Modeling and Identification of Dynamic Systems

1 Systems and Models 11

1 1 To Describe Reality with Models 11

1 2 Systems and Experiments 11

1 3 What is a Model? 13

1 4 Models and Simulation 14

1 5 How to Build Models 14

1 6 How to Verify Models 15

1 7 What are Models Used for? 17

1 8 Modeling as a Scientific Discipline 18

 

2 Examples of Models 19

2 1 Introduction 19

2 2 An Ecological System 19

2 3 A Flow System 22

2 4 A Simple Electrical Circuit 27

2 5 Models of Human Speech 28

2 6 A Connected Mechanical System 30

2 7 Model Characteristics 31

2 8 Comments 33

 

3 Types of Models 35

3 1 Models 35

3 2 Black Boxes and Simple Experiments 38

3 3 Variables and Signals 49

3 4 State-space Models 53

3 5 Stationary Solutions and Linearization 55

3 6 Connecting State-space Models 62

3 7 Comments 64

 

4 Principles of Physical Modeling 65

4 1 Introduction 65

4 2 The Phases of Modeling 65

4 3 What are the Requirements for a Modeling Tool? 69

4 4 Dimensionless Variables and Scaling 72

4 5 Simplified Models 83

4 6 Comments 90

4 7 Appendix 90

 

5 Some Basic Relationships in Physics 93

5 1 Introduction 93

5 2 Electrical Circuits 93

5 3 Mechanical Translation 98

5 4 Mechanical Rotation 102

5 5 Flow Systems 105

5 6 Thermal Systems 109

5 7 Domain Independent Modeling 112

5 8 Connecting Different Domains 113

5 9 Comments 115

 

6 Bond Graphs 117

6 1 Efforts and Flows 117

6 2 Junctions 120

6 3 Simple Bond Graphs 124

6 4 Transformers and Gyrators 126

6 5 Systems with Mixed Physical Variables 127

6 6 Simplifications in Bond Graphs 130

6 7 From Bond Graphs to Equations – Causality 133

6 8 Causality and Equations 141

6 9 Controlled Elements 146

6 10 Systematic Bond Graph Modeling 151

6 11 Further Remarks 154

6 12 Comments 156

 

7 DAE Models 157

7 1 Introduction 157

7 2 DAE Models 157

7 3 Linear DAE Systems 160

7 4 Nonlinear DAE models 166

7 5 DAE Models and Model Simplification 168

7 6 Comments 174

7 7 Appendix 174

 

8 Object-oriented Modeling 177

8 1 Introduction 177

8 2 Model Libraries and Graphical Interfaces 178

8 3 Object-oriented Modeling – Simscape and Modelica 179

8 4 Model Libraries and Model Extensions 184

8 5 Aggregated Models in Modelica 188

8 6 Equation-based Models 191

8 7 Comments 192

 

9 Models with Disturbances 193

9 1 Discrete Time Models 193

9 2 Disturbances in Dynamic Models 195

9 3 Description of Signals in the Time Domain 200

9 4 Description of Signals in the Frequency Domain 203

9 5 Linking Continuous Time and Discrete Time Models 211

9 6 Comments 218

9 7 Appendix 220

 

10 Correlation and Spectral Analysis 221

10 1 Correlation Analysis 221

10 2 Fourier Analysis 224

10 3 Estimation of Signal Spectra from Discrete Time Data 228

10 4 Estimating Transfer Functions Using Spectral Analysis 237

10 5 Comments 241

10 6 Appendix 242

 

11 Parameter Estimation in Linear Models 247

11 1 Grey-box Models 248

11 2 Linear Black-Box Models 251

11 3 Fitting Parameterized Models to Data 259

11 4 Model Properties 267

11 5 Comments 278

11 6 Appendix 279

 

12 Parameter Estimation in Nonlinear Models 283

12 1 The Basic Principle – Minimize the Prediction Errors 283

12 2 Light-Grey-Box Nonlinear Models 284

12 3 Dark-Grey-box Nonlinear Models 291

12 4 Neural Network as Nonlinear Black-box Models 302

12 5 Parameter Estimation Techniques 309

12 6 Comments 311

12 7 Appendix: Derivatives of the Prediction Function 312

 

13 System Identification as a Tool for Modeling 315

13 1 Program Packages for Identification 316

13 2 Design of Identification Experiments 318

13 3 Post-treatment of Data 325

13 4 Choice of Model Structure 331

13 5 Model Validation 339

13 6 An Example 342

13 7 Comments 346

 

14 Simulation of Mathematical Models 349

14 1 Introduction 349

14 2 Simulating State-space Models 349

14 3 Solution Methods for DAE Models 359

14 4 Comments 360

 

15 Model Validation and Model Use 361

15 1 Model Validation 361

15 2 Domain of Validity of the Model 364

15 3 Remaining Critical of the Model 365

15 4 Use of Several Models 368

 

A Linear Systems: Description and Properties 369

A 1 Continuous Time Systems 369

A 2 Discrete Time Models 371

A 3 Links between Continuous and Discrete Time Models 373

A 4 Alias 373

 

B Linearization 377

B 1 Continuous Time Models 377

B 2 Discrete Time Models 379

 

C Random Variables and Stochastic Processes 381

C 1 Probabilities and Random Variables 381

C 2 Stochastic Processes 384

C 3 Two Basic Convergence Concepts 385

 

D Signal Spectra 387

D 1 Time-continuous Deterministic Signal with Finite Energy 387

D 2 Sampled Deterministic Signals with Finite Energy 388

D 3 Signals with Infinite Energy: The Power Spectrum 389

D 4 Connections between the Continuous and the Sampled Signals 390

D 5 Stochastic Processes 391