## System Dynamics (4th Edition)

### Katsuhiko Ogata

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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 TOPICS Specific 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.

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From the Publisher:

This comprehensive examination of the analysis and design of linear systems provides extensive coverage of both mechanical and electrical systems, and includes analyses of pneumatic systems, hydraulic systems, thermal systems, and water-tank systems.

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 better understanding of the subject matter discussed. In addition, a number of solved problems (A problems) are provided at the end of each chapter, except Chapter 1. These problems constitute an integral part of the text. It is suggested that the reader study all these problems carefully to obtain a deeper understanding of the topics discussed. Many unsolved problems (B problems) are also provided for use as homework or quiz problems. An instructor using this text for his/her system dynamics course may obtain a complete solutions manual for B problems from the publisher.

Most of the materials presented in this book have been class tested in courses in the field of system dynamics and control systems in the Department of Mechanical Engineering, University of Minnesota over many years.

If this book is used as a text for a quarter-length course (with approximately 30 lecture hours and 18 recitation hours), Chapters 1 through 7 may be covered. After studying these chapters, the student should be able to derive mathematical models for many dynamic systems with reasonable simplicity in the forms of transfer function or state-space equation. Also, he/she will be able to obtain computer solutions of system responses with MATLAB. If the book is used as a text for a semester-length course (with approximately 40 lecture hours and 26 recitation hours), then the first nine chapters may be covered or, alternatively, the first seven chapters plus Chapters 10 and 11 may be covered. If the course devotes 50 to 60 hours to lectures, then the entire book may be covered in a semester.

Finally, I wish to acknowledge deep appreciation to the following professors who reviewed the third edition of this book prior to the preparation of this new edition: R. Gordon Kirk (Virginia Institute of Technology), Perry Y Li (University of Minnesota), Sherif Noah (Texas A & M University), Mark L. Psiaki (Cornell University), and William Singhose (Georgia Institute of Technology). Their candid, insightful, and constructive comments are reflected in this new edition.

KATSUHIKO OGATA

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