Foreword

Chapter 1. Computer Simulation of Dynamic Systems

INTRODUCTION AND OVERVIEW

DYNAMIC- SYSTEM MODELS

1-1. Continuous-system Simulation and Discrete-event Simulation
1-2. Models, Time Histories, and State Equations
1-3. Differential-equation Models
1-4. State-variable Models with Defined Variables
1-5. Classical Applications and Higher-order Differential Equations

SIMULATION PROGRAMS AND SIMULATION LANGUAGES

1-6. Model Definition and Experiment Protocol
1-7. The Simulation-run Procedure
(a) Initialization, Integration, and Time-history Output
(b) Integration Rules

1-8. Simulation Programs: Subroutine Packages and Equation Languages
1-9. Block-diagram Models and Block-diagram Editors

USER-INTERFACE REQUIREMENTS FOR COMPUTER SIMULATION

1-10. A Wish List for Interactive Modeling
1-11. Interactive Experiments Need Direct Execution as well as High Speed
1-12. Interactive Experiments Must Display Results Immediately
1-13. Simulation with DESIRE
(a) A Complete Simulation Program
(b) A User-friendly Environment for Interactive Experiments


Chapter 2. Examples of Complete Simulation Programs

OVERVIEW

INTERACTIVE MODELING AND SIMULATION

2-1. Getting Started
2-2. Interactive Windows Operations

SIMPLE EXAMPLES FROM PHYSICS

2-3. Linear Oscillators
2-4. Nonlinear Oscillations and Phase-plane Plots
(a) Van der Pol's Differential Equation
(b) Simulation of a Simple Pendulum
(c) Lorenz Differential Equations: an Example of Chaos

2-5. Nuclear-reactor Simulation
2-6. An Electric-circuit Simulation with 1583 Differential Equations

AEROSPACE AND RELATED APPLICATIONS

2-7. Ballistic Trajectories
2-8. Simple Flight Simulation
(a) Pitch-plane Flight Equations
(b) Linearized Flight Equations

2-9. A Simplified Autopilot
2-10. Torpedo Trajectory
2-11. Translunar Satellite Orbit

MODELS FROM PHYSIOLOGY AND POPULATION DYNAMICS

2-12. Simulation of a Glucose-tolerance Test
2-13. Simulation of Epidemic Propagation
2-14. Simulation in Ecology. A Predator-prey System

Chapter 3. Simulation Runs and DYNAMIC Program Segments

OVERVIEW

INTERPRETED EXPERIMENT PROTOCOL, COMPILED SIMULATION UNS

3-1. The Experiment-protocol Program
3-2. Simulation Runs, Simulation Time, and Communication Points
(a) Simulation-run Procedure and DYNAMIC Program Segments
(b) Run Termination and Continued Runs
(c) Simulation Time Histories and Communication Points

3-3. DYNAMIC Segments with Differential Equations. Default Parameter Values
(a) Integration Routines
(b) Simulation-time Range and Default Parameter Values
(c) Resetting Initial Conditions: reset and drunr

3-4. DYNAMIC Segments Without Differential Equations

PROGRAMMING SIMPLE DYNAMIC SEGMENTS

3-5. The DYNAMIC Statement. DYNAMIC-segment Code
3-6. Scalar Defined Variables
(a) Defined-variable Assignments
(b) Defined Variables: Order of Computation

3-7. Scalar Differential Equations
3-8. User-defined Functions
3-9. Runtime Time-history Output:
(a) Time-history Listings and Graphs: type, dispt, dispxy, and DISPXY
(b) Display Coordinate Net , Labels, and Colors
(c) Display Scaling
(d) Stripchart-type Displays
(e) Time-history Listings on Files and Printers
(f) Printing and Saving Time-history Graphics

3-10. Sampling Operations
(a) The OUT Statement
(b) SAMPLE and step Statements

SCALAR DIFFERENCE EQUATIONS

3-11. Recursive Assignments and Difference Equations
3-12. Multiple Difference Equations: State Equations and Predicted Values
3-13. Pure Difference-equation Problems
(a) General Case
(b) Pure Difference Equations with Integer Time Steps
(c) Examples: Some Difference Equations Generate Chaos

3-14. Models with Both Differential Equations and Difference Equations

CONDITIONAL RUN TERMINATION AND if STATEMENTS

3-15. The Run-termination Operator
3-16. if Statements in DYNAMIC Program Segments

Chapter 4. Models with Vector and Matrix Operations

OVERVIEW

VECTOR ASSIGNMENTS IN DYNAMIC PROGRAM SEGMENTS

4-1. Arrays and Subscripted Variables
4-2. Simple VECTOR Expressions
(a) Vector Sums
(b) Sums of Product Terms

