Linear Feedback Controls - 1st Edition - ISBN: 9780124058750, 9780124055131

Linear Feedback Controls

1st Edition

The Essentials

Authors: Mark Haidekker
Hardcover ISBN: 9780124058750
eBook ISBN: 9780124055131
Imprint: Elsevier
Published Date: 1st July 2013
Page Count: 282
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The design of control systems is at the very core of engineering. Feedback controls are ubiquitous, ranging from simple room thermostats to airplane engine control. Helping to make sense of this wide-ranging field, this book provides a new approach by keeping a tight focus on the essentials with a limited, yet consistent set of examples. Analysis and design methods are explained in terms of theory and practice. The book covers classical, linear feedback controls, and linear approximations are used when needed. In parallel, the book covers time-discrete (digital) control systems and juxtaposes time-continuous and time-discrete treatment when needed. One chapter covers the industry-standard PID control, and one chapter provides several design examples with proposed solutions to commonly encountered design problems.

The book is ideal for upper level students in electrical engineering, mechanical engineering, biological/biomedical engineering, chemical engineering and agricultural and environmental engineering and provides a helpful refresher or introduction for graduate students and professionals

Key Features

  • Focuses on the essentials of control fundamentals, system analysis, mathematical description and modeling, and control design to guide the reader
  • Illustrates the theory and practical application for each point using real-world examples
  • Strands weave throughout the book, allowing the reader to understand clearly the use and limits of different analysis and design tools


Advanced undergraduate and graduate students as well as professionals  in the fields of electrical, mechanical, biological/biomedical, chemical, agricultural and environmental engineering.

Table of Contents



List of Commonly Used Symbols

Chapter 1. Introduction to Linear Feedback Controls

1.1 What are Feedback Control Systems?

1.2 Some Terminology

1.3 Design of Feedback Control Systems

1.4 Two-Point Control

Chapter 2. Systems and Signals

2.1 Example First-Order System: The Lowpass

2.2 Example Second-Order System: The Spring-Mass-Damper System

2.3 Obtaining the System Response from a Step Input

2.4 State-Space Models

2.5 Systems and Signals in Scilab

Chapter 3. Solving Differential Equations in the Laplace Domain

3.1 The Laplace Transform

3.2 Fourier Series and the Fourier Transform

3.3 Representation of the RC Lowpass and Spring-Mass-Damper Systems in the Laplace Domain

3.4 Transient and Steady-State Response

3.5 Partial Fraction Expansion

3.6 Building Blocks of Linear Systems

Chapter 4. Time-Discrete Systems

4.1 Analog-to-Digital Conversion and the Zero-Order Hold

4.2 The z-Transform

4.3 The Relationship between Laplace- and z-domains

4.4 The w-Transform

4.5 Building Blocks for Digital Controllers

Chapter 5. First Comprehensive Example: The Temperature-Controlled Waterbath

5.1 Mathematical Model of the Process

5.2 Determination of the System Coefficients

5.3 Determining the Transfer Function—General Remarks

5.4 Introducing Feedback Control

5.5 Comparison of the Open-Loop and Closed-Loop Systems

Chapter 6. Laplace- and -Domain Description of the Waterbath Example

6.1 Laplace-Domain Description of the Process

6.2 The Closed-Loop System

6.3 Sensitivity and Tracking Error

6.4 Using a PI Controller

6.5 Time-Discrete Control

Chapter 7. Block Diagrams: Formal Graphical Description of Linear Systems

7.1 Symbols of a Block Diagram

7.2 Block Diagram Manipulation

7.3 Block Diagram Simplification Examples

7.4 Signal Flow Graphs

Chapter 8. Linearization of Nonlinear Components

8.1 Linearization of Components with Analytical Description

8.2 Linearization of Tabular Data

8.3 Linearization of Components with Graphical Data

8.4 Saturation Effects

Chapter 9. A Tale of Two Poles: The Positioner Example and the Significance of the Poles in the -Plane

9.1 A Head-Positioning System

9.2 Introducing Feedback Control

9.3 Dynamic Response of the Closed-Loop System

9.4 Dynamic Response Performance Metrics

9.5 Time-Integrated Performance Metrics

9.6 Feedback Control with a Time-Discrete Controller

Chapter 10. Stability Analysis for Linear Systems

10.1 The Routh-Hurwitz Scheme

10.2 Routh Arrays for Low-Order Systems

10.3 Stability of Time-Discrete Systems with the -Transform

10.4 The Jury Test

10.5 Jury Arrays for Low-Order Systems

10.6 Example Applications

Chapter 11. Frequency-Domain Analysis and Design Methods

11.1 Frequency Response of LTI Systems

11.2 Frequency Response and Stability

11.3 Bode Plots

11.4 Definition of Phase and Gain Margin

11.5 Construction of Bode Diagrams

11.6 Frequency Response of a Second-Order System

11.7 Frequency Response of Digital Filters

11.8 The Nyquist Stability Criterion

Chapter 12. The Root Locus Method

12.1 Graphical Construction of Root Locus Plots

12.2 Root Locus Diagrams in Scilab

12.3 Design Example: Positioner with PI Control

12.4 Design Example: Resonance Reduction

12.5 The Root Locus Method for Time-Discrete Systems

Chapter 13. The PID Controller

13.1 Intuitive Introduction

13.2 Transfer Functions with PID Control

13.3 Frequency-Domain Aspects of Control

13.4 Time-Discrete PID Controllers

13.5 Controller Tuning

13.6 Variations and Alternatives of PID Control

13.7 Conclusion

Chapter 14. Design Examples

14.1 Precision Temperature Control

14.2 Fast-Tracking Temperature Control

14.3 Motor Speed and Position Control

14.4 Resonant Sine Oscillator

14.5 Low-Distortion (Hi-Fi) Amplifiers with Feedback

14.6 Phase-Locked Loop Systems

14.7 Stabilizing an Unstable System

Appendix A. Laplace Correspondence Tables

Appendix B. Z-Transform Correspondence Tables

Appendix C Introduction to Operational Amplifiers

Appendix D. Relevant Scilab Commands

References and Further Reading



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About the Author

Mark Haidekker

Affiliations and Expertise

Professor, College of Engineering, University of Georgia, Athens, GA, U.S.A.


"Contending that nonlinear control theory is a completely separate field, Hadekker focuses on linear systems to describe the core areas of classical feedback control systems, including the mathematical tools needed for control analysis and design."--Reference & Research Book News, October 2013