal diodes and switches [2,3], or mechanical systems with Coulomb friction [4]. In those applications, the steadystate behaviour is generally depicted by a periodic motion [5,6]. Since they tend to periodically oscillate also when no external excitation is applied, the period related to the periodic solution is difficult to be predicted a priori.…”

Limit cycles in an industrially applied hybrid system

“…After impact with the ellipse 1, below the plane y=0, the control variable is chosen to 1 . The switching surfaces are the plane 0, the elliptic cylinder surface, the top of the cylinder Note that this kind of switched system containing logic states is quite different from systems defined as piecewise, for example the LCC -converter defined in Melin et al (2008).…”

“…See for instance [8] and [9]. When modelling with three continuous states the solution set will increase even more, see [10]. In [11] a controller for an industrially applied resonant converter is analyzed.…”

Asymmetric Limit Cycles in an Industrially Applied Controlled Resonant Converter

“…See for instance Melin et al (2003) and Melin and Hultgren (2006). When modelling with three continuous states the solution set will increase even more, see Melin et al (2008). Higher order models and derivation of an observer for the converter model can be found in Hultgren and Lenells (2004a, b).…”