4-3. Linear Transformations
(a) Matrix/vector Products
(b) Syntax Rules
(c) Example: Rotation Matrices

4-4. Vector Functions
(a) Library Functions
(b) Output-limited Vectors
(c) Finding Maximum and Minimum Elements

4-5. VECTOR Index-shift Operations and Convolutions
(a) Index-shifted Vectors
(b) Convolutions

DOT PRODUCTS, SUMS, AND VECTOR NORMS IN DYNAMIC SEGMENTS

4-6. DOT Products and Euclidean Norms of Vectors
(a) Simple DOT Products
(b) Absolute Value (Euclidean Norm) of a Vector
4-7. Simple Sums and Taxicab Norms
4-8. More General DOT Products

VECTOR DIFFERENTIAL EQUATIONS AND DIFFERENCE EQUATIONS

4-9. STATE Arrays and Vector Differential Equations
4-10. State-variable Declarations
4-11. Vector Difference Equations

TIME-HISTORY FUNCTION STORAGE AND TIME-DELAY SIMULATION

4-12. Introduction

4-13. Function Storage and Recovery with store and get Operations
(a) store and get Operations
(b) Applications

4-14. Time-delay Simulation
4-15. Time-history Storage and Recovery Using Binary Files

Chapter 5. Function Generation and Submodels

OVERVIEW

GENERAL-PURPOSE FUNCTION GENERATION

5-1. Library Functions
5-2. Table Lookup and Interpolation
5-3. User-written Functions

TRICKS AND TREATS: SPECIAL PIECEWISE-LINEAR FUNCTIONS

5-4. Limiters and Combinations of Limiters
(a) Using Simple Limiters
(b) Relations between Functions. Maximum and Minimum Functions
(c) Example: Automatic Display Scaling and Envelope Generation
(d) Output-limited Integrators

5-5. Switches and Comparators
5-6. Hysteresis, Backlash, and Special Signal Generators
(a) A Comparator with Hysteresis
(b) Signal Generators
(c) Modulation Waveforms
(d) Hysteresis and Backlash

5-7. Simulation of Signal Quantization

SUBMODEL DECLARATION AND INVOCATION

5-8. Submodel Definition, Invocation, and Nesting
5-9. Submodels with Differential Equations
5-10. Example: Simulation of a Satellite Roll-control System

Chapter 6. More Advanced Simulation Programs

OVERVIEW

PROGRAMMING THE EXPERIMENT PROTOCOL

6-1. Declarations and Array Initialization
6-2. Setting Simulation-run Parameters
6-3. Display Scaling and Display Control
6-4. Setting Initial Conditions

TWO MULTIRUN SIMULATION STUDIES

6-5. One Way to Create Logarithmic Plots
6-6. Solution Envelopes for Multiple Random-process Runs

MULTIPLE RUNS CAN SPLICE COMPLICATED TIME HISTORIES

6-7. Simulation of Hard Impact: The Bouncing Ball
6-8. The EUROSIM Peg-and-pendulum Problem
6-9. The EUROSIM Switched-amplifier Problem

PROGRAMS WITH MULTIPLE DYNAMIC SEGMENTS

6-10. Multiple DYNAMIC Program Segments
6-11. Crossplotting Results from Multiple Runs: the Pilot-ejection Problem

MORE EXAMPLES

6-12. Simulation of Human Blood Circulation
6-13. System Dynamics and World Simulation

INTERACTIVE CONTROL-SYSTEM SIMULATION

6-14. Introduction
6-15. Simulation of a Servomechanism. Test Inputs and Error Measures
6-16. Parameter-sensitivity Studies and Parameter Optimization
(a) Parameter Sensitivity
(b) Iterative Optimization

6-17. Model Changes and Nonlinear Transfer Characteristics
6-18. Using Vector Differential Equations and Difference Equations
6-19. A Sampled-data Control System: Analog Plant with Digital Controller
6-20. Frequency-response studies
(a) State-equation Models for Linear Time-invariant Systems
(b) Impulse Response and Frequency Response of a Linear System

6-21. Control Systems with Neural Networks and Fuzzy Logic

TRICKS AND TREATS: INTERACTIVE MODELING IN MULTIPLE WINDOWS

6-22. Run and Compare Programs from Multiple Editor Windows
6-23. Program-line Numbers and Special Dialog-editor Windows
(a) Editing Selected Program Lines
(b) Programs with Line Numbers
(c) Editor Windows for Selected Program Lines
(d) Adding Comments and User Instructions

