Introduction to the Simulation of Dynamics Using Simulink

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 systemsStep 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 simulationWritten 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 MotivationSystems Dynamical Models of Physical Systems Constructing Simulations from Dynamical Models How Simulators Are Used The Basics of Simulation in SimulinkSimplest Model to Simulate Models in Simulink Simulation of the Simplest ModelUnderstanding How Time Is Handled in Simulation A Model with Time as a VariableHow Simulink Propagates Values in Block Diagrams A Model with Uniform Circular MotionA Model with Spiraling Circular Motion Uncertainty in Numbers and Significant Figures Simulation of First-Order Difference Equation ModelsWhat Is a Difference Equation? Examples of Systems with Difference Equation Models First-Order Difference Equation SimulationExamining the Internals of a Simulation Organizing the Internal Structure of a Simulation Using Vector and Matrix Data Simulation of First-Order Differential Equation ModelsWhat Is a Differential Equation?Examples of Systems with Differential Equation Models Reworking First-Order Differential Equations into Block Form First-Order Differential Equation SimulationSaving Simulation Data in MATLAB Fixed-Step Solvers and Numerical Integration MethodsWhat 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 SystemsWhat 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 DynamicsSimulation of Second-Order Difference Equation Models Simulation of Second-Order Differential Equation Models Second-Order Differential Equation Models with First-Order TermsConditional Dynamics Simulation of Second-Order Equation Models: Periodic DynamicsOrbital SystemsMasked SubsystemsCreating Libraries Higher-Order Models and Variable-Step Solvers Direct Simulation by Multiple IntegrationsProducing Function Forms for Simulation Results Variable-Step SolversVariable-Step Solvers in Simulink Advanced Topics: Transforming Ordinary Differential Equations, Simulation of Chaotic Dynamics, and Simulation of Partial Differential Equations Transforming Ordinary Differential EquationsSimulation of Chaotic Dynamics Simulation of Partial Differential Equations Appendix A: Alphabetical List of Simulink BlocksAppendix B: The Basics of MATLAB for Simulink UsersAppendix C: Debugging a Simulink Model Index A Summary, References, and Additional Reading appear at the end of each chapter.

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