the Simulation of Dynamics Using Simulink

Transcription

1 INTRODUCTION TO the Simulation of Dynamics Using Simulink Michael A. Gray CRC Press Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group an informa business A CHAPMAN & HALL BOOK

2 Table of Contents Preface, xv CHAPTER 1 Introduction and Motivation SYSTEMS Examples of Systems Classifying Systems DYNAMICAL MODELS OF PHYSICAL SYSTEMS Discrete-Time Models Continuous Models CONSTRUCTING SIMULATIONS FROM DYNAMICAL MODELS Block-Diagram Models Block-Diagram Simulations HOW SIMULATORS ARE USED SUMMARY 8 REFERENCES AND ADDITIONAL READING 8 CHAPTER 2 The Basics of Simulation in Simulink SIMPLEST MODEL TO SIMULATE The Feedforward Block Diagram MODELS IN SIMULINK Documenting a Model SIMULATION OF THE SIMPLEST MODEL Output Blocks from the Sinks Library 16 vii

3 viii Table of Contents The Scope Block Input Blocks from the Sources Library The Constant Block Block Connections A Running the Simulation The Configuration Parameters Observing the Simulation Output Default Ranges and Autoscale Making the Scope Output Printable UNDERSTANDING HOW TIME IS HANDLED IN SIMULATION A MODEL WITH TIME AS A VARIABLE The Clock Block from the Sources Library Processing Blocks from the Math Operations Library The Product Block The Add Block HOW SIMULINK PROPAGATES VALUES IN BLOCK DIAGRAMS A MODEL WITH UNIFORM CIRCULAR MOTION The Sine Wave Block from the Sources Library The Gain Block from the Math Operations Library The XY Graph Block from the Sinks Library A MODEL WITH SPIRALING CIRCULAR MOTION The Math Function Block from the Math Operations Library UNCERTAINTY IN NUMBERS AND SIGNIFICANT FIGURES SUMMARY 52 REFERENCES AND ADDITIONAL READING 52

4 Table of Contents ix CHAPTER 3 Simulation of First-Order Difference Equation Models WHAT IS A DIFFERENCE EQUATION? Difference Equation Terminology EXAMPLES OF SYSTEMS WITH DIFFERENCE EQUATION MODELS FIRST-ORDER DIFFERENCE EQUATION SIMULATION The Input and Output Ports of a Block The Memory Block from the Discrete Library The Feedback Block Diagram The 1С Block from the Signal Attributes Library Setting Initial Conditions with the Initial Conditions Field of the Memory Block EXAMINING THE INTERNALS OF A SIMULATION The Floating Scope Block from the Sinks Library ORGANIZING THE INTERNAL STRUCTURE OF A SIMULATION The Subsystem Block from the Ports and Subsystems Library USING VECTOR AND MATRIX DATA Vector and Matrix Constants The Display Block from the Sinks Library Colors for Displaying Scope Vector Input SUMMARY 85 REFERENCES AND ADDITIONAL READING 86 CHAPTER 4 Simulation of First-Order Differential Equation Models WHAT IS A DIFFERENTIAL EQUATION? Differential Equation Terminology 88

5 x Table of Contents 4.2 EXAMPLES OF SYSTEMS WITH DIFFERENTIAL EQUATION MODELS REWORKING FIRST-ORDER DIFFERENTIAL EQUATIONS INTO BLOCK FORM FIRST-ORDER DIFFERENTIAL EQUATION SIMULATION The Integrator Block from the Continuous Library Specifying Initial Values for First-Order Differential Equation Simulations SAVING SIMULATION DATA IN MATLAB The To Workspace Block from the Sinks Library Saving Simulation Data in a File SUMMARY 103 REFERENCES AND ADDITIONAL READING 105 CHAPTER 5 Fixed-Step Solvers and Numerical Integration Methods WHAT IS A SOLVER? UNDERSTANDING THE BASICS OF NUMERICAL INTEGRATION ALGORITHMS The Euler Method Taylor's Theorem A Graphical View of the Euler Method UNDERSTANDING SOLVER ERRORS IMPROVING THE BASIC ALGORITHMS Runge-Kutta Methods Corrector Methods Multistep Methods FIXED-STEP SOLVERS IN THE SIMULINK SOFTWARE SUMMARY 131 REFERENCES AND ADDITIONAL READING 132