6-24. Testing Program Changes with Keyboard Commands
6-25. Use the ADD Button to Combine Program Segments, Submodels,
and Library Functions

6-26. You Need Electronic Notes to Track Simulation Studies

Chapter 7. General-purpose Scientific Computation

OVERVIEW

COMPILED PROGRAMS NEED NOT BE SIMULATION MODELS

7-1. Dummy Integration Repeats the DYNAMIC-segment Code
7-2. Application: Fast Graph Plotting
(a) A Simple Function Plot
(b) Plotting Array Values

7-3. Fast Array Manipulation
7-4. Using Simple Difference Equations
7-5. Statistical Computations

COMPLEX-NUMBER OPERATIONS AND INTERPRETER GRAPHICS

7-6. INTEGER and COMPLEX Quantities in the Interpreter Program
7-7. Interpreter Graphics, Complex-number Plots, and Conformal Mapping

FAST FOURIER TRANSFORMS AND CONVOLUTIONS

7-8. Fast Fourier Transforms
(a) Complex FFTs
(b) Simultaneous Transformation of Two Real Arrays
(c) Cyclical Convolutions

INTERPRETED MATRIX OPERATIONS

7-10. Interpreted versus Compiled VECTOR and DOT Assignments
7-11. Interpreter Matrix Multiplication
7-12. Null and Identity Matrices
7-13. Matrix Inversion and Solution of Linear Equations
7-14. Matrix Transposition

Appendix A. Simulation Accuracy and Integration Techniques

SIMULATION ACCURACY AND TEST PROGRAMS

A-1. Introduction
A-2. Roundoff Errors
A-3. Choice of Integration Rule and DT
A-4. Programs for Testing Integration Routines
(a) Sensitivity Tests
(b) Testing a Protracted Simulation Run


DESIRE INTEGRATION RULES

A-5. Runge-Kutta and Euler Rules
A-6. Variable-order/variable-order Rules and Stiff Differential-equation Systems
(a) Implicit Adams and Gear Rules
(b) Stiff Differential-equation Systems
(c) Examples Using Gear-type Integration

A-7. Integration of Discontinuous Functions

MISCELLANEOUS TOPICS

A-8. Perturbation Methods can Improve Accuracy
A-9. Avoiding Division

Appendix B. Supplementary Reference Material

COMMAND-WINDOW OPERATIONS

B-1. Command Lines and Function Keys in the Command Window
B-2. Function-key Commands on Personal Computers
B-3. Using Operating-system Commands
B-4. Command-window Editing and User-written Menus on Personal Computers

EXPERIMENT-PROTOCOL PROGRAMMING: ASSIGNMENTS

B-5. Expressions and Functions
B-6. data Lists and read Assignments

EXPERIMENT-PROTOCOL PROGRAM CONTROL

B-7. Labels, Branching, and Hot Keys
B-8. Conditional Branching: if ... then ... proceed
B-9. for, while, and repeat Loops
B-10. Interpreter Procedures
B-11. new, clear, and STOP

EXPERIMENT-PROTOCOL INPUT/OUTPUT

B-12. Console, Text-file, and Device Output
B-13. Writing to Files or Devices
B-14. Console, File, and Device Input
B-15. Octal and Hexadecimal Numbers

DEBUGGING, AUTOMATIC NOTEBOOK FILE, AND HELP FACILITY

B-16. Interactive Error Correction
B-17. Debugging Experiment Protocols with Programmed STOP Statements
B-18. trace and dump Facilities
B-19. The Automatic Notebook File
B-20. The time Statement

Appendix C. Using the Program Diskettes

RUNNING DESIRE UNDER MICROSOFT WINDOWS 95 OR NT

C-1. Introduction
C-2. Program Installation
C-3. Starting DESIRE. Editor Windows and Command Window
C-4. How to Load, Edit, Save, Print, and Run Simulation Programs
(a) File and Edit Menus and Buttons
(b) Transfer Menu and Buttons
(c) Compiling and Running the Edited Program
(d) Restoring the Windows Display

C-5. Saving Graphs and Window Screens
C-6. How to Quit
(a) Ending a Session
(b) Uninstallation

C-7. Help Facilities
(a) Help for Editor Windows
(b) Command-window Help and User-written Help Screens

RUNNING DESIRE UNDER MS-DOS

C-8. Switching to MS-DOS Operation
C-9. Keyboard Commands
(a) Editing under MS-DOS
(b) File Manipulation
(c) Program Listing and Printing

RUNNING DESIRE UNDER WINDOWS NT

C-10. Command-window Operations

Appendix D. Large Differential-equation Systems in Matrix Notation

Selected References