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Overview
For senior or graduatelevel students taking a first course in Control Theory (in departments of Mechanical, Electrical, Aerospace, and Chemical Engineering).
A comprehensive, seniorlevel textbook for control engineering.
Ogata’s Modern Control Engineering, 5/e , offers the comprehensive coverage of continuoustime control systems that all senior students must have, including frequency response approach, rootlocus approach, and statespace approach to analysis and design of control systems. The text provides a gradual development of control theory, shows how to solve all computational problems with MATLAB, and avoids highly mathematical arguments. A wealth of examples and worked problems are featured throughout the text.
The new edition includes improved coverage of RootLocus Analysis (Chapter 6) and FrequencyResponse Analysis (Chapter 8). The author has also updated and revised many of the worked examples and endofchapter problems. This text is ideal for control systems engineers.
Editorial Reviews
Booknews
A comprehensive treatment of the analysis and design of continuous time control systems written for senior engineering students. The new edition integrates MATLAB into the text, using the program to solve all problems. As in former publications, the structural outline includes introductory materials, the basic Laplace transform, mathematical modeling of dynamic systems, transferfunction models, statespace models, transientresponse analysis of first and second order systems, basic control actions, the rootlocus analysis, design and compensation techniques using frequencyresponse methods, and Liapunov stability analysis applications to design. An appendix supplies the background materials need for MATLAB use. Includes charts, tables, equations, and examples. Annotation c. Book News, Inc., Portland, OR booknews.comProduct Details
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This book presents a comprehensive treatment of the analysis and design of control systems. It is written at the level of the senior engineering (mechanical, electrical, aerospace, and chemical) student and is intended to be used as a text for the first course in control systems. The prerequisite on the part of the reader is that he or she has had introductory courses on differential equations, vectormatrix analysis, circuit analysis, and mechanics.
The main revision made in the fourth edition of the text is to present twodegreesoffreedom control systems to design high performance control systems such that steadystate errors in following step, ramp, and acceleration inputs become zero. Also, newly presented is the computational (MATLAB) approach to determine the polezero locations of the controller to obtain the desired transient response characteristics such that the maximum overshoot and settling time in the step response be within the specified values. These subjects are discussed in Chapter 10. Also, Chapter 5 (primarily transient response analysis) and Chapter 12 (primarily pole placement and observer design) are expanded using MATLAB. Many new solved problems are added to these chapters so that the reader will have a good understanding of the MATLAB approach to the analysis and design of control systems. Throughout the book computational problems are solved with MATLAB.
This text is organized into 12 chapters. The outline of the book is as follows. Chapter 1 presents an introduction to control systems. Chapter 2 deals with Laplace transforms of commonly encountered time functions and some of the useful theorems on Laplace transforms. (If the students have anadequate background on Laplace transforms, this chapter may be skipped.) Chapter 3 treats mathematical modeling of dynamic systems (mostly mechanical, electrical, and electronic systems) and develops transfer function models and statespace models. This chapter also introduces signal flow graphs. Discussions of a linearization technique for nonlinear mathematical models are included in this chapter.
Chapter 4 presents mathematical modeling of fluid systems (such as liquidlevel systems, pneumatic systems, and hydraulic systems) and thermal systems. Chapter 5 treats transient response analyses of dynamic systems to step, ramp, and impulse inputs. MATLAB is extensively used for transient response analysis. Routh's stability criterion is presented in this chapter for the stability analysis of higher order systems. Steadystate error analysis of unityfeedback control systems is also presented in this chapter.
Chapter 6 treats the rootlocus analysis of control systems. Plotting root loci with MATLAB is discussed in detail. In this chapter rootlocus analyses of positivefeedback systems, conditionally stable systems, and systems with transport lag are included. Chapter 7 presents the design of lead, lag, and laglead compensators with the rootlocus method. Both series and parallel compensation techniques are discussed.
Chapter 8 presents basic materials on frequencyresponse analysis. Bode diagrams, polar plots, the Nyquist stability criterion, and closedloop frequency response are discussed including the MATLAB approach to obtain frequency response plots. Chapter 9 treats the design and compensation techniques using frequencyresponse methods. Specifically, the Bode diagram approach to the design of lead, lag, and laglead compensators is discussed in detail.
