System Dynamics

by Ogata, Katsuhiko

• ISBN13: 9780131424623
• ISBN10: 0131424629
• Edition: 4th
• Format: Hardcover
• Copyright: 2003-08-13
• Publisher: Pearson

Summary

This text presents the basic theory and practice of system dynamics. It introduces the modeling of dynamic systems and response analysis of these systems, with an introduction to the analysis and design of control systems.KEY TOPICSSpecific chapter topics include The Laplace Transform, mechanical systems, transfer-function approach to modeling dynamic systems, state-space approach to modeling dynamic systems, electrical systems and electro-mechanical systems, fluid systems and thermal systems, time domain analyses of dynamic systems, frequency domain analyses of dynamic systems, time domain analyses of control systems, and frequency domain analyses and design of control systems.For mechanical and aerospace engineers.

Table of Contents

PREFACE	vii
1 INTRODUCTION TO SYSTEM DYNAMICS 1
1-1 Introduction	1	(2)
1-2 Mathematical Modeling of Dynamic Systems	3	(2)
1-3 Analysis and Design of Dynamic Systems	5	(1)
1-4 Summary	6	(2)
2 THE LAPLAGE TRANSFORM	8	(45)
2-1 Introduction	8	(1)
2-2 Complex Numbers, Complex Variables, and Complex Functions	8	(6)
2-3 Laplace Transformation	14	(15)
2-4 Inverse Laplace Transformation	29	(5)
2-5 Solving Linear, Time-Invariant Differential Equations	34	(2)
Example Problems and Solutions	36	(13)
Problems	49	(4)
3 MECHANICAL SYSTEMS	53	(53)
3-1 Introduction	53	(4)
3-2 Mechanical Elements	57	(4)
3-3 Mathematical Modeling of Simple Mechanical Systems	61	(12)
3-4 Work, Energy, and Power	73	(8)
Example Problems and Solutions	81	(19)
Problems	100	(6)
4 TRANSFER-FUNCTION APPROACH TO MODELING DYNAMIC SYSTEMS	106	(63)
4-1 Introduction	106	(3)
4-2 Block Diagrams	109	(3)
4-3 Partial-Fraction Expansion with MATLAB	112	(7)
4-4 Transient-Response Analysis with MATLAB	119	(16)
Example Problems and Solutions	135	(27)
Problems	162	(7)
5 STATE SPACE APPROACH TO MODELING DYNAMIC SYSTEMS	169	(82)
5-1 Introduction	169	(5)
5-2 Transient-Response Analysis of Systems in State-Space Form with MATLAB	174	(7)
5-3 State-Space Modeling of Systems with No Input Derivatives	181	(6)
5-4 State-Space Modeling of Systems with Input Derivatives	187	(15)
5-5 Transformation of Mathematical Models with MATLAB	202	(7)
Example Problems and Solutions	209	(30)
Problems	239	(12)
6 ELECTRICAL SYSTEMS AND ELECTROMECHANICAL SYSTEMS	251	(72)
6-1 Introduction	251	(3)
6-2 Fundamentals of Electrical Circuits	254	(7)
6-3 Mathematical Modeling of Electrical Systems	261	(9)
6-4 Analogous Systems	270	(4)
6-5 Mathematical Modeling of Electromechanical Systems	274	(7)
6-6 Mathematical Modeling of Operational-Amplifier Systems	281	(7)
Example Problems and Solutions	288	(24)
Problems	312	(11)
7 FLUID SYSTEMS AND THERMAL SYSTEMS	323	(60)
7-1 Introduction	323	(1)
7-2 Mathematical Modeling of Liquid-Level Systems	324	(8)
7-3 Mathematical Modeling of Pneumatic Systems	332	(5)
7-4 Linearization of Nonlinear Systems	337	(3)
7-5 Mathematical Modeling of Hydraulic Systems	340	(8)
7-6 Mathematical Modeling of Thermal Systems	348	(4)
Example Problems and Solutions	352	(23)
Problems	375	(8)
8 TIME-DOMAIN ANALYSIS OF DYNAMIC SYSTEMS	383	(48)
8-1 Introduction	383	(1)
8-2 Transient-Response Analysis of First-Order Systems	384	(4)
8-3 Transient-Response Analysis of Second-Order Systems	388	(11)
8-4 Transient-Response Analysis of Higher Order Systems	399	(1)
8-5 Solution of the State Equation	400	(9)
Example Problems and Solutions	409	(15)
Problems	424	(7)
9 FREQUENCY-DOMAIN ANALYSIS OF DYNAMIC SYSTEMS	431	(60)
9-1 Introduction	431	(1)
9-2 Sinusoidal Transfer Function	432	(6)
9-3 Vibrations in Rotating Mechanical Systems	438	(3)
9-4 Vibration Isolation	441	(6)
9-5 Dynamic Vibration Absorbers	447	(6)
9-6 Free Vibrations in Multi-Degrees-of-Freedom Systems	453	(5)
Example Problems and Solutions	458	(26)
Problems	484	(7)
10 TIME-DOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS	491	(117)
10-1 Introduction	491	(3)
10-2 Block Diagrams and Their Simplification	494	(7)
10-3 Automatic Controllers	501	(5)
10-4 Transient-Response Analysis	506	(7)
10-5 Transient-Response Specifications	513	(9)
10-6 Improving Transient-Response and Steady-State Characteristics	522	(16)
10-7 Stability Analysis	538	(7)
10-8 Root-Locus Analysis	545	(17)
10-9 Root-Locus Plots with MATLAB	562	(4)
10-10 Tuning Rules for PID Controllers	566	(10)
Example Problems and Solutions	576	(24)
Problems	600	(8)
11 FREQUENCY-DOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS	608	(87)
11-1 Introduction	608	(1)
11-2 Bode Diagram Representation of the Frequency Response	609	(20)
11-3 Plotting Bode Diagrams with MATLAB	629	(1)
11-4 Nyquist Plots and the Nyquist Stability Criterion	630	(10)
11-5 Drawing Nyquist Plots with MATLAB	640	(3)
11-6 Design of Control Systems in the Frequency Domain	643	(25)
Example Problems and Solutions	668	(22)
Problems	690	(5)
APPENDIX A SYSTEMS OF UNITS	695	(5)
APPENDIX B CONVERSION TABLES	700	(5)
APPENDIX C VECTOR-MATRIX ALGEBRA	705	(15)
APPENDIX D INTRODUCTION TO MATLAB	720	(37)
REFERENCES	757	(2)
INDEX	759

