Instability conditions for a class of switched linear systems with switching delays based on sampled-data analysis: applications to DC–DC converters

Abstract

Design-oriented boundary conditions for subharmonic oscillations are of great interest recently. Based on a subharmonic oscillation boundary condition reported in a PhD thesis more than a decade ago, extended new boundary conditions are derived in closed forms for general switching DC-DC converters. Sampled-data and harmonic balance analyses are applied and generate equivalent results. It is shown that the equivalent series resistance causes the boundary conditions for voltage/current mode control to have similar forms. Some recently reported boundary conditions become special cases in view of the general boundary conditions derived. New Nyquist-like designoriented plots are proposed to predict or prevent the occurrence of the subharmonic oscillation. The relation between the crossover frequency and the subharmonic oscillation is also analyzed.

Analytical multi‐parametric stability boundaries of DC‐DC buck converters under V1 control concept

“…Note that without excluding the integral variable from x , the problem will be ill‐posed and this matrix will be singular because the integral variable cannot reach a constant steady‐state without closing the loop by the switching condition . With the aim to avoid such an ill‐posedness problem, in and in other works by the same author of , the pole of the integrator at the origin was replaced by a small pole δ hence hiding the effect of the integral action on the subharmonic oscillation boundary. Here, the nature of the integrator is maintained, and its effect on this undesired phenomenon will be explicitly revealed for the case of the buck converter under V 1 control strategy.…”

“…The effect of the main parameters such as the duty cycle, the slope or amplitude of the ramp modulator, the poles, and the zeros of the controller as well as that of the parasitic parameters such as the ESL of the capacitor is revealed. The integral action will be shown to have a negligible effect on the subharmonic oscillation boundary in this control strategy.Multi-parametric stability boundaries of switching converters are usually tackled by using numerical techniques such as in [9,10], semi-analytical approaches like in [11][12][13][14], or analytical methods as recently reported in [15][16][17]. In this paper, we carry out study of the stability limits of the buck converter under the novel and advanced V 1 control strategy.…”

“…Multi-parametric stability boundaries of switching converters are usually tackled by using numerical techniques such as in [9,10], semi-analytical approaches like in [11][12][13][14], or analytical methods as recently reported in [15][16][17]. In this paper, we carry out study of the stability limits of the buck converter under the novel and advanced V 1 control strategy.…”

Subharmonic Instability Limits for <inline-formula><tex-math>${\rm V}^2$</tex-math></inline-formula> -Controlled Buck Converter With Outer Loop Closed/Open

“…In this paper, the S-plots are expressed in terms of α(D, p) and its coefficients. They have other equivalent expressions in terms of system matrices [15], [16], giving new perspectives.…”

Unified Equivalent Circuit Model and Optimal Design of <inline-formula><tex-math>$V^{2}$</tex-math> </inline-formula> Controlled Buck Converters

“…However, it is too complex for practical use. In [13][38]- [41], the sampled-data modeling techniques are employed to derive the stability criterion by judging whether the eigenvalues are less than unity in discrete-time domain. For sampled-data modeling method, it is conducted in discrete-time domain and is difficult for practical engineers.…”