Linear Feedback Controls
The Essentials
Description
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
Readership
Table of Contents
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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
Product details
- No. of pages: 398
- Language: English
- Copyright: © Elsevier 2020
- Published: May 11, 2020
- Imprint: Elsevier
- Paperback ISBN: 9780128187784
- eBook ISBN: 9780128188125