Linear Feedback Controls

Linear Feedback Controls

The Essentials

1st Edition - July 1, 2013

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  • Author: Mark Haidekker
  • Hardcover ISBN: 9780124058750
  • eBook ISBN: 9780124055131

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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

  • 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


Product details

  • No. of pages: 282
  • Language: English
  • Copyright: © Elsevier 2013
  • Published: July 1, 2013
  • Imprint: Elsevier
  • Hardcover ISBN: 9780124058750
  • eBook ISBN: 9780124055131

About the Author

Mark Haidekker

Mark A. Haidekker is Professor at College of Engineering in the University of Georgia, Athens, GA, USA

Affiliations and Expertise

Professor, College of Engineering, University of Georgia, Athens, GA, USA

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