Designed for undergraduate students in the general science, engineering, and mathematics community, Introduction to the Simulation of Dynamics Using Simulink(R) 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.
Michael A. Gray is an associate professor in the Department of Computer Science at American University in Washington, D.C.