Chapter 10 first deals with the basic and modified PID controls and then presents computational (MATLAB) approach to obtain optimal choices of parameter values of controllers to satisfy requirements on step response characteristics. Next, it presents twodegreesoffreedom control systems. The chapter concludes with the design of high performance control systems that will follow a step, ramp, or acceleration input without steadystate error. The zeroplacement method is used to accomplish such performance.
Chapter 11 presents a basic analysis of control systems in state space. Concepts of controllability and observability are given here. This chapter discusses the transformation of system models (from transferfunction model to statespace model, and vice versa) with MATLAB. Chapter 12 begins with the pole placement design technique, followed by the design of state observers. Both fullorder and minimumorder state observers are treated. Then, designs of type 1 servo systems are discussed in detail. Included in this chapter are the design of regulator systems with observers and design of control systems with observers. Finally, this chapter concludes with discussions of quadratic optimal regulator systems.
In this book, the basic concepts involved are emphasized and highly mathematical arguments are carefully avoided in the presentation of the materials. Mathematical proofs are provided when they contribute to the understanding of the subjects presented. All the material has been organized toward a gradual development of control theory.
Throughout the book, carefully chosen examples are presented at strategic points so that the reader will have a clear understanding of the subject matter discussed. In addition, a number of solved problems (Aproblems) are provided at the end of each chapter, except Chapter 1. These solved problems constitute an integral part of the text. Therefore, it is suggested that the reader study all these problems carefully to obtain a deeper understanding of the topics discussed. In addition, many problems (without solutions) of various degrees of difficulty are provided (Bproblems). These problems may be used as homework or quiz purposes. An instructor using this text can obtain a complete solutions manual (for Bproblems) from the publisher.
Most of the materials including solved and unsolved problems presented in this book have been class tested in senior level courses on control systems at the University of Minnesota.
If this book is used as a text for a quarter course (with 40 lecture hours), most of the materials in the first 10 chapters (except perhaps Chapter 4) may be covered. The first nine chapters cover all basic materials of control systems normally required in a first course on control systems. Many students enjoy studying computational (MATLAB) approach to the design of control systems presented in Chapter 10. It is recommended that Chapter 10 be included in any control courses. If this book is used as a text for a semester course (with 56 lecture hours), all or a good part of the book may be covered with flexibility in skipping certain subjects. Because of the abundance of solved problems (Aproblems) that might answer many possible questions that the reader might have, this book can also serve as a selfstudy book for practicing engineers who wish to study basic control theory.
I would like to express my sincere appreciation to Professors Athimoottil V Mathew (Rochester Institute of Technology), Richard Gordon (University of Mississippi), Guy Beale (George Mason University), and Donald T. Ward (Texas A & M University), who made valuable suggestions at the early stage of the revision process, and anonymous reviewers who made many constructive comments. Appreciation is also due to my former students, who solved many of the Aproblems and Bproblems included in this book.
Katsuhiko Ogata
Table of Contents
Contents
Preface
Chapter 1 Introduction to Control Systems
1—1 Introduction
1—2 Examples of Control Systems
1—3 ClosedLoop Control versus OpenLoop Control
1—4 Outline of the Book
Chapter 2 Mathematical Modeling of Control Systems
2—1 Introduction
2—2 Transfer Function and impulse Response Function
2—3 Atomatic Control Systems
2—4 Modeling in state space
2—5 StateSpace Representation of Scalar Differential Equation System
2—6 Transformation of Mathematical models with MATLAB
2—7 Linearization of Nonlinear Mathematical Models
Example Problems and Solutions Problems
Chapter 3 Mathematical Modeling of Mechanical Systems and Electrical Systems
3—1 Introduction
3—2 Mathematical Modeling of Mechanical Systems
3—3 Mathematical Modeling of Electrical Systems
Example Problems and Solutions Problems
Chapter 4 Mathematical Modeling of Fluid Systems
