Generalized Discontinuous Conduction Modes in the Complementarity Formalism

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 the Čuk converter. Simulation results, showing a variety of behaviors, such as persistent or re-entering GDCM, are presented.Peer Reviewe

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

An averaged model of a coupled-inductor boost converter using the piecewise complementarity model of the converter under sliding motions is obtained. The model takes into account the idealized voltage–current characteristic of passive switches (diodes) present in the converter. Because of its lower complexity, the averaged model is more suitable for control design purposes when compared with the linear complementarity systems (LCS) model of the converter. The dynamic performance of the LCS model and the averaged models of the converter are validated through computer simulations using Matlab.Postprint (author's final draft

Modeling and numeriacal study of nonsmooth dynamical systems. Applications to Mechanical and Power Electronics Systems.

This thesis is concerned with the modeling and numerical study of nonsmooth dynamical systems (NSDS). The first part of the thesis deals with the modeling of some DC-DC power converters using the complementarity formalism. This mathematical theoretical framework allows us to ensure existence and uniqueness of solutions in a "natural" and synthetic way. Specifically, it works pretty well in power electronic converters because it incorporates 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 are stated and simulation results, showing a variety of behaviours, such as persistent or re-entering GDCM, are also presented. Furthermore, the analysis and simulation of a parallel resonant converter (PRC), which has four diodes, illustrate the convenience of the complementarity formalism to simulate electrical systems with a large number of ideal diodes. We also present the simulation of a boost converter with a sliding mode control, even though a general control theory for complementarity systems is not still developed.In the second part of the thesis we focus on the bifurcation analysis in NSDS, and in particular, we have studied different mechanical systems which involve impacts and dry-friction. It is known that nonsmooth or discontinuous dynamical systems can exhibit the bifurcations also exhibited by smooth systems. In addition to these, there are also some novel transitions so-called discontinuity-induced bifurcations (DIBs) which are unique to these systems. We have investigated the complex behaviour occurring in an impacting mechanical system. DIBs such as corner impact bifurcations and transitions from complete to uncomplete chattering motions have been analysed in detail. Another type of DIBs recently classified are the so-called sliding bifurcations. Such bifurcations are a characteristic feature of so-called Filippov systems. We present detailed examples of all the different sliding bifurcation scenarios in a dry friction oscillator using a measured friction characteristic firstly introduced by Popp. Furthermore, a codimension-two degenerate switching-sliding bifurcation is displayed. In this case of degenerate switching-sliding bifurcation two curves of codimension-one sliding bifurcations, crossing-sliding and adding-sliding, branch out from the codimension-two point. Also, a cusp smooth codimension-two bifurcation is shown and coexistence of periodic orbits in the region between both fold codimension-one curves is studied.We have also investigated the dynamic behaviour of the two-block Burridge model for earthquake simulations. Previous numerical studies investigated by Ruina verified that, with a friction force of Coulomb type, the system presents only periodic behaviour. We show that chaotic regions can be observed in a symmetric configuration even if a Coulomb friction is considered with the relaxation of one of the assumptions assumed in the seismological literature. Furthermore, we have studied the behaviour of the system with asymmetric configuration. Different periodic solutions and regions of chaos can be observed varying the asymmetry of the system. With respect to the bifurcation point of view, we have analysed several smooth bifurcations (smooth and DIBs) observed in this system.Chapter 6 of this thesis presents the SICONOS software platform dedicated to simulation of NSDS. We give an overview of the SICONOS software and the way NSDS are modeled and simulated within the platform. Routines for analysis (stability, bifurcations, invariant manifolds,.) of NSDS implemented in the platform are explained in detail. To conclude this part, several representative samples are shown in order to illustrate the SICONOS platform abilities.Conclusion and some open problems are presented in the last chapter

The nonsmooth dynamical systems approach for the analog simulation of switched circuits within the Siconos framework

The numerical integration of switching circuits is known to be a tough issue when the number of switches is high, or when sliding modes exist. Then classical analog simulators may behave poorly, or even fail. In this paper it is shown on two examples that the nonsmooth dynamical systems (NSDS) approach, which is made of 1) a specific modelling of the piecewise- linear electronic devices (ideal diodes, Zener diodes, transistors), 2) the Moreau's time-stepping scheme, and 3) specific iterative one-step solvers, supersedes simulators of the SPICE family and hybrid simulators. An academic example constructed in [Maffezzoni et al, IEEE Trans. on CADICS, Vol 25, No 11, November 2006], so that the Newton-Raphson scheme does not converge, and the buck converter, are used to make extensive comparisons between the NSDS method and other methods of the SPICE family and a hybrid-like method. The NSDS method, implemented in the Siconos platform developed at INRIA, proves to be on these two examples much faster and more robust with respect to the models parameters variations