Excerpts

A course in system dynamics that deals with mathematical modeling and response analyses of dynamic systems is required in most mechanical and other engineering curricula. This book is written as a textbook for such a course. It is written at the junior level and presents a comprehensive treatment of modeling and analyses of dynamic systems and an introduction to control systems.Prerequisites for studying this book are first courses in linear algebra, introductory differential equations, introductory vector-matrix analysis, mechanics, circuit analysis, and thermodynamics. Thermodynamics may be studied simultaneously.Main revisions made in this edition are to shift the state space approach to modeling dynamic systems to Chapter 5, right next to the transfer function approach to modeling dynamic systems, and to add numerous examples for modeling and response analyses of dynamic systems. All plottings of response curves are done with MATLAB. Detailed MATLAB programs are provided for MATLAB works presented in this book.This text is organized into 11 chapters and four appendixes. Chapter 1 presents an introduction to system dynamics. Chapter 2 deals with Laplace transforms of commonly encountered time functions and some theorems on Laplace transform that are useful in analyzing dynamic systems. Chapter 3 discusses details of mechanical elements and simple mechanical systems. This chapter includes introductory discussions of work, energy, and power.Chapter 4 discusses the transfer function approach to modeling dynamic systems. Transient responses of various mechanical systems are studied and MATLAB is used to obtain response curves. Chapter 5 presents state space modeling of dynamic systems. Numerous examples are considered. Responses of systems in the state space form are discussed in detail and response curves are obtained with MATLAB.Chapter 6 treats electrical systems and electromechanical systems. Here we included mechanical-electrical analogies and operational amplifier systems. Chapter 7 deals with mathematical modeling of fluid systems (such as liquid-level systems, pneumatic systems, and hydraulic systems) and thermal systems. A linearization technique for nonlinear systems is presented in this chapter.Chapter 8 deals with the time-domain analysis of dynamic systems. Transient-response analysis of first-order systems, second-order systems, and higher order systems is discussed in detail. This chapter includes analytical solutions of state-space equations. Chapter 9 treats the frequency-domain analysis of dynamic systems. We first present the sinusoidal transfer function, followed by vibration analysis of mechanical systems and discussions on dynamic vibration absorbers. Then we discuss modes of vibration in two or more degrees-of-freedom systems.Chapter 10 presents the analysis and design of control systems in the time domain. After giving introductory materials on control systems, this chapter discusses transient-response analysis of control systems, followed by stability analysis, rootlocus analysis, and design of control systems. Finally, we conclude this chapter by giving tuning rules for PID controllers. Chapter 11 treats the analysis and design of control systems in the frequency domain. Bode diagrams, Nyquist plots, and the Nyquist stability criterion are discussed in detail. Several design problems using Bode diagrams are treated in detail. MATLAB is used to obtain Bode diagrams and Nyquist plots.Appendix A summarizes systems of units used in engineering analyses. Appendix B provides useful conversion tables. Appendix C reviews briefly a basic vector-matrix algebra. Appendix D gives introductory materials on MATLAB. If the reader has no prior experience with MATLAB, it is recommended that he/she study Appendix D before attempting to write MATLAB programs.Throughout the book, examples are presented at strategic points so that the reader will have a bett