Control-oriented modelling and identification : theory and practice

This comprehensive book covers the state-of-the-art in control-oriented modelling and identification techniques. With contributions from leading researchers in the subject, Control-oriented Modelling and Identification: Theory and practice covers the main methods and tools available to develop advanced mathematical models suitable for control system design, including: object-oriented modelling and simulation; projection-based model reduction techniques; integrated modelling and parameter estimation; identification for robust control of complex systems; subspace-based multi-step predictors for predictive control; closed-loop subspace predictive control; structured nonlinear system identification; and linear fractional LPV model identification from local experiments using an H1-based glocal approach.

This book also takes a practical look at a variety of applications of advanced modelling and identification techniques covering spacecraft dynamics, vibration control, rotorcrafts, models of anaerobic digestion, a brake-by-wire racing motorcycle actuator, and robotic arms.

rotorcrafts, models of anaerobic digestion, a brake-by-wire racing motorcycle actuator, and robotic arms.rotorcrafts, models of anaerobic digestion, a brake-by-wire racing motorcycle actuator, and robotic arms.rotorcrafts, models of anaerobic digestion, a brake-by-wire racing motorcycle actuator, and robotic arms.

Marco LoveraFrancesco CasellaPierre Vuiilemin and Charles Poussot-Vassal and Daniel Alazard AbstractMarco Lovera and Francesco CasellaTom Oomen and Maarien SteinbuchMarzia Cescon and Rolf JohanssonGijs van der Veen and Jan-Willem van Wingerden and Michel VerhaegenTyrone Vincent and Karneshwar Poolla and Carlo NovaraDaniel Vizer and Guillaume Mercère and Edouard Laroche and Olivier ProtMarco Lovera and Francesco CasellaCharles Poussot-Vassal and Clement Roos and Pierre Vuillemin and Olivier Cantinaud and Jean-Patrick LacosteGijs van der Veen and Jan-Willem van Wingerden and Michel VerhaegenMarco Bergamasco and Marco LoveraAlessandro Delia Bona and Gianni Ferretti and Elena Ficara and France sea MalpeiMatteo Corno and Fabio Todeschini and Giulio Panzani and Sergio M. SavaresiDaniel Vizer and Guillaume Mercère and Edouard Laroche and Olivier Prot

