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Linear Feedback Controls - 2nd Edition - ISBN: 9780128187784, 9780128188125

Linear Feedback Controls

2nd Edition

The Essentials

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Author: Mark Haidekker
Paperback ISBN: 9780128187784
eBook ISBN: 9780128188125
Imprint: Elsevier
Published Date: 12th May 2020
Page Count: 398
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Control systems are one of the most important engineering fields, and recent advances in microelectonics and microelectromechanical systems have made feedback controls ubiquitous – a simple cell phone, for example, can have dozens of feedback control systems. Recent research focuses on advanced controls, such as nonlinear systems, adaptive controls, or controls based on computer learning and artificial intelligence. Conversely, classical (linear) control theory is well established; yet, it provides the crucial foundation not only for advanced control topics, but also for the many everyday control systems ranging from cell phone backlight control to self-balancing hoverboard scooters. Linear Feedback Controls provides a comprehensive, yet compact introduction to classical control theory. The present Second Edition has been expanded to include important topics, such as state-space models and control robustness. Moreover, aspects of the practical realization have been significantly expanded with complete design examples and with typical building blocks for control systems.

The book is ideal for upper level students in electrical and mechanical engineering, for whom a course in Feedback Controls is usually required. Moreover, students in bioengineering, chemical engineering, and agricultural and environmental engineering can benefit from the introductory character and the practical examples, and the book provides an introduction or helpful refresher 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 how control theory is linked to design of control systems and their performance by introducing theoretical elements as tools in a designer’s toolbox
  • Guides the reader through the different analysis and design tools with strands of examples that weave throughout the book
  • Highlights both the design process and typical applications by presenting detailed practical examples and their realization and performance, complete with circuit diagrams and measured performance data


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

Table of Contents

Preface to the second edition ix

Preface to the first edition xi

Acknowledgments xiii

List of commonly used symbols xv

1 Introduction to linear feedback controls 1

1.1 What are feedback control systems? 4

1.2 Some terminology 6

1.3 Design of feedback control systems 7

1.4 Two-point control 10

2 Systems and signals 15

2.1 Example first-order system: the RC lowpass 17

2.2 Example second-order system: the spring-mass-damper system 18

2.3 Obtaining the system response from a step input 19

2.4 Systems and signals in Scilab 21

3 Solving differential equations in the Laplace domain 25

3.1 The Laplace transform 25

3.2 Fourier series and the Fourier transform 29

3.3 Representation of the RC lowpass and spring-mass-damper

systems in the Laplace domain 35

3.4 Transient and steady-state response 39

3.5 Partial fraction expansion 42

4 Time-discrete systems 51

4.1 Analog-to-digital conversion and the zero-order hold 52

4.2 The z-transform 55

4.3 The relationship between Laplace- and z-domains 59

4.4 The w-transform 64

5 First comprehensive example: the temperature-controlled waterbath 65

5.1 Mathematical model of the process 65

5.2 Determination of the system coefficients 67

5.3 Laplace-domain model 72

5.4 Introducing feedback control 75

5.5 Comparison of the open-loop and closed-loop systems 77

5.6 Using a PI-controller 79

5.7 Time-discrete control 83

5.8 Time-discrete control with the bilinear transform 85

6 A tale of two poles: the positioner example and the significance of the

poles in the s-plane 87

6.1 A head-positioning system 87

6.2 Introducing feedback control 89

6.3 Dynamic response of the closed-loop system 90

6.4 Feedback control with a time-discrete controller 93

6.5 Dynamic response performance metrics 97

6.6 Time-integrated performance metrics 102

6.7 The dynamic response of higher-order systems 105

7 State-space models 109

7.1 General equations for state-space models 109

7.2 Feedback control systems in state-space form 115

7.3 Reachability and observability 118

7.4 State-space feedback control with observers 119

7.5 State-space models in Scilab 121

8 Block diagrams: formal graphical description of linear systems 123

8.1 Symbols of block diagrams and signal flow graphs 123

8.2 Block diagram manipulation 124

8.3 Block diagram simplification examples 127

9 Linearization of nonlinear components 133

9.1 Linearization of components with analytical description 134

9.2 Linearization of components with multiple input variables 136

9.3 Linearization of tabular data 139

9.4 Linearization of components with graphical data 140

9.5 Saturation effects 141

10 Stability analysis for linear systems 145

10.1 The Routh–Hurwitz scheme 148

10.2 Routh arrays for low-order systems 149

10.3 Stability of time-discrete systems with the w-transform 151

10.4 The Jury test 152

10.5 Jury arrays for low-order systems 153

10.6 Example applications 154

11 The root locus method 157

11.1 Graphical construction of root locus plots 158

11.2 Root-locus diagrams in Scilab 164

11.3 Design example: positioner with PI control 165

11.4 Design example: resonance reduction 170

11.5 The root locus method for time-discrete systems 173

12 Frequency-domain analysis and design methods 177

12.1 Frequency response of LTI systems 177

12.2 Frequency response and stability 179

12.3 Bode plots 181

12.4 Definition of phase and gain margin 182

12.5 Construction of Bode diagrams 185

12.6 Frequency response of a second-order system 186

12.7 Frequency response of digital filters 190

12.8 The Nyquist stability criterion 193

12.9 The Nyquist stability criterion for time-discrete systems 199

12.10 Nyquist stability in Scilab 201

13 Robustness of feedback control systems 203

13.1 System sensitivity 204

13.2 Pole sensitivity 208

13.3 The role of the sensor 211

13.4 Robustness of digital control systems 216

14 Building blocks of linear systems 219

14.1 Brief introduction to operational amplifiers 219

14.2 Building blocks for time-continuous systems 226

14.3 A sample digital control system with microcontroller 239

14.4 Building blocks for time-discrete systems and digital controllers 243

15 The PID controller 253

15.1 Intuitive explanation 253

15.2 Transfer functions with PID control 254

15.3 Frequency-domain aspects of PID control 258

15.4 Time-discrete PID controllers 260

15.5 PID controller tuning 264

15.6 Integral windup 266

15.7 PID control of nonlinear processes 272

15.8 Conclusion 272

16 Design of feedback controls 275

16.1 Definition of the control goals 275

16.2 Analysis of the process or plant 277

16.3 Choice and design of the sensors 280

16.4 Design of the controller 282

16.5 Testing and validation 293

17 Application and design examples 297

17.1 Precision temperature control 297

17.2 Fast-tracking temperature control 300

17.3 Start-to-end design example: personal climate control 303

17.4 Motor speed and position control 311

17.5 Resonant sine oscillator 319

17.6 Low-distortion (Hi-Fi) amplifiers with feedback 327

17.7 Phase-locked loop systems 332

17.8 Start-to-end design example: 60 Hz phase-locked loop for a model

solar inverter 337

17.9 Stabilizing an unstable system 342

17.10 Start-to-end design example: inverted pendulum 352

A Laplace correspondence tables 363

B Z-transform correspondence tables 367

C Relevant Scilab commands 369

References and further reading 371

Index 373


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© Elsevier 2020
12th May 2020
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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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