This text ventures into areas which the majority of control system books avoid. It was written to look at the area in a much wider form than the usual process control or machine control-systems. Many topics which are covered in other specialities are covered such as the stability of amplifiers, phase-locked loops, structural resonance and parasitic oscillations. It also covers the application and implementation of real-time digital controllers and for the first time the Amplitude-locked loop. An even wider look at the area is shown by examining classical or historic mathematical algorithms in terms of control-theory. Despite its wide range, the book is tutorial in nature and tries to avoid where possible an obtuse mathematical approach. It comes with MATLAB, LabView and a few Mathematica examples. The book is an ideal undergraduate text for engineers and a refresher for many practising engineers. It gives a thorough background in the analogue domain before moving on to digital-control and its applications. The proceeds from author royalties of this book will be donated to charity.
Author(s): Tom Moir
Publisher: Spirnger
Year: 2020
Language: English
Pages: 478
Tags: Control
Preface......Page 7
Acknowledgements......Page 9
Contents......Page 10
1 Introduction to Feedback Control......Page 16
1.1 Historical Notes on Automatic-Control......Page 17
1.2 Some Basic Mathematical Models and Templates for Signals and Systems......Page 24
2.1 The Laplace Transform......Page 35
2.1.1 Examples of Laplace Transform of Signals......Page 36
2.1.2 Laplace Transform of Systems......Page 38
2.2.1 Linear Systems......Page 40
2.2.2 Time-Invariant Systems......Page 41
2.3 Cascading Systems......Page 42
2.4 The Ubiquitous Integrator......Page 46
2.5 The Inverse Laplace Transform......Page 48
3.1 First and Second-Order Transfer-Functions......Page 51
3.2 Step-Response of Second-Order Systems......Page 55
3.2.1 Case A: No Damping \upzeta = 0......Page 56
3.2.2 Case B: Critical Damping \upzeta = 1......Page 57
3.2.4 Case D: Underdamped Case \upzeta \lt 1......Page 58
3.3 Poles and Zeros......Page 64
3.4 Stability of Transfer-Functions......Page 65
3.5 The Final-Value Theorem......Page 68
3.6 A Note on the Routh Stability Criterion......Page 70
4.1 The Need for Feedback......Page 74
4.2 Speed or Velocity Control of dc Motors......Page 78
4.3 Position Control of dc Motors......Page 90
4.3.1 The No-Load-Torque Case......Page 97
4.3.2 Effect of Load-Torque......Page 100
5.1 Frequency-Response of Linear Systems......Page 102
5.1.2 Integrator Plus Gain......Page 104
5.1.3 First-Order System......Page 106
5.2 Composite Bode-Plots......Page 108
5.3 Bode-Plots with Complex Poles......Page 112
5.4 Some Commonly Met Bode-Plots......Page 115
5.4.1 Phase-Lead Compensator (Passive)......Page 116
5.4.2 Phase-Lead Compensator (Active)......Page 118
5.4.3 Three Classes of Integrator......Page 119
5.4.4 Lag-Lead Circuit......Page 122
5.4.5 Leaky Integrator......Page 123
5.5 Non Minimum-Phase Systems......Page 124
5.6 Time-Delays in Linear-Systems......Page 128
6.1 Root-Locus Method......Page 131
6.1.1 First-Order System......Page 132
6.1.2 Second-Order System......Page 133
6.1.3 Third Order System with Feedback......Page 135
6.1.4 Fourth Order System with Feedback......Page 136
6.2 Recognising Closed-Loop Instability Using Bode-Plots......Page 138
6.2.1 Ideal and Practical Differentiator Circuit......Page 143
6.2.2 Capacitance Loading in an Op-Amp......Page 146
6.3 The Ideal Bode-Plot......Page 149
6.4 Example. Bode Based Compensation of a Motor + Load (Position Feedback)......Page 151
6.5 Compensation with Structural Resonance......Page 159
6.6 PID Controllers and Auto-tuning......Page 168
6.6.1 Proportional Control KP Only......Page 169
6.6.5 Comparison with Lag-Lead Type Control......Page 170
6.6.6 PID Example......Page 171
6.7.1 Type-0 System: Step-Input {\varvec r}\left( {s} \right) = {{1}}/{s}......Page 173
6.7.3 Type-1 System: Step Input {\varvec r}\left( s \right) = {1}/s......Page 174
6.7.5 Type-2 System: Step Input {\varvec r}\left( s \right) = {1}/s......Page 175
6.7.6 Type-2 System: Ramp Input {\varvec r}\left( s \right) = {1}/s^{2}......Page 176
7.1 Introduction to State-Space......Page 177
7.1.1 Example of State-Space Realisation......Page 180
7.1.2 State-Space Realisations with Zeros......Page 185
7.2 Canonical Forms......Page 187
7.2.1 Example, Transfer-Function to State-Space Controllable Canonical Form......Page 188
7.2.2 Observable Canonical Form......Page 189
7.2.3 Biproper Systems......Page 190
7.3 Converting from State-Space to Transfer-Function......Page 193
7.3.1 Example Conversion to Transfer-Function......Page 194
7.4 Poles and Zeros from State-Space......Page 195
7.5.1 Example of an RLC Circuit......Page 198
7.5.2 Example of a Coupled Mesh Network......Page 200
7.5.3 Example of Mass-Spring-Damper......Page 202
