Solved problems in dynamical systems and control / J. Tenreiro Machado [and three others].

Format:

Book

Author/Creator:

Machado, J. A. Tenreiro, author.

Series:

IET control, robotics and sensors series ; 107.

IET control, robotics and sensors series ; 107

Language:

English

Subjects (All):

Differentiable dynamical systems.

Physical Description:

ix, 437 pages ; 24 cm.

Place of Publication:

Stevenage, Herts : Institute of Engineering and Technology, 2016.

Contents:

1 Block diagram algebra and system transfer functions 1

1.1 Fundamentals 1

1.1.1 List of symbols 1

1.1.2 Laplace transform and Laplace domain 1

1.1.3 Transfer function 2

1.1.4 Block diagram 2

1.1.5 Block diagram algebra 3

1.2 Worked examples 3

1.3 Proposed exercises 9

1.4 Block diagram analysis using computer packages 20

1.4.1 MATLAB 20

1.4.2 SCILAB 24

1.4.3 OCTAVE 26

2 Mathematical models 29

2.1 Fundamentals 29

2.1.1 List of symbols 29

2.1.2 Modeling of electrical systems 31

2.1.3 Modeling of mechanical systems 32

2.1.4 Modeling of liquid-level systems 36

2.1.5 Modeling of thermal systems 38

2.2 Worked examples 39

2.24 Electrical systems 39

2.2.2 Mechanical systems 40

2.2.3 Liquid-level systems 42

2.2.4 Thermal systems 45

2.3 Proposed exercises 47

2.3.1 Electrical systems 47

2.3.2 Mechanical systems 53

2.3.3 Liquid-level systems 60

2.3.4 Thermal systems 68

3 Analysis of continuous systems in the time domain 73

3.1 Fundamentals 73

3.1.1 List of symbols 73

3.1.2 Time response of a continuous LTI system 74

3.1.3 Time response of first-order systems 74

3.1.4 Time response of second-order systems 77

3.1.5 Routh's stability criterion 84

3.1.6 Steady-state errors 85

3.2 Worked examples 86

3.2.1 Routh-Hurwitz criterion 86

3.2.2 Transient response 87

3.2.3 Steady-state errors 89

3.3 Proposed exercises 89

3.3.1 Routh-Hurwitz criterion 89

3.3.2 Transient response 94

3.3.3 Steady-state errors 102

3.4 Time response analysis using computer packages 107

3.4.1 MATLAB 108

3.4.2 SCILAB 110

3.4.3 OCTAVE 112

4 Root-locus analysis 115

4.1 Fundamentals 115

4.1.1 List of symbols 115

4.1.2 Root-locus preliminaries 115

4.1.3 Root-locus practical sketching rules (K > 0) 117

4.1.4 Root-locus practical sketching rules (K < 0) 118

4.2 Solved problems 119

4.3 Proposed problems 124

4.4 Root-locus analysis using computer packages 131

4.4.1 MATLAB 131

4.4.2 SCILAB 132

4.4.3 OCTAVE 133

5 Frequency domain analysis 135

5.1 Fundamentals 135

5.1.1 List of symbols 135

5.1.2 Frequency response preliminaries 136

5.1.3 Bode diagram 136

5.1.4 Nyquist diagram 137

5.1.5 Nichols diagram 139

5.1.6 Nyquist stability 139

5.1.7 Relative stability 140

5.2 Solved problems 142

5.2.1 Bode diagram and phase margins 142

5.2.2 Nyquist and Nichols diagrams 145

5.3 Proposed problems 148

5.3.1 Bode diagram and phase margins 148

5.3.2 Nyquist and Nichols diagrams 160

5.3.3 Root-locus and frequency domain analysis 164

5.4 Frequency domain analysis using computer packages 173

5.4.1 MATLAB 173

5.4.2 SCILAB 177

5.4.3 OCTAVE 181

6 PID controller synthesis 185

6.1 Fundamentals 185

6.1.1 List of symbols 185

6.1.2 The PID controller 185

6.1.3 PID tuning 187

6.2 Solved problems 190

6.3 Proposed problems 191

7 State space analysis of continuous systems 195

7.1 Fundamentals 195

7.1.1 List of symbols 195

7.1.2 State space representation 196

7.1.3 The Cayley-Hamilton theorem 203

7.1.4 Matrix exponential 203

7.1.5 Computation of the matrix exponential 204

7.1.6 Solution of the state-space equation 206

7.1.7 Controllability 207

7.1.8 Observability 207

7.2 Solved problems 207

7.3 Proposed problems 215

7.4 State space analysis of continuous systems using computer packages 237

7.4.1 MATLAB 237

7.4.2 SCILAB 240

7.4.3 OCTAVE 242

8 Controller synthesis by pole placement 245

8.1 Fundamentals 245

8.1.1 List of symbols 245

8.1.2 Pole placement using an input-output representation 246

8.1.3 Preliminaries of pole placement in state space 248

8.1.4 Calculation of the feedback gain 250

8.1.5 Estimating the system state 250

8.1.6 Calculation of the state estimator gain 252

8.1.7 Simultaneous pole placement and state estimation 253

8.2 Solved problems 254

8.2.1 Pole placement using an input-output representation 254

8.2.2 Pole placement in state space 256

8.3 Proposed problems 257

8.3.1 Pole placement using an input-output representation 257

8.3.2 Pole placement in state space 262

9 Discrete-time systems and F-transform 265

9.1 Fundamentals 265

9.1.1 List of symbols 265

9.1.2 Discrete-time systems preliminaries 266

9.1.3 The F-transform 267

9.1.4 Discrete-time models 268

9.1.5 Controllability and observability 271

9.1.6 Stability and the Routh-Hurwitz criterion 272

9.2 Solved problems 272

9.3 Proposed problems 276

9.4 Discrete-time systems and F-transform analysis using computer packages 283

9.4.1 MATLAB 283

9.4.2 SCILAB 285

9.4.3 OCTAVE 286

10 Analysis of nonlinear systems with the describing function method 287

10.1 Fundamentals 287

10.1.1 List of symbols 287

10.1.2 The describing function 287

10.1.3 Describing functions of common nonlinearities 288

10.1.4 Nonlinear systems analysis 288

10.2 Solved problems 290

10.3 Proposed problems 292

10.4 Describing function method using computer packages 310

10.4.1 MATLAB 311

10.4.2 SCILAB 313

10.4.3 OCTAVE 315

11 Analysis of nonlinear systems with the phase plane method 317

11.1 Fundamentals 317

11.1.1 List of symbols 317

11.1.2 Phase plane method preliminaries 317

11.1.3 Singular points 318

11.1.4 Limit cycles 319

11.2 Solved problems 320

11.3 Proposed problems 324

11.4 Phase plane analysis using computer packages 336

11.4.1 MATLAB 336

11.4.2 SCILAB 337

11.4.3 OCTAVE 339

12 Fractional order systems and controllers 341

12.1 Fundamentals 341

12.1.1 List of symbols 341

12.1.2 Grünwald-Letnikov definition 341

12.1.3 Riemann-Liouville definition 342

12.1.4 Equivalence of definitions and Laplace transforms 343

12.1.5 Caputo definition 343

12.1.6 Fractional transfer functions 344

12.1.7 Fractional controllers 346

12.1.8 Integer approximations 346

12.2 Solved problems 347

12.3 Proposed problems 352

12.4 Fractional control using computer packages 358

12.4.1 MATLAB 358

12.4.2 SCILAB 361

12.4.3 OCTAVE 363.

ISBN:

9781785611742

1785611747

OCLC:

957505564

Publisher Number:

99975320300