Nonsmooth modeling and simulation for switched circuits.
The book under review is divided into three parts. In the first part the theoretical background behind the circuits is presented. In this part there are two chapters. The first one is an introduction to switched circuits, such as RCD, RCD, RLZD, RCZD, order-two and order-three circuits. The second chapter is devoted to present the mathematical tools which are used in the book to analyze the nonsmooth circuits and their time-discretizations. The results are given without proofs. A brief recall of some basic tools and to the circuits of chapter 1 is done and their dynamics using new mathematical frameworks are rewritten. Many of the tools which are presented in this chapter, will be used, or presented in another way in chapter 4. In the third chapter, some basic facts on the circuit equation formulation and simulation which are shared by most of the analog SPICE-like simulators are presented. The formulation of the circuit equations is based on two basic ingredients: conservative laws given by the Kirchhoff laws in currents and voltages and constitutive equations of the electrical components, which lead to a Differential Algebraic Equation (DAE). The fourth chapter is an approach to NonSmooth Dynamical Systems (NSDS). Standard description of elements by means of explicit and smooth functions is enriched by new elements described by generalized equations. The characteristics of the electronic devices can be then nonsmooth and even multivalued. These elements are called the electrical ``nonsmooth elements''. The description of nonsmooth components relies a lot on mathematical notions from Convex Analysis and Mathematical Programming theory. In this chapter, the authors take advantage of the material of the foregoing chapters to arrive at the general mathematical formalisms which are used in the NSDS approach to simulate the electrical circuits of chapters 7 and 8. In chapter 5, several mathematical formalisms are presented. These formalisms incorporate not only the nonsmooth and multivalued models of the electronic devices (ideal diodes, Zener diodes, etc.), but also the equations obtained from the MNA. In the last part it is shown how numerical simulations on circuits can be done. Chapter 6 is dedicated to SlCONOS software that aims at providing a general and common tool for nonsmooth problems in various scientific fields like applied mathematics, mechanics, robotics, electrical circuits. The Automatic Circuit Equations Formulation (ACEF) module is the implementation of the automatic circuit equation extended to general nonsmooth components. From a SPICE netlist, possibly augmented by some nonsmooth components, the ACEF builds a dynamical formulation that can be simulated by SlCONOS. Chapter 7 is devoted to present numerical simulation results obtained with the SICONOS platform, on several simple circuits: the first circuit has been built to show that conventional analog simulators fail to converge, the other circuits are classical diode-bridge wave rectifiers, and the last one is a circuit that exhibits a sliding mode. Chapter 8 is dedicated to the numerical simulation of the buck and the delta-sigma converters. Comparisons between the results obtained with the NSDS SICONOS approach and other approaches are presented. In the chapters 7 and 8 five simulation software packages are used.
scientific article; zbMATH DE number 5763647