Nonsmooth Modeling and Simulation for Switched Circuits

01/2010; DOI: 10.1007/978-90-481-9681-4
Source: OAI

ABSTRACT Nonsmooth Modeling and Simulation for Switched Circuits concerns the modeling and the numerical simulation of switched circuits with the nonsmooth dynamical systems (NSDS) approach, using piecewise-linear and multivalued models of electronic devices like diodes, transistors, switches. Numerous examples (ranging from introductory academic circuits to various types of power converters) are analyzed and many simulation results obtained with the INRIA open-source SICONOS software package are presented. Comparisons with SPICE and hybrid methods demonstrate the power of the NSDS approach. Nonsmooth Modeling and Simulation for Switched Circuits is intended to researchers and engineers in the field of circuits simulation and design, but may also attract applied mathematicians interested by the numerical analysis for nonsmooth dynamical systems, as well as researchers from Systems and Control.

  • [Show abstract] [Hide abstract]
    ABSTRACT: At a certain level of abstraction power converters can be represented as linear circuits connected to diodes and controlled electronic switches. The evolutions of the electrical variables are determined by the state-dependent switchings, which complicate the mathematical modeling of controlled power converters. Differently from the complementarity models previ- ously presented in the literature, the model proposed in this paper allows to represent as a linear complementarity system also closed-loop power converters, without requiring the a pri- ori knowledge of the converter modes. A model construction procedure, not dependent on the specific converter topology, is presented. The discretization of the continuous-time model allows to formulate mixed linear complementarity problems for the computation of the control-to-output frequency response and the evolutions of both transient and steady-state currents and voltages. As illustrative examples Z-source, boost and buck DC– DC power converters under voltage-mode control and current- mode control operating both in continuous and discontinuous conduction modes are considered.
    IEEE Transactions on Power Electronics 12/2014; 29(12). DOI:10.1109/TPEL.2014.2306975 · 5.73 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we prove a result on the existence of solutions of a differential inclusion governed by a class of nonconvex state-dependent sweeping process with perturbation depending on all the variables and with delay. The moving set involved in the process is prox-regular and depends both on the time and on the state.
    Applicable Analysis 05/2014; DOI:10.1080/00036811.2014.918259 · 0.68 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, we analyze and discuss the well-posedness of two newvariants of the so-called sweeping process, introduced by Moreau in the early 70s (Moreau in Sém Anal Convexe Montpellier, 1971) with motivation in plasticity theory. The first new variant is concerned with the perturbation of the normal cone to the moving convex subset C(t), supposed to have a bounded variation, by a Lipschitz mapping. Under some assumptions on the data, we show that the perturbed differential measure inclusion has one and only one right continuous solution with bounded variation. The second variant, for which a large analysis is made, concerns a first order sweeping process with velocity in the moving set C(t). This class of problems subsumes as a particular case, the evolution variational inequalities [widely used in applied mathematics and unilateral mechanics (Duvaut and Lions in Inequalities in mechanics and physics. Springer, Berlin, 1976]. Assuming that the moving subset C(t) has a continuous variation for every t ∈ [0, T ] with C(0) bounded, we show that the problem has at least a Lipschitz continuous solution. The well-posedness of this class of sweeping process is obtained under the coercivity assumption of the involved operator.We also discuss some applications of the sweeping process to the study of vector hysteresis operators in the elastoplastic model (Krejˇcı in Eur J Appl Math 2:281–292, 1991), to the planning procedure inmathematical economy (Henry in J Math Anal Appl 41:179– 186, 1973 and Cornet in J. Math. Anal. Appl. 96:130–147, 1983), and to nonregular electrical circuits containing nonsmooth electronic devices like diodes (Acary et al. Nonsmooth modeling and simulation for switched circuits. Lecture notes in electrical engineering. Springer, New York 2011). The theoretical results are supported by some numerical simulations to prove the efficiency of the algorithm used in the existence proof.Our methodology is based only on tools from convex analysis. Like other papers in this collection, we show in this presentation how elegant modern convex analysis was influenced by Moreau’s seminal work
    Mathematical Programming 12/2014; DOI:10.1007/s10107-014-0754-4 · 1.98 Impact Factor