1st Edition

Introduction to the Simulation of Dynamics Using Simulink

By Michael A. Gray Copyright 2011
    332 Pages 32 Color & 211 B/W Illustrations
    by Chapman & Hall

    332 Pages 32 Color & 211 B/W Illustrations
    by Chapman & Hall

    Designed for undergraduate students in the general science, engineering, and mathematics community, Introduction to the Simulation of Dynamics Using Simulink® shows how to use the powerful tool of Simulink to investigate and form intuitions about the behavior of dynamical systems. Requiring no prior programming experience, it clearly explains how to transition from physical models described by mathematical equations directly to executable Simulink simulations.

    Teaches students how to model and explore the dynamics of systems
    Step by step, the author presents the basics of building a simulation in Simulink. He begins with finite difference equations and simple discrete models, such as annual population models, to introduce the concept of state. The text then covers ordinary differential equations, numerical integration algorithms, and time-step simulation. The final chapter offers overviews of some advanced topics, including the simulation of chaotic dynamics and partial differential equations.

    A one-semester undergraduate course on simulation
    Written in an informal, accessible style, this guide includes many diagrams and graphics as well as exercises embedded within the text. It also draws on numerous examples from the science, engineering, and technology fields. The book deepens students’ understanding of simulated systems and prepares them for advanced and specialized studies in simulation. Ancillary materials are available at http://nw08.american.edu/~gray

     

    Introduction and Motivation
    Systems
    Dynamical Models of Physical Systems
    Constructing Simulations from Dynamical Models
    How Simulators Are Used

    The Basics of Simulation in Simulink
    Simplest Model to Simulate
    Models in Simulink
    Simulation of the Simplest Model
    Understanding How Time Is Handled in Simulation
    A Model with Time as a Variable
    How Simulink Propagates Values in Block Diagrams
    A Model with Uniform Circular Motion
    A Model with Spiraling Circular Motion
    Uncertainty in Numbers and Significant Figures

    Simulation of First-Order Difference Equation Models
    What Is a Difference Equation?
    Examples of Systems with Difference Equation Models
    First-Order Difference Equation Simulation
    Examining the Internals of a Simulation
    Organizing the Internal Structure of a Simulation
    Using Vector and Matrix Data

    Simulation of First-Order Differential Equation Models
    What Is a Differential Equation?
    Examples of Systems with Differential Equation Models
    Reworking First-Order Differential Equations into Block Form
    First-Order Differential Equation Simulation
    Saving Simulation Data in MATLAB

    Fixed-Step Solvers and Numerical Integration Methods
    What Is a Solver?
    Understanding the Basics of Numerical Integration Algorithms
    Understanding Solver Errors
    Improving the Basic Algorithms
    Fixed-Step Solvers in the Simulink Software

    Simulation of First-Order Equation Systems
    What Is a First-Order Difference Equation System?
    Examples of First-Order Difference Equation Systems
    Simulating a First-Order Difference Equation System
    What Is a First-Order Differential Equation System?
    Examples of First-Order Differential Equation Systems
    Simulating a First-Order Differential Equation System
    Combining Connections on a Bus

    Simulation of Second-Order Equation Models: Nonperiodic Dynamics
    Simulation of Second-Order Difference Equation Models
    Simulation of Second-Order Differential Equation Models
    Second-Order Differential Equation Models with First-Order Terms
    Conditional Dynamics

    Simulation of Second-Order Equation Models: Periodic Dynamics
    Orbital Systems
    Masked Subsystems
    Creating Libraries

    Higher-Order Models and Variable-Step Solvers
    Direct Simulation by Multiple Integrations
    Producing Function Forms for Simulation Results
    Variable-Step Solvers
    Variable-Step Solvers in Simulink

    Advanced Topics: Transforming Ordinary Differential Equations, Simulation of Chaotic Dynamics, and Simulation of Partial Differential Equations
    Transforming Ordinary Differential Equations
    Simulation of Chaotic Dynamics
    Simulation of Partial Differential Equations

    Appendix A: Alphabetical List of Simulink Blocks
    Appendix B: The Basics of MATLAB for Simulink Users
    Appendix C: Debugging a Simulink Model

    Index

    A Summary, References, and Additional Reading appear at the end of each chapter.

    Biography

    Michael A. Gray is an associate professor in the Department of Computer Science at American University in Washington, D.C.