Advances in Industrial Control

By: Hugues Garnier (Editor), Liuping Wang (Editor)

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Hardcover | 28 March 2008

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Identification of Continuous-time Models from Sampled Data presents an up-to-date view of this active area of research, describing recent methods and software tools and offering new results in areas such as: time and frequency domain optimal statistical approaches to identification; parametric identification for linear, nonlinear and stochastic systems; identification using instrumental variable, subspace and data compression methods; closed-loop and robust identification; and continuous-time modeling from non-uniformly sampled data and for systems with delay.

The CONTSID toolbox discussed in the final chapter gives an overview of developments and practical examples in which MATLAB^(R) can be used for direct time-domain identification of continuous-time systems. A valuable reference for a broad audience drawn from researchers and graduate students in signal processing as well as in systems and control this book also covers material suitable for specialised graduate courses in these areas.

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Published: 21st October 2010

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List of Abbreviations and Symbols	p. xviii
List of Contributors	p. xxiii
Direct Identification of Continuous-time Models from Sampled Data: Issues, Basic Solutions and Relevance	p. 1
Introduction	p. 1
System Identification Problem and Procedure	p. 2
Basic Discrete-time Model Identification	p. 5
Difference Equation Models	p. 5
The Traditional Least Squares Method	p. 5
Example: First-order Difference Equation	p. 6
Models for the Measurement Noise	p. 7
Issues in Direct Continuous-time Model Identification	p. 7
Differential Equation Models	p. 7
Input-Output Time Derivatives	p. 8
Models for the Measurement Noise	p. 8
Basic Direct Continuous-time Model Identification	p. 9
The Traditional State-variable Filter Method	p. 9
Example: First-order Differential Equation	p. 11
Motivations for Identifying Continuous-time Models Directly from Sampled Data	p. 11
Physical Insight into the System Properties	p. 12
Preservation of a priori Knowledge	p. 12
Inherent Data Filtering	p. 13
Non-uniformly Sampled Data	p. 13
Transformation between CT and DT Models	p. 13
Sensitivity Problems of DT Models at High Sampling Rates	p. 14
Stiff Systems	p. 14
Specialised Topics in System Identification	p. 15
Identification of the Model Structure	p. 15
Identification of Pure Time (Transportation) Delay	p. 15
Identification of Continuous-time Noise Models	p. 15
Identification of Multi-variable Systems	p. 16
Identification in Closed Loop	p. 16
Identification in the Frequency Domain	p. 16
Software for Continuous-time Model Identification	p. 16
Historical Review	p. 16
Outline of the Book	p. 20
Main References	p. 25
References	p. 26
Estimation of Continuous-time Stochastic System Parameters	p. 31
Background and Motivation	p. 31
Modelling of Continuous-time Stochastic Systems	p. 33
Sampling of Continuous-time Stochastic Models	p. 34
Sampling of CARMA Systems	p. 35
Sampling of Systems with Inputs	p. 37
A General Approach to Estimation of Continuous-time Stochastic Models	p. 38
Direct and Indirect Methods	p. 40
Introductory Examples	p. 42
Derivative Approximations for Direct Methods	p. 46
Non-uniformly Sampled Data	p. 52
The Cramér-Rao Bound	p. 54
The Cramér-Rao Bound for Irregularly Sampled CARMA Models	p. 55
Numerical Studies of Direct Methods	p. 58
Conclusions	p. 62
References	p. 63
Robust Identification of Continuous-time Systems from Sampled Data	p. 67
Overview	p. 68
Limited-bandwidth Estimation	p. 69
Frequency-domain Maximum Likelihood	p. 72
Robust Continuous-time Model Identification	p. 75
Effect of Sampling Zeros in Deterministic Systems	p. 75
Effect of Sampling Zeros in Stochastic Systems	p. 79
Continuous-time Undermodelling	p. 82
Restricted-bandwidth FDML Estimation	p. 84
Conclusions	p. 86
References	p. 87