6 Table of Contents xi CHAPTER 6 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 The Two-Input Scope Block Algebraic Loops 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 The Bus Creator Block from the Signals Routing Library SUMMARY 152 REFERNCES AND ADDITIONAL READING 153 CHAPTER 7 Simulation of Second-Order Equation Models: Nonperiodic Dynamics SIMULATION OF SECOND-ORDER DIFFERENCE EQUATION MODELS Sequential Structure Layered Structure SIMULATION OF SECOND-ORDER DIFFERENTIAL EQUATION MODELS Sequential Structure Layered Structure SECOND-ORDER DIFFERENTIAL EQUATION MODELS WITH FIRST-ORDER TERMS 168

7 xii Table of Contents Viscosity Modeled by a Linear Function of Velocity Viscosity Modeled by a Quadratic Function of Velocity CONDITIONAL DYNAMICS Object Moving at the Earth's Surface The Switch Block from the Signal Routing Library The Zero-Order Hold Block from the Discrete Library The If Action Subsystem from the Ports & Subsystems Library The If Block from the Ports & Signals Library The Merge Block from the Signal Routing Library SUMMARY 187 REFERENCES AND ADDITIONAL READING 187 CHAPTER 8 Simulation of Second-Order Equation Models: Periodic Dynamics ORBITAL SYSTEMS The Gravitational Attraction between Two Objects The Earth-Sun System Circular Orbits The Earth-Satellite System MASKED SUBSYSTEMS A Simple Example Parameterizing the Subsystem Components Creating the Subsystem Mask CREATING LIBRARIES SUMMARY 212 REFERENCES 214

8 Table of Contents xiii CHAPTER 9 Higher-Order Models and Variable-Step Solvers DIRECT SIMULATION BY MULTIPLE INTEGRATIONS An Automobile Suspension Model The Terminator Block from the Sinks Library Transformation into a First-Order Equation System PRODUCING FUNCTION FORMS FOR SIMULATION RESULTS VARIABLE-STEP SOLVERS Example Variable-Step-Size Algorithm Example Variable-Step, Fourth-Order Runge- Kutta Solver VARIABLE-STEP SOLVERS IN SIMUUNK SUMMARY 228 REFERENCES AND ADDITIONAL READING 229 CHAPTER 10 Advanced Topics: Transforming Ordinary Differential Equations, Simulation of Chaotic Dynamics, and Simulation of Partial Differential Equations TRANSFORMING ORDINARY DIFFERENTIAL EQUATIONS The Laplace Transform A Laplace Transform Example Simulation by Nested Transforms Simulation by Partitioned Transforms The Transfer Fen Block from the Continuous Library Examples of Transfer Function Simulation Impulse-Driven Spring Analog Signal Filter Disk Drive Motion under Control 251

9 xiv Table of Contents 10.2 SIMULATION OF CHAOTIC DYNAMICS Example of a Chaotic System the Lorenz Model The Logistic Map SIMULATION OF PARTIAL DIFFERENTIAL EQUATIONS What Is a Partial Differential Equation? Examples of Systems with Partial Differential Equation Models Simulating Partial Differential Equation Models The Embedded MATLAB Function Block from the User-Defined Functions Library SUMMARY 276 REFERENCES AND ADDITIONAL READING 278 APPENDIX A: ALPHABETICAL LIST OF SIMULINK BLOCKS, 281 APPENDIX B: THE BASICS OF MATLAB FOR SIMULINK USERS, 283 B.1 THE MATLAB MAIN WINDOW B.2 THE DEFAULT FOLDER IN MATLAB B.3 LAUNCHING SIMULINK FROM MATLAB B.4 SIMULINK MODEL FILES IN MATLAB REFERENCES AND ADDITIONAL READING APPENDIX C: DEBUGGING A SIMULINK MODEL, 289 C.1 STARTING THE DEBUGGER C.2 RUNNING THE MODEL IN STEP MODE C.3 RUNNING THE MODEL IN TRACE MODE ADDITIONAL READING INDEX, 301