7.6 Similarity Transformations......Page 203
7.7 Step-Response of State-Space Systems......Page 206
7.7.1 Step-Response of a Mass with Force......Page 208
8.1 State-Variable Feedback......Page 211
8.1.1 Example of State-Feedback......Page 213
8.2 Controllability of a System......Page 219
8.2.1 Rank of a Matrix......Page 220
8.2.2 Rank Test for Controllability......Page 221
8.3 Tuning a State-Space System......Page 222
8.4.1 Observability......Page 224
8.4.2 Theory of the Observer......Page 225
8.5 The Separation Principle......Page 233
9 Digital Sampled Systems......Page 235
9.1 Analogue Versus Digital Hardware......Page 236
9.2 Sampled-Data......Page 237
9.3 Sampling Theory......Page 239
9.4 Aliasing......Page 243
9.5 The D-A Reconstruction......Page 245
9.6 The z-Transform......Page 249
9.6.1 z-Transform of a Decaying Sequence......Page 251
9.7 Step-Response Example......Page 253
9.8 Stability of Discrete-Time Systems......Page 255
9.9 Normalised Frequency and Frequency-Response......Page 257
9.10 Impulse-Response and Convolution......Page 260
9.10.1 Example, FIR Notch Filter......Page 262
9.11 A Note on Two-Sided Sequences and the z-Transform......Page 265
10.1 Difference Equations......Page 267
10.2 Pseudo-code for Implementing Difference-Equations......Page 269
10.3 Converting from s-Domain to z-Domain......Page 270
10.4 Analysis of the Bilinear Transform......Page 274
10.5.1 Example 1: First-Order System......Page 276
10.5.2 Integral Compensator......Page 279
10.5.3 Phase-Lead (Advance) Compensator......Page 280
10.5.4 Digitally Cascading Compensators......Page 281
10.6 The Link with Numerical Integration......Page 283
10.7 Discrete-Time PID Controllers......Page 285
11.1 The Discrete-Time State-Space from the Continuous-Time Case......Page 289
11.1.1 Example. Newton’s Law in Discrete State-Space......Page 292
11.2.1 Example. Second-Order System. Discrete State-Space to Transfer-Function......Page 295
11.3 Transfer-Function to State-Space......Page 296
11.3.1 Example. Second-Order System to Discrete State-Space......Page 298
11.3.2 Second Realisation......Page 300
11.4 Signal-Flow Graphs......Page 301
11.5 Solution of the Discrete-Time State-Equations......Page 304
11.6 Discrete-Time State-Feedback......Page 306
11.7 Discrete-Time Observers......Page 312
11.7.1 Example of a Discrete-Time Observer......Page 314
12.1 White Noise and Probability......Page 315
12.2 Coloured Noise......Page 319
12.3 Whitening-Filter......Page 323
12.4.1 Discrete-Time Spectrum and Autocorrelation Example......Page 324
12.5 The Wiener Filter......Page 327
12.5.1 Wiener-Filter Example, Continuous-Time......Page 328
12.5.2 Discrete-Time Wiener-Filter......Page 331
12.5.3 Illustrative Example of Discrete-Time Wiener-Filter......Page 334
12.6 State-Space Systems with Noise......Page 338
12.7 ARMAX Models......Page 341
13.1 Kalman-Bucy Filter......Page 343
13.1.1 Kalman-Filter Example Continuous-Time......Page 346
13.2 Discrete-Time Kalman-Filter......Page 349
13.2.1 Illustrative Example for Discrete-Time Kalman Filter......Page 351
13.3 The Kalman-Filter for Inertial Measurements......Page 354
13.4 System Identification Using the Kalman-Filter and Recursive-Least-Squares......Page 357
13.4.1 RLS Estimation Example......Page 359
13.4.2 RLS Estimation of System Transfer-Function......Page 360
14 Implementing Digital Real-Time Servos......Page 364
14.1 Implementing Digital PID Control......Page 366
14.1.1 Integrator Windup......Page 372
14.2 Implementing Digital Lag-Lead Control......Page 373
14.3 Sensor Fusion and Embedded Control of a Camera Stabilising System......Page 379
14.3.1 Sensor Fusion Using the Kalman Filter......Page 380
14.3.2 Method of Control......Page 382
15.1 Linear and Nonlinear......Page 387
15.1.1 Equilibrium Points......Page 390
15.2 Linearizing Systems......Page 392
15.3 Phase-Locked Loop (A Servo for Frequency-Demodulation)......Page 407
15.3.1 Demodulation of Frequency-Modulation (FM)......Page 409
15.4 Amplitude-Locked Loop (A Servo Used to Remove Amplitude Variations)......Page 413
15.5 Nonlinearity in the Feedback Path......Page 420
16.1 Gradient Descent Method as a Control-System......Page 426
16.2 Newton’s Method as a Control-System......Page 429
16.3.1 Continuous-Time Cases......Page 432
16.3.2 Discrete-Time Cases......Page 435
16.4 Vector Based Loops......Page 441
16.5 Matrix Inversion Using Negative Feedback......Page 448
17.1 A Brief Overview......Page 451
17.2 Discrete-Time Linear-Quadratic (LQ) Control-Problem or Linear Regulator......Page 452
17.3 Optimal Output Tracking Problem......Page 457
17.4 Optimal Tracking......Page 459
17.5 Discrete-Time Stochastic Optimal Control......Page 464
17.6 Polynomial or Transfer-Function Methods in LQG Control......Page 466
17.7 Conclusions......Page 473
Conclusions......Page 474
References......Page 476
