Application of Filippov method for the analysis of subharmonic instability in dc–dc converters

Abstract

SUMMARYWe propose a method of estimating the fast-scale stability margin of dc-dc converters based on Filippov's theory-originally developed for mechanical systems with impacts and stick-slip motion. In this method one calculates the state transition matrix over a complete clock cycle, and the eigenvalues of this matrix indicate the stability margin. Important components of this matrix are the state transition matrices across the switching events, called saltation matrices. We applied this method to estimate the stability margins of a few commonly used converter and control schemes. Finally, we show that the form of the saltation matrix suggests new control strategies to increase the stability margin, which we experimentally demonstrate using a voltage-mode-controlled buck converter.

A Closed Form Expression for Predicting Fast Scale Instability in Switching Buck Converters

“…In the past studies, the prediction of fast scale instability has been mainly based on deriving an accurate discrete time model and then linearizing it in the vicinity of the operating point [5], [3]. Recently, Filippov's method and the monodromy matrix have been used to predict these instabilities in DC-DC converters and similar results to those obtained from the discrete time approach were derived [7], [8]. However, the results obtained from both approaches, although very accurate, are not suited to obtain clear design-oriented criteria in the parametric design space.…”

“…Numerical simulations are not repeated here to save space. Interested readers can see [4], [7] and [8] for both numerical simulations and experimental measurements. Traditionally the dynamic behavior of the system in this example has been studied in terms of the input voltage v g [4], [5], [7], [8].…”

Dinámicas No-Lineales y No-Suaves en Procesos Estrés-Enfermedad / Nonlinear and Nonsmooth Dynamics in Stress-Sickness Processes

“…Finalmente, como se trata del caso en que existen fronteras que se cruzan, es necesario detectar el cruce y las ecuaciones de flujo en la intersección g i jkl , lo cual depende de los cuatro campos vectoriales involucrados en el cruce, de acuerdo a la ecuación: (13) donde α se define como antes, en la Ecuación (14) y…”

“…En ingeniería se ha utilizado para modelar motores eléctricos y convertidores de potencia [13]. También se ha utilizado para modelar sistemas donde a través de cambios abruptos en la dieta o en el hábitat se controla una determinada población [14] o sistemas que representan la explotación de algún recurso natural cuando su extracción se prohíbe al alcanzarse el máximo de explotación permitido [15].…”

Stability analysis of a high-step-Up DC grid-connected two-stage boost DC-DC converter

“…A large variety of complex nonlinear instability phenomena, such as period doubling leading to subharmonic oscillations, and Hopf or Neimark-Sacker bifurcations leading to slow-scale instabilities or saddle-node bifurcation leading to jump phenomenon between different steady-state solutions have been reported in switchedmode DC-DC converters. These studies, which are mostly based on accurate approaches coping with nonlinear behavior such as discrete-time mappings [3] or the Floquet theory together with Filippov's method [4]. These phenomena can have harmful effects on the system operation and may cause system failure, malfunctioning or even damages caused by the increase of the stress on the switching components which would rise the working temperature and this in turn would shorten the lifetime of the system.…”