1 Introduction to control-oriented modelling	p. 1
Abstract	p. 1
1.1 Introduction	p. 1
1.1.1 Detailed models for system simulation	p. 2
1.1.2 Compact models for control design	p. 3
1.1.3 Building models for control system synthesis	p. 3
1.2 Overview of the book	p. 5
1.2.1 Part 1: theory	p. 5
1.2.2 Part 2: applications	p. 6
2 Object-oriented modelling and simulation of physical systems	p. 9
Abstract	p. 9
2.1 Introduction	p. 9
2.2 Basic concepts and principles	p. 10
2.3 Modelica	p. 14
2.4 Mathematical processing of OO models	p. 20
2.5 Plant modelling, analysis and identification	p. 25
2.6 Control system performance verification	p. 26
2.7 Direct use of OO models for optimal control	p. 28
2.8 Conclusions	p. 32
References	p. 32
3 Projection-based model reduction techniques	p. 35
3.1 Introduction	p. 35
3.1.1 Motivations	p. 35
3.1.2 Model reduction by projection	p. 38
3.2 Model reduction by truncation	p. 41
3.2.1 State-space truncation and residualization	p. 41
3.2.2 Balanced truncation	p. 45
3.2.3 Conclusion	p. 57
3.3 Moment matching methods	p. 59
3.3.1 Moment matching through Krylov subspaces	p. 59
3.3.2 H 2 optimal model reduction	p. 66
3.3.3 Conclusion	p. 74
3.4 Conclusion	p. 74
References	p. 74
4 Integrated modelling and Parameter estimation: an LFR-Modelica approach	p. 77
Abstract	p. 77
4.1 Introduction	p. 77
4.2 Applicable models and LFRs	p. 78
4.2.1 Applicable plant models	p. 78
4.2.2 Linear fractional representations	p. 79
4.3 Transformation of non-linear DAE models into LFR	p. 80
4.3.1 Definitions and assumptions	p. 80
4.3.2 Re-ordering of the system equations	p. 82
4.3.3 Elimination of known parameters	p. 83
4.3.4 Solving the system equations	p. 84
4.3.5 Formulation of the system equations as a cascaded connection of LFRs	p. 85
4.3.6 Construction of the LFR of the DAE	p. 87
4.3.7 Implementation of the algorithm	p. 89
4.3.8 Simulation of the LFR	p. 90
4.4 Application example: identification of LFR models	p. 91
4.5 Conclusions	p. 98
References	p. 99
5 Identification for robust control of complex systems: algorithm and motion application	p. 101
Abstract	p. 101
5.1 Introduction	p. 101
5.2 Coprime factor identification for refined uncertainty structures in robust control	p. 103
5.2.1 Robust control framework	p. 103
5.2.2 Identification for robust control approach	p. 105
5.2.3 Identifying robust-control-relevant coprime factorizations	p. 107
5.3 Generalized SK-iterations for closed-loop coprime factor identification	p. 108
5.3.1 Model parameterization	p. 108
5.3.2 Frequency domain identification involving l∞-norms via Lawson's algorithm	p. 109
5.3.3 A closed-loop generalization of SK iterations	p. 110
5.4 Orthogonal polynomials w.r.t. a data-dependent discrete inner product	p. 111
5.5 Experimental application	p. 112
5.5.1 Experimental system	p. 112
5.5.2 Coprime factor identification results	p. 115
5.5.3 Numerical conditioning	p. 118
5.5.4 Illustration of robust-control-relevance	p. 119
5.6 Conclusions	p. 121
Acknowledgments	p. 121
References	p. 122
6 Subspace-based multi-step predictors for predictive control	p. 125
Abstract	p. 125
6.1 Introduction	p. 125
6.1.1 Model description	p. 126
6.1.2 Notation	p. 127
6.1.3 Statement of the problem	p. 128
6.2 Subspace-based linear multi-step predictors	p. 128
6.2.1 Computing projections	p. 130
6.3 Example	p. 132
6.3.1 Diabetes mellitus	p. 132
6.3.2 Experimental conditions	p. 133
6.3.3 Prediction strategy	p. 133
6.3.4 Results	p. 134
6.4 Discussion and conclusions	p. 139
References	p. 140
7 Closed-loop subspace predictive control	p. 143
Abstract	p. 143
7.1 Introduction	p. 143
7.2 Discrete-time identification framework	p. 144
7.2.1 Preliminaries and notation	p. 146
7.2.2 Data equations	p. 146
7.2.3 Relation to the ARX model structure	p. 147
7.2.4 Closed-loop identification issues	p. 148
7.2.5 Estimating the predictor Markov parameters	p. 148
7.2.6 Recursive solution of the parameter estimation problem	p. 149
7.2.7 Using directional forgetting	p. 150
7.3 Deriving the subspace predictor	p. 151
7.4 Setting up the predictive control problem	p. 152
7.4.1 Real time solution of the QP	p. 154
7.4.2 Parameter selection	p. 154
7.5 Concluding remarks	p. 155
7.5.1 Algorithm summary	p. 155
References	p. 155
8 Structured nonlinear system identification	p. 159
Abstract	p. 159
8.1 Introduction	p. 159
8.2 Specification of model structures using the LFR	p. 160
8.2.1 Simple examples with linear N	p. 163
8.2.2 Simple examples with nonlinear N	p. 165
8.2.3 LFRs of block-oriented models	p. 166
8.2.4 Discussion: L known or unknown?	p. 167
8.3 Examples of model structure specification	p. 168
8.3.1 High-dimensional model representation	p. 168
8.3.2 Automobile suspension	p. 169
8.3.3 Nonlinear friction: drill-string	p. 171
8.3.4 Linear parameter varying systems	p. 172
8.4 Properties of the LFR model structure	p. 174
8.4.1 Measurability	p. 174
8.4.2 Identifiability	p. 175
8.4.3 Persistence of excitation	p. 176
8.5 Identification algorithms	p. 176
8.5.1 Parametric estimates	p. 176
8.5.2 Nonparametric estimates	p. 178
