Title Details

Preface  ix

Introduction xiii

Part 1 Analog Feedback Control Systems    1

Chapter 1 Models of Dynamic Processes    3

1.1 Introduction to dynamic processes    3

1.1.1 Definition, hypotheses and notations    3

1.1.2 Implications of hypotheses 4

1.1.3 Dynamic model: an automation perspective   5

1.2 Transfer functions 6

1.2.1 Existence conditions   6

1.2.2 Construction 6

1.2.3 General structure of a transfer function    8

1.2.4 Tools for the analysis of the properties of transfer functions 8

1.2.5 First- and second-order transfer functions   8

1.3 State models    12

1.3.1 Definition 12

1.3.2 Illustrative example    13

1.3.3 General structure of the state model   14

1.4 Linear state models with constant parameters    15

1.4.1 Linearization-based construction    15

1.4.2 Structure of a linear state model with constant parameters   16

1.4.3 Properties of a model without pure input delay (τ0 = 0)   18

1.5 Similarity transformation   20

1.6 Exercises and solutions    21

Chapter 2 Experimental Modeling Approach of Dynamic Processes    39

2.1 Introduction to experimental modeling   39

2.1.1 Problem statement    39

2.1.2 Principle of experimental modeling   39

2.1.3 Experimental modeling methodology    40

2.2 Step response-based modeling 44

2.2.1 Model of order 1    44

2.2.2 Under-damped model of order 2 (ξ < 1)   44

2.2.3 Damped model of order ≥ 2 (Strejc method)   46

2.3 Frequency response-based modeling    50

2.4 Modeling based on ARMA model    52

2.4.1 ARMA model 52

2.4.2 Parameter estimation of an ARMA model   54

2.5 Matlab-aided experimental modeling    56

2.6 Exercises and solutions    58

Chapter 3 Review of Analog Feedback Control Systems    73

3.1 Open-loop analog control   73

3.1.1 Principle    73

3.1.2 Open-loop control    74

3.2 Analog control system    74

3.3 Performances of an analog control system    75

3.3.1 Closed-loop transfer functions    75

3.3.2 Performance quantities    76

3.4 Simple analog controllers   76

3.5 PID/PIDF controllers    77

3.5.1 Structure and role of the parameters of a PID/PIDF controller    77

3.5.2 Ziegler–Nichols methods for parameter calculation    79

3.5.3 Calculation of parameters by pole placement   79

3.5.4 Direct calculation of optimal PID parameters   81

3.5.5 LQR-based indirect calculation of optimal PID parameters    85

3.5.6 Implementation of analog controllers    85

3.6 Controllers described in the state space   86

3.6.1 Principle and block diagram of a linear state feedback    86

3.6.2 Techniques for calculating the state feedback gain    87

3.6.3 Integral action state feedback    88

3.6.4 State feedback with integral action and observer  90

3.6.5 State feedback with output error compensator   92

3.7 Principle of equivalence between PID and LQR controllers    92

3.7.1 Proof of the equivalence principle    93

3.7.2 Equivalence relation   96

3.7.3 Case study 96

3.8 Exercises and solutions    99

Part 2 Synthesis and Computer-aided Simulation of Digital Feedback Control Systems    123

Chapter 4 Synthesis of Digital Feedback Control Systems in the Frequency Domain 125

4.1 Synthesis methodology    125

4.2 Transfer function G(z) of a dynamic process    125

4.2.1 Sampled dynamic model 125

4.2.2 Discretization of Gc(p) if input delay τ0 = 0   126

4.2.3 Discretization of Gc(s) if input delay τ0 # 0   128

4.2.4 Examples of calculation of G(z) by discretization of Gc(s)    132

4.3 Transfer function D(z): discretization method    136

4.3.1 Interest of discretization 136

4.3.2 Discretization of Dc(s) by invariance methods   137

4.3.3 Discretization of Dc(s) by transformation methods    139

4.3.4 z-Transfer functions of simple controllers   142

4.3.5 General structure of D(z) and recurrence equation   144

4.3.6 Discretization of transfer functions with Matlab  145

4.4 Transfer function D(z): model method    146

4.4.1 Principle of the model method    146

4.4.2 Examples of direct design of digital controllers  146

4.4.3 Conditions for the use of model approach   148

4.4.4 Practical rules for using the model approach   149

4.5 Discrete block diagram of digital control    150

4.5.1 Closed-loop characteristic transfer functions   151

4.5.2 Sampling frequency    152

4.6 Exercises and solutions    154

Chapter 5 Computer-aided Simulation of Digital Feedback Control Systems 177

5.1 Approaches to computer-aided simulation    177

5.2 Programming of joint recurrence equations    178

5.2.1 Formulation 178

5.2.2 Example of Matlab® programming   179

5.3 Simulation using Matlab macro programming   183

5.4 Graphic simulation    186

5.5 Case study: simulation of servomechanisms    187

5.5.1 Simulation of a speed servomechanism    187

5.5.2 Simulation of a position servomechanism   191

5.6 Exercises and solutions    194

Chapter 6 Discrete State Models of Dynamic Processes    199

6.1 Discretization of the state model of a dynamic process    199

6.1.1 Discretization of a state model    200

6.1.2 Discretization of a state model with input delay  201

6.2 Calculation of {A, B, C, D} parameters of a discrete state model    204

6.2.1 Calculation of A = eAT    204

6.2.2 Calculation of B    206

6.2.3 Calculation of C and D    208

6.3 Properties of a discrete state model {A, B, C, D}   208

6.3.1 Infinity of state models of one dynamic process  208

6.3.2 Stability    209

6.3.3 Controllability and stabilizability    209

6.3.4 Observability and detectability    210

6.4 Exercises and solutions    210

Appendices 215

Appendix 1 Table of Z-transforms 217

Appendix 2 Matlab® Elements Used in This Book   219

Bibliography 223

Index 227