# Modern Control Engineering, 5th edition

Published by Pearson (August 25, 2009) Â© 2010

**Katsuhiko Ogata**

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**For senior or graduate-level students taking a first course in Control Theory (in departments of Mechanical, Electrical, Aerospace, and Chemical Engineering).**

*A comprehensive, senior-level textbook for control engineering**.*

Ogataâ€™s * Modern Control Engineering, 5/e,* offers the comprehensive coverage of continuous-time control systems that all senior students must have, including frequency response approach, root-locus approach, and state-space 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 Root-Locus Analysis (Chapter 6) and Frequency-Response Analysis (Chapter 8). The author has also updated and revised many of the worked examples and end-of-chapter problems.

**Chapter 8 first discusses PID control** **in general and then presents two-degrees-of-freedom control systems** â€” Presents a computational (MATLAB) method to determine system parameters so the system will have the desired transient characteristics.

**An improved chapter on the design of control systems in state space** (Chapter 10) â€” This chapter treats pole placement and observer design and includes quadratic optimal control. MATLAB is extensively used in the design problems using pole placement and observer design.

**An in-depth treatment of topics **emphasizes both the basic concepts and the design aspects of control systems.

**An accessible presentation** **that avoids highly mathematical arguments**. The author introduces mathematical proofs only when they contribute to an understanding of the material.

**Over 150 chapter-end worked problems and 180 unsolved problems ** clarify students' understanding of the material at strategic points throughout the text.

**An introduction to the two-degrees-of-freedom control system and introduction to robust control**. Presents a MATLAB approach to the design of high performance control systems.

**A comprehensive coverage of root-locus analyses** not found in other texts.

**Detailed coverage** of frequency response of control systems.

**MATLAB**is expanded to many control systems analysis and design problems (See Section 8-4). Computational optimization approach with MATLAB is emphasized throughout the text.

**Over 150 chapter-end worked problems and 180 unsolved problems**help students fully understand the text material. Many of the solved problems are new.

**Improved chapter on the design of control systems in state space (Chapter 10)**â€” Treats pole placement and observer design. Chapter includes quadratic optimal control. MATLAB is extensively used in the design problems using pole placement and observer design.

**Significantly revised chapters**include: â€” Chapter 6 â€” Control Systems Analysis and Design by the Root-Locus Method

â€” Chapter 7 â€” Control Systems Analysis and Design by the Frequency Response Method â€” Chapter 8 â€” PID Controllers and Modified PID Controllers â€” Chapter 8 first discusses PID control in general and then presents two-degrees-of-freedom control systems. MATLAB methods determine system parameters so the system will have the desired transient characteristics.

**Updated Appendices**

â€” Laplace Transform tables and partial fraction expansion with MATLAB are presented in Appendix A and B. â€” Short summary of vector matrix analysis is presented in Appendix C. This Appendix will be useful in obtaining the inverses of n x n matrices that may be involved in the analysis and design of control systems.

â€” Modeling of mechanical systems and electrical systems are shortened and combined into one chapter â€” Fluid systems and thermal systems are combined into one chapter.

â€” Root locus analysis and root locus design of control systems are combined into one chapter. â€” Frequency response analysis and frequency response design of control systems are combined into one chapter.

## Contents

**Preface**

**Chapter 1 Introduction to Control Systems**- 1â€“1 Introduction
- 1â€“2 Examples of Control Systems
- 1â€“3 Closed-Loop Control versus Open-Loop Control
- 1â€“4 Outline of the Book

**Chapter 2 Mathematical Modeling of Control Systems**- 2â€“1 Introduction
- 2â€“2 Transfer Function and impulse Response Function
- 2â€“3 Atomatic Control Systems
- 2â€“4 Modeling in state space
- 2â€“5 State-Space Representation of Scalar Differential Equation System
- 2â€“6 Transformation of Mathematical models with MATLAB
- 2â€“7 Linearization of Nonlinear Mathematical Models

- Example Problems and Solutions Problems

**Chapter 3 Mathematical Modeling of Mechanical Systems and Electrical Systems**- 3â€“1 Introduction
- 3â€“2 Mathematical Modeling of Mechanical Systems
- 3â€“3 Mathematical Modeling of Electrical Systems