Time-stepping numerical simulation of switched circuits with the nonsmooth dynamical systems approach

International audienceThe numerical integration of switching circuits is known to be a tough issue when the number of switches is large, or when sliding modes exist. Then, classical analog simulators may behave poorly, or even fail. In this paper, it is shown on two examples that the nonsmooth dynamical systems (NSDS) approach, which is made of: 1) a specific modeling of the piecewise-linear electronic devices (ideal diodes, Zener diodes, transistors); 2) the Moreau's time-stepping scheme; and 3) specific iterative one-step solvers, supersedes simulators of the simulation program with integrated circuit emphasis (SPICE) family and hybrid simulators. An academic example constructed in [Maffezzoni, , IEEE Trans. CADICS, vol 25, no. 11, Nov. 2006], so that the Newton-Raphson scheme does not converge, and the buck converter are used to make extensive comparisons between the NSDS method and other methods of the SPICE family and a hybrid-like method. The NSDS method, implemented in the siconos platform developed at INRIA, proves to be on these two examples much faster and more robust with respect to the model parameter variations

An introduction to Siconos

In this document, a brief overview of the Siconos Platform is given. One of the goal is to give a flavor on a simple example of the ability of the platform to model and simulate the so-called non smooth dynamical systems (NSDS). In particular, some examples of Lagrangian mechanical systems with contact and friction or electrical circuits with ideal and piecewise linear components (diodes, MOS transistors, \ldots) are commented. Finally, the Siconos software is presented, starting from its architecture to a non exhaustive presentation of its components and functionalities. The aim of this document is not to serve as a reference guide but more as a illustrative introduction document to promote the use of the platform

Wave theory of turbulence in compressible media (acoustic theory of turbulence)

The generation and the transmission of sound in turbulent flows are treated as one of the several aspects of wave propagation in turbulence. Fluid fluctuations are decomposed into orthogonal Fourier components, with five interacting modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. Wave interactions, governed by the inhomogeneous and nonlinear terms of the perturbed Navier-Stokes equations, are modeled by random functions which give the rates of change of wave amplitudes equal to the averaged interaction terms. The statistical framework adopted is a quantum-like formulation in terms of complex distribution functions. The spatial probability distributions are given by the squares of the absolute values of the complex characteristic functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation

Modeling and control of electromechanical systems

The material presented in the these notes covers the sessions Modelling of electromechanical systems, Passive control theory I and Passive control theory II of the II EURON/GEOPLEX Summer School on Modelling and Control of Complex Dynamical Systems. We start with a general description of what an electromechanical system is from a network modelling point of view. Next, a general formulation in terms of PHDS is introduced, and some of the previous electromechanical systems are rewritten in this formalism. Power converters, which are variable structure systems (VSS), can also be given a PHDS form. We conclude the modelling part of these lectures with a rather complex example, showing the interconnection of subsystems from several domains, namely an arrangement to temporally store the surplus energy in a section of a metropolitan transportation system based on dc motor vehicles, using either arrays of supercapacitors or an electric powered flywheel. The second part of the lectures addresses control of PHD systems. We first present the idea of control as power connection of a plant and a controller. Next we discuss how to circumvent this obstacle and present the basic ideas of Interconnection and Damping Assignment (IDA) passivity-based control of PHD systems

Range separation: The divide between local structures and field theories

This work presents parallel histories of the development of two modern theories of condensed matter: the theory of electron structure in quantum mechanics, and the theory of liquid structure in statistical mechanics. Comparison shows that key revelations in both are not only remarkably similar, but even follow along a common thread of controversy that marks progress from antiquity through to the present. This theme appears as a creative tension between two competing philosophies, that of short range structure (atomistic models) on the one hand, and long range structure (continuum or density functional models) on the other. The timeline and technical content are designed to build up a set of key relations as guideposts for using density functional theories together with atomistic simulation.Comment: Expanded version of a 30 minute talk delivered at the 2018 TSRC workshop on Ions in Solution, to appear in the March, 2019 issue of Substantia (https://riviste.fupress.net/index.php/subs/index