Refined Instrumental Variable Identification of Continuous-time Hybrid Box-Jenkins Models	p. 91
Introduction	p. 91
Problem Formulation	p. 93
Optimal RIVC Estimation: Theoretical Motivation	p. 96
The Hybrid Box-Jenkins Estimation Model	p. 96
RIVC Estimation	p. 97
The RIVC and SRIVC Algorithms	p. 100
The RIVC Algorithm	p. 100
The SRIVC Algorithm	p. 101
Multiple-input Systems	p. 103
Non-uniformly Sampled Data	p. 103
Theoretical Background and Statistical Properties of the RIVC Estimates	p. 104
Optimality of RIVC Estimation	p. 104
The Asymptotic Independence of the System and Noise Model Parameter Estimates	p. 105
Model Order Identification	p. 108
Simulation Examples	p. 109
The Rao Garnier Test System	p. 109
Noise-free Case	p. 110
Noisy-output Case	p. 112
Practical Examples	p. 119
Hadley Centre Global Circulation Model (GCM) Data	p. 120
A Multiple-input Winding Process	p. 122
Conclusions	p. 127
References	p. 129
Instrumental Variable Methods for Closed-loop Continuous-time Model Identification	p. 133
Introduction	p. 133
Problem Formulation	p. 135
Basic Instrumental Variable Estimators	p. 138
Consistency Properties	p. 138
Accuracy Analysis	p. 139
Extended Instrumental Variable Estimators	p. 139
Consistency Properties	p. 140
Accuracy Analysis	p. 140
Optimal Instrumental Variable Estimators	p. 140
Main Results	p. 140
Implementation Issues	p. 141
Multi-step Approximate Implementations of the Optimal IV Estimate	p. 144
Iterative Implementations of the Optimal IV Estimate	p. 147
Summary	p. 152
Numerical Examples	p. 153
Example 1: White Noise	p. 154
Example 2: Coloured Noise	p. 155
Conclusions	p. 159
References	p. 159
Model Order Identification for Continuous-time Models	p. 161
Introduction	p. 161
Instrumental Variable Identification	p. 162
Instrumental Variable Estimation using a Multiple-model Structure	p. 166
Augmented Data Regressor	p. 166
Instrumental Variable Solution Using UDV Factorisation	p. 168
Computational Procedure	p. 172
Model Structure Selection Using PRESS	p. 174
Simulation Studies	p. 179
Conclusions	p. 185
References	p. 186
Estimation of the Parameters of Continuous-time Systems Using Data Compression	p. 189
Introduction	p. 189
Data Compression Using Frequency-sampling Filters	p. 189
FSF Model	p. 190
FSF Model in Data Compression	p. 192
Estimation Using FSF Structure	p. 195
Data Compression with Constraints	p. 197
Formulation of the Constraints	p. 197
Solution of the Estimation Problem with Constraints	p. 198
Monte Carlo Simulation Study	p. 199
Physical-model-based Estimation	p. 201
Example: Inverted Pendulum	p. 203
FSF Estimation	p. 205
PMB Estimation	p. 207
Conclusions	p. 210
References	p. 212
Frequency-domain Approach to Continuous-time System Identification: Some Practical Aspects	p. 215
Introduction	p. 215
The Inter-sample Behaviour and the Measurement Setup	p. 216
Plant Modelling	p. 216
Noise Modelling	p. 220
Summary	p. 222
Parametric Models	p. 223
Plant Models	p. 223
Noise Models	p. 225
Summary	p. 226
The Stochastic Framework	p. 227
Periodic Excitations	p. 227
Arbitrary Excitations	p. 228
Identification Methods	p. 229
Asymptotic Properties of the Frequency-domain Gaussian Maximum Likelihood Estimators	p. 231
Periodic Excitations	p. 231
Arbitrary Excitations: Generalised Output Error	p. 234
Arbitrary Excitations: Errors-in-variables	p. 236
Real Measurement Examples	p. 237
Operational Amplifier	p. 237
Flight-flutter Analysis	p. 240
Guidelines for Continuous-time Modelling	p. 241
Prime Choice: Uniform Sampling, Band-limited Measurement Setup, Periodic Excitation	p. 241
Second Choice: Uniform Sampling, Band-limited Measurement Setup, Arbitrary Excitation	p. 242
Third Choice: Uniform Sampling, Zero-order-hold Measurement Setup	p. 242
Last Resort: Non-uniform Sampling	p. 243
To be Avoided	p. 243
Conclusions	p. 243
References	p. 243
The CONTSID Toolbox: A Software Support for Data-based Continuous-time Modelling	p. 249
Introduction	p. 249
General Procedure for Continuous-time Model Identification	p. 250
Overview of the CONTSID Toolbox	p. 250
Parametric Model Estimation	p. 250
Model Order Selection and Validation	p. 256