- Example Problems and Solutions Problems

**Chapter 4 Mathematical Modeling of Fluid Systems and Thermal Systems**- 4â€“1 Introduction
- 4â€“2 Liquid-Level Systems
- 4â€“3 Pneumatic Systems
- 4â€“4 Hydraulic Systems
- 4â€“5 Thermal Systems

- Example Problems and Solutions Problems

**Chapter 5 Transient and Steady-State Response Analyses**- 5â€“1 Introduction
- 5â€“2 First-Order Systems
- 5â€“3 Second-Order Systems
- 5â€“4 Higher Order Systems
- 5â€“5 Transient-Response Analysis with MATLAB
- 5â€“6 Routh's Stability Criterion
- 5â€“7 Effects of Integral and Derivative Control Actions on System Performance
- 5â€“8 Steady-State Errors in Unity-Feedback Control Systems

- Example Problems and Solutions Problems

**Chapter 6 Control Systems Analysis and design by the Root-Locus Method**- 6â€“1 Introduction
- 6â€“2 Root-Locus Plots
- 6â€“3 plotting Root Loci with MATLAB
- 6â€“4 Root-Locus Plots of Positive Feedback Systems
- 6â€“5 Root-Locus Approach to control Systems Design
- 6â€“6 Lead Compensation
- 6â€“7 Lag Compensation
- 6â€“8 Lag-Lead Compensation

- Example Problems and Solutions Problems

**Chapter 7 Control Systems Analysis and Design by the Frequency Response Method**- 7â€“1 Introduction
- 7â€“2 Bode Digrams
- 7â€“3 Polar Plots
- 7â€“4 Log-Magnitude-versus-Phase plots
- 7â€“5 Nyquist Stability Criterion
- 7â€“6 Stability Analysis
- 7â€“7 Relative Stability Analysis
- 7â€“8 Closed-Loop Frequency Response of Unity-feedback Systems
- 7â€“9 Experimental Determination of Transfer functions
- 7â€“10 Control Systems design by Frequency Response Approach
- 7â€“11 Lead Compensation
- 7â€“12 Lag Compensation
- 7â€“13 Lag-Lead Compensation

- Example Problems and Solutions Problems

**Chapter 8 PID Controllers and Modified PID Controllers**- 8â€“1 Introduction
- 8â€“2 Ziegler- Nichols Rules for tuning PID controllers
- 8â€“3 Design of PID Controllers with Frequency Response Approach
- 8â€“4 Design of PID Controllers with Computational Optimization Approach
- 8â€“5 Modification of PID Control Schemes
- 8â€“6 Two-Degrees-of-freedom PID Control Schemes
- 8â€“7 Zero Placement Approach to Improve Response

- Example Problems and Solutions Problems

**Chapter 9 Control Systems Analysis in State Space**- 9â€“1 Introduction
- 9â€“2 State-space Representations of Transfer-Function Systems
- 9â€“3 Transformation of System Models with MATLAB
- 9â€“4 Solving the Time-Invariant State Equation
- 9â€“5 Some Useful Results in vector-Matrix Analysis
- 9â€“6 Controllability
- 9â€“7 Observability

- Example Problems and Solutions Problems

**Chapter 10 Control Systems Design of in State Space**- 10â€“1 Introduction
- 10â€“2 Pole Placement
- 10â€“3 Solving Pole-Placement Problems with MATLAB
- 10â€“4 Design of Servo Systems
- 10â€“5 State Observers
- 10â€“6 Design of Regulator Systems with Observers
- 10â€“7 Design of Control Systems with Observers
- 10â€“8 Quadratic Optimal Regulator Systems
- 10â€“9 Robust Control Solutions

- Example Problems and Solutions Problems

### Appendix A

### Appendix B

### Appendix C

#### References

#### Index

**Dr. Katsuhiko Ogata**graduated from the University of Tokyo (BS), earned an MS degree from the University of Illinois, and his Ph.D from the University of California, Berkeley. He is Professor Emeritus at the University of Minnesota.

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