Identification of Continuous-time Models from Sampled Data (eBook)

Professor Hugues Garnier was appointed Associate Professor in 1995 at Université Henri Poincaré, Nancy 1. From Sept. 2003 to Aug. 2004, he visited the Centre for Complex Dynamic System and Control, University of Newcastle, Australia. Currently Hugues Garnier is a Professor at Université Henri Poincaré, Nancy 1 where he is the leader of the System Identification Project at the Centre de Recherche en Automatique de Nancy. He is the co-leader of the French working group on "System identification" of the GdR MACS and is member of the IFAC Technical Committee TC-1.1. Modelling, Identification & Signal Processing. He is also a member of the International Program Committe for the IFAC Symposium on System Identification (SYSID'2006), to be held in Newcastle, Australia in March 2006. Professor Hugues Garnier's main research interest is related to analysis and modelling of stochastic dynamical systems. This includes signal processing, time series analysis and prediction, parameter estimation and system identification, especially of continuous-time systems. Professor Hugues Garnier has written several recent contributions on new techniques for continuous-time model identification and organised many invited sessions at international congresses (ECC'1999, World IFAC Congresses 2002 and 2005, SYSID'2003, SYSID'2006) on this research area in the past decade. He is also behind CONTSID, a MATLAB® toolbox for Identification of continuous-time linear models (http://www.iris.cran.uhp-nancy.fr/contsid/). Professor Hugues Garnier has published over 60 research papers and is a regular reviewer for Automatica, Journal of Process Control, International Journal of Control, IEE, and IEEE Journals. Upon completion of her PhD in 1989, Liuping Wang moved from Sheffield to work in the Department of Chemical Engineering, the University of Toronto, Canada for eight years in the field of process control. From the beginning of 1998 to the beginning of 2002, she was a Senior lecturer and Research Coordinator in the Center for Integrated Dynamics and Control, University of Newcastle, Australia. In February 2002, she joined the School of Electrical and Computer Engineering, RMIT University where she is currently an Associate Professor of Control Engineering and the Head of Discipline for Electrical Engineering. Dr Liuping Wang has published more than 100 articles in the areas of process identification, PID controller design, adaptive control, model predictive control and robust control. Her book (Wang and Cluett, Publisher: Taylor and Francis, London, 2000) documented many innovative ideas for process identification and PID controller design. Dr Liuping Wang has been actively engaged in industry-oriented research and development since the completion of her PhD studies. While working at the University of Toronto, Canada, she was the co-founder of an Industry Consortium for identification of chemical processes. Since her arrival at Australia in 1998, she has been working with Australian government organisations and companies in the areas of food manufacturing, mining, automotive and power services, including Food Science Australia, Uncle Ben’s Australia, CSR, BHP-Billiton, Pacific Group Technologies, Holden Innovation, National Power Services. Dr Liuping Wang serves on the editorial board of Journal of Control Engineering and Systems, and is a regular reviewer for Automatica, Journal of Process Control, International Journal of Control, IEE, and IEEE Journals. In recent years, Dr. Liuping Wang has written several journal articles on new techniques and application for continuous time system identification and co-organised several invited sessions at international conferences (IFAC World Congress 2005 and IFAC Symposium on System Identification 2006).

Preface 9
Contents 11
List of Abbreviations and Symbols 19
List of Contributors 23
Salim Ahmed 23
Thierry Bastogne 23
Michel Fliess 23
Hugues Garnier 23
Peter J. Gawthrop 23
Marion Gilson 24
Graham C. Goodwin 24
Biao Huang 24
Rolf Johansson 24
Erik K. Larsson 24
Michel Mensler 24
Magnus Mossberg 24
Rik Pintelon 25
Yves Rolain 25
Johan Schoukens 25
Sirish L. Shah 25
Hebertt Sira-Ram ´ .rez 25
Torsten S¨ oderstr¨ om 25
Paul Van den Hof 25
Zi-Jiang Yang 26
Peter C. Young 26
Juan I. Yuz E. 26
Liuping Wang 26
1 Direct Identification of Continuous-time Models from Sampled Data: Issues, Basic Solutions and Relevance 27
1.1 Introduction 27
1.2 System Identification Problem and Procedure 28
1.3 Basic Discrete-time Model Identification 31
1.4 Issues in Direct Continuous-time Model Identification 33
1.5 Basic Direct Continuous-time Model Identification 35
1.6 Motivations for Identifying Continuous-time Models Directly from Sampled Data 37
