Continuous System Simulation

Description

Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.

Modern modeling and simulation environments relieve the occasional user from having to understand how simulation really works. Once a mathematical model of a process has been formulated, the modeling and simulation environment compiles and simulates the model, and curves of result trajectories appear magically on the user’s screen. Yet, magic has a tendency to fail, and it is then that the user must understand what went wrong, and why the model could not be simulated as expected.

Continuous System Simulation is written by engineers for engineers, introducing the partly symbolical and partly numerical algorithms that drive the process of simulation in terms that are familiar to simulation practitioners with an engineering background, and yet, the text is rigorous in its approach and comprehensive in its coverage, providing the reader with a thorough and detailed understanding of the mechanisms that govern the simulation of dynamical systems.

Continuous System Simulation is a highly software-oriented text, based on MATLAB. Homework problems, suggestions for term project, and open research questions conclude every chapter to deepen the understanding of the student and increase his or her motivation.

Continuous System Simulation is the first text of its kind that has been written for an engineering audience primarily. Yet due to the depth and breadth of its coverage, the book will also be highly useful for readers with a mathematics background. The book has been designed to accompany senior and graduate students enrolled in a simulation class, but it may also serve as a reference and self-study guide for modeling and simulation practitioners.

 

Table of Contents

Introduction, Scope, Definitions.- Modeling and Simulation: A Circuit Example.- Modeling vs. Simulation.- Time and Again.- Simulation as a Problem Solving Tool.- Simulation Software: Today and Tomorrow.-

Basic Principles of Numerical Integration.- Introduction.- The Approximation Accuracy.- Euler Integration.- The Domain of Numerical Stability.- The Newton Iteration.- Semi–analytic Algorithms.- Spectral Algorithms.-

Single–step Integration Methods.- Introduction.- Runge–Kutta Algorithms.- Stability Domains of RK Algorithms.- Stiff Systems.- Extrapolation Techniques.- Marginally Stable Systems.- Backinterpolation Methods.- Accuracy Considerations.- Step–size and Order Control.-

Multi–step Integration Methods.- Introduction.- Newton–Gregory Polynomials.- Numerical Integration Through Polynomial Extrapolation.- Explicit Adams–Bashforth Formulae.- Implicit Adams–Moulton Formulae.- Adams–Bashforth–Moulton Predictor–Corrector Formulae.- Backward Difference Formulae.- Nyström and Milne Algorithms.- In Search for Stiffly–stable Methods.- High–order Backward Difference Formulae.- Newton Iteration.- Step–size and Order Control.- The Startup Problem.- The Readout Problem.-

Second Derivative Systems.- Introduction.- Conversion of Second–derivative Models to State–space Form.- Velocity–free Models.- Linear Velocity Models.- Nonlinear Velocity Models.- Stability and Damping of Godunov Scheme.- Explicit and Implicit Godunov Algorithms of Different Orders.- The Newmark Algorithm.-

Partial Differential Equations.- Introduction.- The Method of Lines.- Parabolic PDEs.- Hyperbolic PDEs.- Shock Waves.- Upwind Discretization.- Grid–width Control.- PDEs in Multiple Space Dimensions.- Elliptic PDEs and Invariant Embedding.- Finite Element Approximations.-

Differential Algebraic Equations.- Introduction.- Causalization of Equations.- Algebraic Loops.- The Tearing Algorithm.- The Relaxation Algorithm.- Structural Singularities.- Structural Singularity Elimination.- The Solvability Issue.-

Differential Algebraic Equation Solvers.- Introduction.- Multi-step Formulae.- Single–step Formulae.- DASSL.- Inline Integration.- Inlining Implicit Runge–Kutta Algorithms.- Stiffly Stable Step–size Control of Radau IIA.- Stiffly Stable Step–size Control of Lobatto IIIC.- Inlining Partial Differential Equations.- Overdetermined DAEs.- Electronic Circuit Simulators.- Multibody System Dynamics Simulators.- Chemical Process Dynamics Simulators.-

