Generalized discontinuous conduction modes in the complementarity formalism

Abstract

Abstract-We model dc-dc power converters using the complementarity formalism. For each position of the switches, the dynamics is given by a linear complementarity system which incorporates, in a natural way, the description of generalized discontinuous conduction modes (GDCM), characterized by a reduction of the dimension of the effective dynamics. For systems with a single diode, analytical state-space conditions for the presence of a GDCM can be stated. As an example, this result is used to identify the GDCM for the switch configurations of theČuk converter. Simulation results, showing a variety of behaviors, such as persistent or re-entering GDCM, are presented.

Averaged dynamics of a coupled-inductor boost converter under sliding mode control using a piecewise linear complementarity model

“…In addition, it is desirable that x 4 > 0; if such condition is not satisfied then the converter under study does not offer any advantages over a conventional boost topology. Statements of the form 0 a⊥b b, known as "complementarity conditions" (CC) (see Camlibel et al (2003), Batlle et al (2005)), mean that both a and b are nonnegative and that if one of them is not zero, then the other one is zero. If a and b are vectors, then these conditions hold component-wise.…”

PI and Sliding Mode Control of a Cuk Converter

“…With three zeros and four poles, (25) is a stable and strictly proper system. If (25) has three zeros in the left half-phase plane, the Cuk converter will have a minimum phase. Otherwise, the Cuk converter will have a nonminimum phase.…”

“…Differentiating (15) for v 2 , v d , and E with respect to time and linearizing it render (28) where p 1 = −(E e v e /R) and p 2 = E e C 1 (E e − v e ). Equation (28) has the same poles as (25). A zero of (28) is 0.…”

“…The small-signal models of the Cuk and other converters are readily derived in terms of h parameter (for buck family) and g parameter (for boost family) [24]. Complementarity formalism is explored for modeling of a Cuk converter in discontinuous conduction modes [25]. Stability aspects of the open loop and closed loop of the Cuk converter are analyzed [26].…”

Robust output regulation of variable structure systems with multivalued controls

“…[1], [2], [3], [4], [5]), the problem of designing a control system using general multivalued laws has been substantially less explored. A notable contribution in this direction takes place in viability theory [6,Ch.…”