and Thermal Systems
4—1 Introduction 152
4—2 LiquidLevel Systems
4—3 Pneumatic Systems
4—4 Hydraulic Systems
4—5 Thermal Systems
Example Problems and Solutions Problems
Chapter 5 Transient and SteadyState Response Analyses
5—1 Introduction
5—2 FirstOrder Systems
5—3 SecondOrder Systems
5—4 Higher Order Systems
5—5 TransientResponse Analysis with MATLAB
5—6 Routh’s Stability Criterion
5—7 Effects of Integral and Derivative Control Actions on System
Performance
5—8 SteadyState Errors in UnityFeedback Control Systems
Example Problems and Solutions Problems
Chapter 6 Control Systems Analysis and design by the RootLocus Method
6—1 Introduction
6—2 RootLocus Plots
6—3 plotting Root Loci with MATLAB
6—4 RootLocus Plots of Positive Feedback Systems
6—5 RootLocus Approach to control Systems Design
6—6 Lead Compensation
6—7 Lag Compensation
68 LagLead Compensation
Example Problems and Solutions Problems
Chapter 7 Control Systems Analysis and Design by the Frequency Response Method
7—1 Introduction
7—2 Bode Digrams
7—3 Polar Plots
7—4 LogMagnitudeversusPhase plots
7—5 Nyquist Stability Criterion
7—6 Stability Analysis
77 Relative Stability Analysis
78 ClosedLoop Frequency Response of Unityfeedback Systems
79 Experimental Determination of Transfer functions
710 Control Systems design by Frequency Response Approach
711 Lead Compensation
712 Lag Compensation
713 LagLead Compensation
Example Problems and Solutions Problems
Chapter 8 PID Controllers and Modified PID Controllers
8—1 Introduction
8—2 Ziegler Nichols Rules for tuning PID controllers
8—3 Design of PID Controllers with Frequency Response Approach
8—4 Design of PID Controllers with Computational Optimization Approach
8—5 Modification of PID Control Schemes
8—6 TwoDegreesoffreedom PID Control Schemes
8—7 Zero Placement Approach to Improve Response
Example Problems and Solutions Problems
Chapter 9 Control Systems Analysis in State Space
9—1 Introduction
9—2 Statespace Representations of TransferFunction Systems
9—3 Transformation of System Models with MATLAB
9—4 Solving the TimeInvariant State Equation
9—5 Some Useful Results in vectorMatrix Analysis
96 Controllability
97 Observability
Example Problems and Solutions Problems
Chapter 10 Control Systems Design of in State Space
10—1 Introduction
10—2 Pole Placement
10—3 Solving PolePlacement Problems with MATLAB
10—4 Design of Servo Systems
10—5 State Observers
10—6 Design of Regulator Systems with Observers
10—7 Design of Control Systems with Observers
10—8 Quadratic Optimal Regulator Systems
109 Robust Control Solutions
Example Problems and Solutions Problems
Appendix A
Appendix B
Appendix C
References
Index
Preface
This book presents a comprehensive treatment of the analysis and design of control systems. It is written at the level of the senior engineering (mechanical, electrical, aerospace, and chemical) student and is intended to be used as a text for the first course in control systems. The prerequisite on the part of the reader is that he or she has had introductory courses on differential equations, vectormatrix analysis, circuit analysis, and mechanics.
The main revision made in the fourth edition of the text is to present twodegreesoffreedom control systems to design high performance control systems such that steadystate errors in following step, ramp, and acceleration inputs become zero. Also, newly presented is the computational (MATLAB) approach to determine the polezero locations of the controller to obtain the desired transient response characteristics such that the maximum overshoot and settling time in the step response be within the specified values. These subjects are discussed in Chapter 10. Also, Chapter 5 (primarily transient response analysis) and Chapter 12 (primarily pole placement and observer design) are expanded using MATLAB. Many new solved problems are added to these chapters so that the reader will have a good understanding of the MATLAB approach to the analysis and design of control systems. Throughout the book computational problems are solved with MATLAB.
This text is organized into 12 chapters. The outline of the book is as follows. Chapter 1 presents an introduction to control systems. Chapter 2 deals with Laplace transforms of commonly encountered time functions and some of the useful theorems on Laplace transforms. (If the studentshave an adequate background on Laplace transforms, this chapter may be skipped.) Chapter 3 treats mathematical modeling of dynamic systems (mostly mechanical, electrical, and electronic systems) and develops transfer function models and statespace models. This chapter also introduces signal flow graphs. Discussions of a linearization technique for nonlinear mathematical models are included in this chapter.
