Acary / Bonnefon / Brogliato Nonsmooth Modeling and Simulation for Switched Circuits

1. Auflage 2010
ISBN: 978-90-481-9681-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 284 Seiten

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. 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.

Autoren/Hrsg.

Acary, Vincent

Bonnefon, Olivier

Brogliato, Bernard

Inhaltsverzeichnis

1;Preface;5
2;Acknowledgements;6
3;Contents;7
4;List of Abbreviations;12
5;List of Algorithms;13
6;List of Figures;14
7;List of Tables;18
8;Theoretical Framework;19
8.1;Introduction to Switched Circuits;20
8.1.1;1.1 Simple Examples of Switched Circuits;20
8.1.2;1.2 A Unified Dynamical Framework: Lur'e Dynamical Systems;43
8.1.3;1.3 An Aside on Nonsmooth Mechanics: The Bouncing Ball;44
8.1.4;1.4 Conclusions;46
8.1.5;1.5 Historical Summary;47
8.2;Mathematical Background;50
8.2.1;2.1 Basics from Convex and Nonsmooth Analysis;50
8.2.2;2.2 Non Convex Sets;68
8.2.3;2.3 Basics from Complementarity Theory;68
8.2.4;2.4 Mathematical Formalisms;76
8.2.5;2.5 The Dynamics of the Simple Circuits;101
8.2.6;2.6 Time-Discretization Schemes;116
8.2.7;2.7 Conclusions and Recapitulation;121
9;Dynamics Generation and Numerical Algorithms;123
9.1;Conventional Circuit Equation Formulation and Simulation;124
9.1.1;3.1 Circuit Topology and Kirchhoff's Laws;124
9.1.2;3.2 The Sparse Tableau Analysis (STA);127
9.1.3;3.3 The Modified Nodal Analysis;127
9.1.4;3.4 The Charge/Flux Oriented MNA;130
9.1.5;3.5 Standard DAEs Stemming from the MNA;130
9.1.6;3.6 Semi-Explicit DAE Forms;139
9.1.7;3.7 Basics on Standard Circuit Simulation;146
9.2;Nonsmooth Modeling of Electrical Components;151
9.2.1;4.1 General Nonsmooth Electrical Element;151
9.2.2;4.2 Nonsmooth Elements as Inclusions into the Subdifferential of Convex Functions and Variational Inequality ( VI);152
9.2.3;4.3 Nonsmooth Elements as Inclusions into Normal Cones and Variational Inequalities;154
9.2.4;4.4 Complementarity Problems;155
9.2.5;4.5 The Linear Input/Output Relation Case;156
9.2.6;4.6 Generic Piecewise-Linear Components;157
9.2.7;4.7 Special Instances of Nonsmooth Components;159
9.3;Time-Stepping Schemes and One Step Solvers;168
9.3.1;5.1 Summary of the Mathematical Formalisms;168
9.3.2;5.2 Principles of the Numerical Time-Integration Scheme;171
9.3.3;5.3 Time-Discretization of the General Cases;192
9.3.4;5.4 One-Step NonSmooth Problems (OSNSP) Solvers;193
10;Numerical Simulations;196
10.1;The Automatic Circuit Equations Formulation ( ACEF) Module and the SICONOS Software;197
10.1.1;6.1 An Insight into SICONOS;197
10.1.2;6.2 SICONOS Software;202
10.1.3;6.3 The ACEF Module and Algorithms;210
10.2;Simple Circuits;227
10.2.1;7.1 Maffezzoni's Example;227
10.2.2;7.2 A First Diode-BridgeWave Rectifier;233
10.2.3;7.3 A Second Diode-Bridge Wave Rectifier;236
10.2.4;7.4 The Cuk Converter;237
10.2.5;7.5 A Circuit Exhibiting Sliding Modes;243
10.3;Buck and Delta-Sigma Converters;250
10.3.1;8.1 The Buck Converter with Load Resistor;250
10.3.2;8.2 The Buck Converter Loaded by a Resistor and an Inverter Chain;264
10.3.3;8.3 The Delta-Sigma Converter;265
10.3.4;8.4 Conclusions;276
10.4;Some Facts in Real Analysis;277
10.4.1;A.1 Absolutely Continuous Functions and Sets;277
10.4.2;A.2 Lipschitz Continuous Functions and Sets;278
10.4.3;A.3 Functions of Bounded Variations in Time;278
10.4.4;A.4 Multifunctions of Bounded Variation in Time;280
10.4.5;A.5 Differential Measures;280
10.4.6;A.6 Measure Differential Inclusion (MDI);281
11;References;283
12;Index;290