Software Description	p. 260
Introductory Example to the Command Mode	p. 261
The Graphical User Interface	p. 267
Advantages and Relevance of the CONTSID Toolbox Methods	p. 271
Successful Application Examples	p. 275
Complex Flexible Robot Arm	p. 275
Uptake Kinetics of a Photosensitising Agent into Cancer Cells	p. 278
Multi-variable Winding Process	p. 283
Conclusions	p. 285
References	p. 287
Subspace-based Continuous-time Identification	p. 291
Introduction	p. 291
Problem Formulation	p. 292
Discrete-time Measurements	p. 292
Continuous-time State-space Linear System	p. 293
System Identification Algorithms	p. 296
Theoretical Remarks on the Algorithms	p. 299
Numerical Example	p. 301
Statistical Model Validation	p. 302
Discussion	p. 306
Conclusions	p. 308
References	p. 309
Process Parameter and Delay Estimation from Non-uniformly Sampled Data	p. 313
Introduction	p. 313
Estimation of Parameters and Delay	p. 315
Second-order Modelling	p. 315
Higher-order Modelling	p. 318
Treatment of Initial Conditions	p. 320
Parameter Estimation	p. 321
Non-minimum Phase Processes	p. 323
Choice of <$>\hat A_0(s)<$> and <$>\hat {\tau}_0<$>	p. 324
Identification from Non-uniformly Sampled Data	p. 324
The Iterative Prediction Algorithm	p. 324
Input-only Modelling Using Basis-function Model	p. 325
Choice of Basis-function Parameters	p. 327
Criterion of Convergence	p. 328
Simulation Results	p. 328
Estimation from Uniformly Sampled Data	p. 329
Estimation from Non-uniformly Sampled Data	p. 330
Experimental Evaluation	p. 331
Identification of a Dryer	p. 331
Identification of a Mixing Process	p. 332
Conclusions	p. 333
References	p. 335
Iterative Methods for Identification of Multiple-input Continuous-time Systems with Unknown Time Delays	p. 339
Introduction	p. 339
Statement of the Problem	p. 341
Approximate Discrete-time Model Estimation	p. 342
SEPNLS Method	p. 343
GSEPNLS Method	p. 347
GSEPNIV Method	p. 351
Numerical Results	p. 355
GSEPNLS Method in the Case of Low Measurement Noise	p. 357
GSEPNIV Method	p. 358
Conclusions	p. 360
References	p. 361
Closed-loop Parametric Identification for Continuous-time Linear Systems via New Algebraic Techniques	p. 363
Introduction	p. 363
A Module-theoretic Approach to Linear Systems: a Short Summary	p. 364
Some Basic Facts about Modules over Principal Ideal Rings	p. 364
Formal Laplace Transform	p. 365
Basic System-theoretic Definitions	p. 366
Transfer Matrices	p. 367
Identifiability	p. 368
Uncertain Parameters	p. 368
The Algebraic Derivative and a New Module Structure	p. 368
Linear Identifiability	p. 368
An Elementary Example	p. 369
Perturbations	p. 370
Structured Perturbations	p. 370
Unstructured Perturbations	p. 370
Linear Identifier	p. 371
Robustness	p. 371
First Example: Dragging an Unknown Mass in Open Loop	p. 371
Description and First Results	p. 371
Denoising	p. 374
A Comparison with an Adaptive-observer Approach	p. 376
Second Example: A Perturbed First-order System	p. 377
Presentation	p. 377
A Certainty Equivalence Controller	p. 378
Parameter Identification	p. 378
Noise-free Simulation Results	p. 380
Noisy Measurements and Plant Perturbations	p. 381
Simulation Results with Noises	p. 381
Comparison with Adaptive Control	p. 381
Simulations for the Adaptive Scheme	p. 383
Third Example: A Double-bridge Buck Converter	p. 383
An Input-Output Model	p. 384
Problem Formulation	p. 385
A Certainty Equivalence Controller	p. 385
Closed-loop Behaviour	p. 385
Algebraic Determination of the Unknown Parameters	p. 386
Simulation Results	p. 387
Conclusion	p. 388
References	p. 389
Continuous-time Model Identification Using Spectrum Analysis with Passivity-preserving Model Reduction	p. 393
Introduction	p. 393
Preliminaries	p. 394
Continuous-time Model Identification	p. 394
Spectrum Analysis and Positivity	p. 396
Spectral Factorisation and Positivity	p. 399
Balanced Model Reduction	p. 399
Problem Formulation	p. 400
Main Results	p. 401
Discussion	p. 405
Conclusions	p. 406
References	p. 406
Index	p. 409
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Advances in Industrial Control

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