1.7 Specialised Topics in System Identification 41
1.8 Historical Review 42
1.9 Outline of the Book 46
1.10 Main References 51
References 52
2 Estimation of Continuous-time Stochastic System Parameters 57
2.1 Background and Motivation 57
2.2 Modelling of Continuous-time Stochastic Systems 59
2.3 Sampling of Continuous-time Stochastic Models 60
2.4 A General Approach to Estimation of Continuous- time Stochastic Models 64
2.5 Introductory Examples 68
2.6 Derivative Approximations for Direct Methods 72
2.7 The Cram ´ er–Rao Bound 80
2.8 Numerical Studies of Direct Methods 84
2.9 Conclusions 88
References 89
3 Robust Identification of Continuous-time Systems from Sampled Data 93
3.1 Overview 94
3.2 Limited-bandwidth Estimation 95
3.3 Robust Continuous-time Model Identification 101
3.4 Conclusions 112
Acknowledgements 113
References 113
4 Refined Instrumental Variable Identification of Continuous- time Hybrid Box – Jenkins Models 117
4.1 Introduction 117
4.2 Problem Formulation 119
4.3 Optimal RIVC Estimation: Theoretical Motivation 122
4.4 The RIVC and SRIVC Algorithms 126
4.5 Theoretical Background and Statistical Properties of the RIVC Estimates 130
4.6 Model Order Identification 134
4.7 Simulation Examples 135
4.8 Practical Examples 145
4.9 Conclusions 153
References 155
5 Instrumental Variable Methods for Closed-loop Continuous- time Model Identification 159
5.1 Introduction 159
5.2 Problem Formulation 161
5.3 Basic Instrumental Variable Estimators 164
5.4 Extended Instrumental Variable Estimators 165
5.5 Optimal Instrumental Variable Estimators 166
5.6 Summary 178
5.7 Numerical Examples 179
5.8 Conclusions 185
References 185
6 Model Order Identification for Continuous- time Models 187
6.1 Introduction 187
6.2 Instrumental Variable Identification 188
6.3 Instrumental Variable Estimation using a Multiple- model Structure 192
6.4 Model Structure Selection Using PRESS 200
6.5 Simulation Studies 205
6.6 Conclusions 211
References 212
7 Estimation of the Parameters of Continuous- time Systems Using Data Compression 215
7.1 Introduction 215
7.2 Data Compression Using Frequency-sampling Filters 215
7.3 Data Compression with Constraints 223
7.4 Physical-model-based Estimation 227
7.5 Example: Inverted Pendulum 229
7.6 Conclusions 236
References 238
8 Frequency-domain Approach to Continuous- time System Identification: Some Practical Aspects 241
8.1 Introduction 241
8.2 The Inter-sample Behaviour and the Measurement Setup 242
8.3 Parametric Models 249
8.4 The Stochastic Framework 253
8.5 Identification Methods 255
8.6 Real Measurement Examples 263
8.7 Guidelines for Continuous-time Modelling 267
8.8 Conclusions 269
References 269
9 The CONTSID Toolbox: A Software Support for Data- based Continuous- time Modelling 275
9.1 Introduction 275
9.2 General Procedure for Continuous-time Model Identification 276
9.3 Overview of the CONTSID Toolbox 276
9.4 Software Description 286
9.5 Advantages and Relevance of the CONTSID Toolbox Methods 297
9.6 Successful Application Examples 301
9.7 Conclusions 311
Acknowledgements 312
References 313
10 Subspace-based Continuous-time Identification 317
10.1 Introduction 317
10.2 Problem Formulation 318
10.3 System Identification Algorithms 322
10.4 Statistical Model Validation 328
10.5 Discussion 332
10.6 Conclusions 334
Acknowledgement 335
References 335
11 Process Parameter and Delay Estimation from Non- uniformly Sampled Data 339
11.1 Introduction 339
11.2 Estimation of Parameters and Delay 341
11.3 Identification from Non-uniformly Sampled Data 350
11.4 Simulation Results 354
11.5 Experimental Evaluation 357
11.6 Conclusions 359
References 361
12 Iterative Methods for Identification of Multiple- input Continuous- time Systems with Unknown Time Delays 365
12.1 Introduction 365
12.2 Statement of the Problem 367
12.3 Approximate Discrete-time Model Estimation 368
12.4 SEPNLS Method 369
12.5 GSEPNLS Method 373
12.6 GSEPNIV Method 377
12.7 Numerical Results 381
12.8 Conclusions 386
References 387
13 Closed-loop Parametric Identification for Continuous- time Linear Systems via New Algebraic Techniques 389
13.1 Introduction 389
13.2 A Module-theoretic Approach to Linear Systems: a Short Summary 390
13.3 Identifiability 394
13.4 Perturbations 396
13.5 First Example: Dragging an Unknown Mass in Open Loop 397
13.6 Second Example: A Perturbed First-order System 403
13.7 Third Example: A Double-bridge Buck Converter 409
13.8 Conclusion 414
References 415
14 Continuous-time Model Identification Using Spectrum Analysis with Passivity- preserving Model Reduction 419
14.1 Introduction 419
14.2 Preliminaries 420
14.3 Problem Formulation 426
14.4 Main Results 427
14.5 Discussion 431
14.6 Conclusions 432
References 432
Index 435