8.6 Identification example	p. 183
References	p. 186
9 Linear fractional LPV model identification from local experiments using an Hco-based glocal approach	p. 189
Abstract	p. 189
9.1 Introduction	p. 189
9.2 Identification method	p. 192
9.2.1 Problem formulation, definitions, and notations	p. 192
9.2.2 Determination of the structure of L(s, ¿(p), )	p. 195
9.2.3 Woe-based optimization technique	p. 197
9.2.4 Computing the H∞-norm	p. 199
9.2.5 Minimizing the H∞-norm	p. 200
9.3 Identification results	p. 202
9.3.1 System description	p. 202
9.3.2 Linear fractional LPV model identification	p. 203
9.3.3 Validation	p. 207
9.4 Conclusions	p. 210
References	p. 211
10 Object-oriented modelling of spacecraft dynamics: tools and case studies	p. 215
Abstract	p. 215
10.1 Introduction	p. 215
10.2 The Modelica Space Flight Dynamics library	p. 217
10.3 Structure of the spacecraft simulation models	p. 220
10.3.1 Extended World model	p. 220
10.3.2 SpacecraftDynamics model	p. 221
10.3.3 Spacecraft model	p. 223
10.4 Case studies	p. 226
10.4.1 Assessing external disturbances via dynamic inversion	p. 226
10.4.2 Magnetic detumbling for small satellite attitude control	p. 228
10.5 Concluding remarks	p. 237
References	p. 237
11 Control-oriented aeroelastic BizJet low-order LFT modeling	p. 241
Abstract	p. 241
11.1 Introduction	p. 241
11.1.1 Foreword on the Dassault-Aviation BizJet models	p. 241
11.1.2 The BizJet aircraft aeroelatic control problem	p. 242
11.1.3 Mathematical problem formulation	p. 243
11.1.4 Structure and notation	p. 245
11.2 Multi-LTI model approximation and interpolation algorithm overview	p. 245
11.3 Frequency-limited large-scale MIMO multi-LTI models approximation	p. 247
11.3.1 Preliminaries on projection-based LTI model approximation	p. 248
11.3.2 Large-scale single-LTI model approximation procedure	p. 248
11.3.3 Large-scale multi-LTI models approximation procedure	p. 250
11.3.4 Application to the BizJet model	p. 253
11.4 Interpolation of the reduced-order models	p. 257
11.4.1 Choice of a suitable state-space form	p. 257
11.4.2 Description of the interpolation method	p. 258
11.4.3 Generation of a simplified LFR	p. 259
11.4.4 Application to the BizJet model	p. 261
11.5 Conclusion	p. 263
Acknowledgments	p. 266
References	p. 266
12 Active vibration control using subspace predictive control	p. 269
Abstract	p. 269
12.1 Introduction	p. 269
12.2 Experimental set-up	p. 270
12.2.1 Control design	p. 271
12.2.2 Notes on the implementation	p. 271
12.3 Results	p. 272
12.4 Conclusions	p. 273
Acknowledgements	p. 274
References	p. 274
13 Rotorcraft system identification: an integrated time-frequency-domain approach	p. 275
Abstract	p. 275
13.1 Introduction	p. 275
13.2 Problem statement and preliminaries	p. 277
13.3 An integrated time-frequency-domain approach	p. 278
13.3.1 Continuous-time predictor-based subspace model identification	p. 279
13.3.2 From unstructured to structured models with an H∞ approach	p. 284
13.4 Bootstrap uncertainty estimation in subspace identification methods	p. 285
13.5 Simulation study: model identification for the BO-105 helicopter	p. 286
13.6 Concluding remarks	p. 298
References	p. 299
14 Parameter identification of a reduced order LFT model of anaerobic digestion	p. 301
Abstract	p. 301
14.1 Introduction	p. 301
14.2 ADM 1 model	p. 303
14.3 Modified AMOCO model	p. 307
14.4 LFT modelling and identification	p. 309
14.5 Parameter identification based on ADM 1 model simulation data	p. 313
14.6 Parameter identification based on experimental data	p. 319
14.7 Conclusion 323 Acknowledgements	p. 324
Appendix A LFT model for parameter identification based on ADMI model simulation data	p. 324
Appendix B LFT model for parameter identification based on experimental data	p. 325
References	p. 326
15 Modeling and parameter identification of a brake-by-wire actuator for racing motorcycles	p. 329
Abstract	p. 329
15.1 Introduction	p. 329
15.2 System description	p. 331
15.3 Brake-by-wire modeling	p. 332
15.3.1 Electric domain modeling	p. 333
15.3.2 Mechanical domain modeling	p. 333
15.3.3 Hydraulic domain	p. 337
15.4 Parameter identification	p. 347
15.4.1 Electric dynamics identification	p. 347
15.4.2 Motor mechanical dynamics - J mot and r vise - identification	p. 350
15.4.3 Friction model identification	p. 353
15.4.4 Final parameter identification	p. 353
15.5 Validation and analysis	p. 354
15.5.1 Validation	p. 354
15.5.2 Discussion on modeling choices	p. 358
15.6 Conclusions	p. 360
References	p. 361
16 LPV modeling and identification of a 2-DOF flexible robotic arm from local experiments using an H∞-based glocal approach	p. 365
Abstract	p. 365
16.1 Introduction	p. 365
16.2 Modeling of a flexible robotic manipulator	p. 367
16.2.1 Description of the 2-DOF robotic manipulator	p. 367
16.2.2 Linear fractional LPV representation: a reminder	p. 370
16.2.3 Nonlinear and linearized dynamic models	p. 370
16.3 Identification results	p. 375
16.4 Conclusions	p. 382
References	p. 383
Index	p. 387

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