Simulation of Discontinuous Systems.- Introduction.- Basic Difficulties.- Time Events.- Simulation of Sampled–data Systems.- State Events (1. Multiple Zero Crossings, 2. Single Zero Crossings, Single–step Algorithms, 3. Single Zero Crossings, Multi-step Algorithms, 4. Non–essential State Events).- Consistent Initial Conditions.- Object–oriented Descriptions of Discontinuities ( 1. The Computational Causality of if–Statements, 2. Multi–valued Functions).- The Switch Equation.- Ideal Diodes and Parameterized Curve Descriptions.- Variable Structure Models.- Mixed–mode Integration.- State Transition Diagrams.- Petri Nets.-

Real–time Simulation.- Introduction.- The Race Against Time.- Suitable Numerical Integration Methods.- Linearly Implicit Methods.- Multi–rate Integration.- Inline Integration.- Mixed–mode Integration.- Discontinuous Systems.- Simulation Architecture.- Overruns.-

Discrete Event Simulation.- Introduction.- Space Discretization: A Simple Example.- Discrete Event Systems and DEVS.- Coupled DEVS Models.- Simulation of DEVS Models.- DEVS and Continuous Systems Simulation.- Quantized State Systems.-

Quantization-based Integration.- Introduction.- Convergence, Accuracy, and Stability in QSS.- Choosing Quantum and Hysteresis Width.- Input Signals in the QSS Method.- Startup and Output Interpolation.- Second-order QSS.- Algebraic Loops in QSS Methods.- DAE Simulation with QSS Methods.- Discontinuity Handling.- Real-time Simulation.- Open Problems in Quantization–based Methods.
  Print version
Recommend to others

All books by these authors
Cellier, Francois E.
Kofman, Ernesto

Related subjects
Computational Science & Engineering
Computer Science
Engineering
Mathematics
Mathematics of Computing

Textbook Evaluation Copy
Order an approval copy
 

描述

《連續系統模擬》系統地和有方法地描述了如何在數位電腦上模擬動態系統的數學模型。這些模型通常由一組常微分方程或偏微分方程以及代數方程組組成。

現代建模和模擬環境使偶爾使用者不需要理解模擬的運作原理。一旦一個過程的數學模型被制定出來，建模和模擬環境會編譯和模擬模型，結果軌跡的曲線就會神奇地出現在使用者的屏幕上。然而，神奇有時會失靈，這時使用者必須理解出了什麼問題，為什麼模型無法按預期進行模擬。

《連續系統模擬》是由工程師為工程師撰寫的，以熟悉工程背景的模擬實踐者為對象，介紹了部分符號和部分數值算法，這些算法驅動著模擬過程。然而，該書在方法上嚴謹且內容全面，為讀者提供了對控制動態系統模擬機制的深入和詳細的理解。

《連續系統模擬》是一本高度軟件導向的教材，基於MATLAB。每章結束時都有作業問題、期末專題建議和開放性研究問題，以加深學生對模擬的理解並提高他們的動力。

《連續系統模擬》是首本主要針對工程師讀者撰寫的教材。然而，由於其廣泛的內容和深度，該書對具有數學背景的讀者也非常有用。該書旨在配合修讀模擬課程的高年級和研究生學生使用，但也可以作為建模和模擬實踐者的參考和自學指南。

目錄

引言、範圍、定義。- 建模和模擬：電路示例。- 建模與模擬的區別。- 一再時間。- 模擬作為問題解決工具。- 模擬軟件：今天和明天。-

數值積分的基本原理。- 引言。- 近似精度。- 歐拉積分。- 數值穩定性的範圍。- 牛頓迭代。- 半解析算法。- 頻譜算法。-

單步積分方法。- 引言。- 龍格-庫塔算法。- RK算法的穩定域。- 剛性系統。- 外插技術。- 邊緣穩定系統。- 反插值方法。- 精度考慮。- 步長和階數控制。-

多步積分方法。- 引言。- 龍格-庫塔算法。- RK算法的穩定域。- 剛性系統。- 外插技術。- 邊緣穩定系統。- 反插值方法。- 精度考慮。- 步長和階數控制。