# SYSTEM DYNAMICS OGATA 4TH PDF

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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. 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.

Chapter 5 presents state space modeling of dynamic systems. Numerous examples are considered. Chapter 6 treats electrical systems and electromechanical systems. Here we included mechanical-electrical analogies and operational amplifier systems. Chapter 7 vii viii Preface 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. Transientresponse analysis of first-order systems, second-order systems, and higher order systems is discussed in detail.

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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, root-locus analysis, and design of control systems.

Fmally, 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.

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. 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.

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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 hislher 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. If the book is used as a text for a semesterlength 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. Preface ix Fmally, 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. Their candid, insightful, and constructive comments are reflected in this new edition. Response analyses are frequently made through computer simulations of dynamic systems. Because many physical systems involve various types of components, a wide variety of different types of dynamic systems will be examined in this book.

The analysis and design methods presented can be applied to mechanical, electrical, pneumatic, and hydraulic systems, as well as nonengineering systems, such as economic systems and biological systems.

It is important that the mechanical engineering student be able to determine dynamic responses of such systems. We shall begin this chapter by defining several terms that must be understood in discussing system dynamics. A system is a combination of components acting together to perform a specific objective. A component is a single functioning unit of a system. By no means limited to the realm of the physical phenomena, the concept of a system can be extended to abstract dynamic phenomena, such as those encountered in economics, transportation, population growth, and biology.

The output of a static system remains constant if the input does not change. The output changes only when the input changes. In a dynamic system, the output changes with time if the system is not in a state of equilibrium. In this book, we are concerned mostly with dynamic systems. Mathematical models. Any attempt to design a system must begin with a prediction of its performance before the system itself can be designed in detail or actually built.

Such prediction is based on a mathematical description of the system's dynamic characteristics. This mathematical description is called a mathematical model. For many physical systems, useful mathematical models are described in terms of differential equations.

Linear and nonlinear differential equations.

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Linear differential equations may be classified as linear, time-invariant differential equations and linear, timevarying differential equations. A linear, time-invariant differential equation is an equation in which a dependent variable and its derivatives appear as linear combinations. In the case of a linear, time-varying differential equation, the dependent variable and its derivatives appear as linear combinations, but a coefficient or coefficients of terms may involve the independent variable.

A differential equation is called nonlinear if it is not linear. Two examples of nonlinear differential equations are and Mathematical Modeling of Dynamic Systems 3 Linear systems and nonlinear systems. For linear systems, the equations that constitute the model are linear. In this book, we shall deal mostly with linear systems that can be represented by linear, time-invariant ordinary differential equations. The most important property of linear systems is that the principle of superposition is applicable.

This principle states that the response produced by simultaneous applications of two different forcing functions or inputs is the sum of two individual responses.

Consequently, for linear systems, the response to several inputs can be calculated by dealing with one input at a time and then adding the results. As a result of superposition, complicated solutions to linear differential equations can be derived as a sum of simple solutions.

In an experimental investigation of a dynamic system, if cause and effect are proportional, thereby implying that the principle of superposition holds, the system can be considered linear.

Although physical relationships are often represented by linear equations, in many instances the actual relationships may not be quite linear. In fact, a careful study of physical systems reveals that so-called linear systems are actually linear only within limited operating ranges. For instance, many hydraulic systems and pneumatic systems involve nonlinear relationships among their variables, but they are frequently represented by linear equations within limited operating ranges.

For nonlinear systems, the most important characteristic is that the principle of superposition is not applicable. In general, procedures for finding the solutions of problems involving such systems are extremely complicated. Because of the mathematical difficulty involved, it is frequently necessary to linearize a nonlinear system near the operating condition.

Once a nonlinear system is approximated by a linear mathematical model, a number of linear techniques may be used for analysis and design purposes.

Continuous-time systems and discrete-time systems. Continuous-time systems are systems in which the signals involved are continuous in time. These systems may be described by differential equations. Discrete-time systems are systems in which one or more variables can change only at discrete instants of time.

These instants may specify the times at which some physical measurement is performed or the times at which the memory of a digital computer is read out.

Discrete-time systems that involve digital signals and, possibly, continuous-time signals as well may be described by difference equations after the appropriate discretization of the continuous-time signals. The materials presented in this text apply to continuous-time systems; discretetime systems are not discussed. Mathematical modeling involves descriptions of important system characteristics by sets of equations.

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By applying physical laws to a specific system, it may be possible to develop a mathematical model that describes the dynamics of the system. Such a model may include unknown parameters, which 4 Introduction to System Dynamics Chap. Sometimes, however, the physical laws governing the behavior of a system are not completely defined, and formulating a mathematical model may be impossible.

If so, an experimental modeling process can be used. In this process, the system is subjected to a set of known inputs, and its outputs are measured.

Then a mathematical model is derived from the input-output relationships obtained. Simplicity of mathematical model versus accuracy of results of analysis.

In attempting to build a mathematical model, a compromise must be made between the simplicity of the model and the accuracy of the results of the analysis. It is important to note that the results obtained from the analysis are valid only to the extent that the model approximates a given physical system.

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Unsourced material may be challenged and removed. The EP program is also structured for those students who have an interest in the physical sciences as well as engineering. Metallurgical Engineering MCQs. Furthermore, the workflows created within the system for staff â€¦ Mechanical engineering - Wikipedia ; Mechanical engineering is the discipline that applies engineering, physics, engineering mathematics, and materials science principles to design, analyze, manufacture, and maintain mechanical systems.Usually, in solving a new problem, it is desirable first to build a simplified model to obtain a general idea about the solution.

Here we included mechanical-electrical analogies and operational amplifier systems. Mechanical Systems.

Here is the data will work with. A linear, time-invariant differential equation is an equation in which a dependent variable and its derivatives appear as linear combinations.