Chapter 4 presents mathematical modeling of fluid systems (such as liquidlevel systems, pneumatic systems, and hydraulic systems) and thermal systems. Chapter 5 treats transient response analyses of dynamic systems to step, ramp, and impulse inputs. MATLAB is extensively used for transient response analysis. Routh's stability criterion is presented in this chapter for the stability analysis of higher order systems. Steadystate error analysis of unityfeedback control systems is also presented in this chapter.
Chapter 6 treats the rootlocus analysis of control systems. Plotting root loci with MATLAB is discussed in detail. In this chapter rootlocus analyses of positivefeedback systems, conditionally stable systems, and systems with transport lag are included. Chapter 7 presents the design of lead, lag, and laglead compensators with the rootlocus method. Both series and parallel compensation techniques are discussed.
Chapter 8 presents basic materials on frequencyresponse analysis. Bode diagrams, polar plots, the Nyquist stability criterion, and closedloop frequency response are discussed including the MATLAB approach to obtain frequency response plots. Chapter 9 treats the design and compensation techniques using frequencyresponse methods. Specifically, the Bode diagram approach to the design of lead, lag, and laglead compensators is discussed in detail.
Chapter 10 first deals with the basic and modified PID controls and then presents computational (MATLAB) approach to obtain optimal choices of parameter values of controllers to satisfy requirements on step response characteristics. Next, it presents twodegreesoffreedom control systems. The chapter concludes with the design of high performance control systems that will follow a step, ramp, or acceleration input without steadystate error. The zeroplacement method is used to accomplish such performance.
Chapter 11 presents a basic analysis of control systems in state space. Concepts of controllability and observability are given here. This chapter discusses the transformation of system models (from transferfunction model to statespace model, and vice versa) with MATLAB. Chapter 12 begins with the pole placement design technique, followed by the design of state observers. Both fullorder and minimumorder state observers are treated. Then, designs of type 1 servo systems are discussed in detail. Included in this chapter are the design of regulator systems with observers and design of control systems with observers. Finally, this chapter concludes with discussions of quadratic optimal regulator systems.
In this book, the basic concepts involved are emphasized and highly mathematical arguments are carefully avoided in the presentation of the materials. Mathematical proofs are provided when they contribute to the understanding of the subjects presented. All the material has been organized toward a gradual development of control theory.
Throughout the book, carefully chosen examples are presented at strategic points so that the reader will have a clear understanding of the subject matter discussed. In addition, a number of solved problems (Aproblems) are provided at the end of each chapter, except Chapter 1. These solved problems constitute an integral part of the text. Therefore, it is suggested that the reader study all these problems carefully to obtain a deeper understanding of the topics discussed. In addition, many problems (without solutions) of various degrees of difficulty are provided (Bproblems). These problems may be used as homework or quiz purposes. An instructor using this text can obtain a complete solutions manual (for Bproblems) from the publisher.
Most of the materials including solved and unsolved problems presented in this book have been class tested in senior level courses on control systems at the University of Minnesota.
If this book is used as a text for a quarter course (with 40 lecture hours), most of the materials in the first 10 chapters (except perhaps Chapter 4) may be covered. The first nine chapters cover all basic materials of control systems normally required in a first course on control systems. Many students enjoy studying computational (MATLAB) approach to the design of control systems presented in Chapter 10. It is recommended that Chapter 10 be included in any control courses. If this book is used as a text for a semester course (with 56 lecture hours), all or a good part of the book may be covered with flexibility in skipping certain subjects. Because of the abundance of solved problems (Aproblems) that might answer many possible questions that the reader might have, this book can also serve as a selfstudy book for practicing engineers who wish to study basic control theory.
I would like to express my sincere appreciation to Professors Athimoottil V Mathew (Rochester Institute of Technology), Richard Gordon (University of Mississippi), Guy Beale (George Mason University), and Donald T. Ward (Texas A & M University), who made valuable suggestions at the early stage of the revision process, and anonymous reviewers who made many constructive comments. Appreciation is also due to my former students, who solved many of the Aproblems and Bproblems included in this book.
Katsuhiko Ogata