Model-Based Control: (eBook)

Foreword 5
Acknowledgements 5
Preface 9
Contents 11
List of Contributors 13
Part I_Fundamentals 16
Linear Systems in Discrete Time 17
1 Introduction 17
2 Linear dynamical systems 18
3 Polynomial annihilators 19
4 Input/output representations 20
5 Representations with rational symbols 21
6 Integer invariants 22
7 Latent variables 22
8 Controllability 23
9 Rational annihilators 24
10 Stabilizability 25
11 Autonomous systems 25
References 25
Robust Controller Synthesis is Convex forSystems without Control Channel Uncertainties 27
1 Introduction 27
2 System Interconnections and Performance Specification 29
3 Robust Performance Analysis 31
4 Parametric-Dynamic Feasibility Problems 33
4.1 Analysis 35
4.2 Synthesis 36
4.3 Elimination 40
5 A Sketch of Further Applications 41
6 Conclusions 42
7 Appendix: Proof of Lemma 1 42
References 44
Conservation Laws andLumped System Dynamics 45
1 Introduction 45
2 Kirchhoff’s laws on graphs and circuit dynamics 46
2.1 Graphs 46
2.2 Kirchhoff’s laws for graphs 47
2.3 Kirchhoff’s laws for open graphs 49
2.4 Constraints on boundary currents and invariance of boundarypotentials 51
2.5 Interconnection of open graphs 52
2.6 Constitutive relations and port-Hamiltonian circuit dynamics 53
3 Conservation laws on higher-dimensional complexes 55
3.1 Kirchhoff behavior on k-complexes 55
3.2 Open k-complexes 57
4 Port-Hamiltonian dynamics on k-complexes 58
4.1 Example: Heat transfer on a 2-complex 59
5 Conclusions 60
References 61
Polynomial Optimization Problems areEigenvalue Problems 63
1 Introduction 63
2 General Theory 64
2.1 Introduction 64
2.2 Polynomial Optimization is Polynomial System Solving 65
2.3 Solving a System of Polynomial Equations is Linear Algebra 66
2.3.1 Motivational Example 66
2.3.2 Preliminary Notions 66
2.3.3 ConstructingMatrices Md 68
2.4 Determining the Number of Roots 70
2.5 Finding the Roots 71
2.5.1 Realization Theory 72
2.5.2 The Stetter-M¨oller Eigenvalue Problem 73
2.6 Finding the Minimizing Root as a Maximal Eigenvalue 74
2.7 Algorithms 78
3 Applications in Systems Theory and Identification 78
4 Conclusions and Future Work 80
References 81
Part II_Bridging Theory and Applied Technology 83
Designing Instrumentation for Control 84
1 Motivation 84
2 Definition of Information Architecture 86
3 Background 86
4 Contributions of this Paper 87
5 Problem Statement 88
6 Solution to the General Integrated Sensor/Actuator Selectionand Control Design Problem 90
7 Particular Cases of the Integrated Sensor/Actuator Selectionand Control Design Problem 91
7.1 State feedback control 91
7.2 Estimation 92
7.3 Economic design problem 93
8 Discrete-time systems 93
9 Sensor and Actuator Selection 95
10 Examples 96
11 Economic sensor/actuator selection 99
12 Conclusion 100
References 101
Uncertain Model Set Calculation fromFrequency Domain Data 102
1 Introduction 102
2 Uncertainty Models 103
2.1 Application to covering a family of models 105
2.2 Containment Metrics 106
3 Application of Over-Bound Uncertainty Modeling to NASAGTM Aircraft 107
3.1 Lateral-Directional GTM Aircraft Linear Model 107
3.2 Generation of Frequency Response Data Sets 108
3.3 Over-Bounding as a LMI Feasibility Problem 110
3.3.1 Data Set I 110
3.3.2 Data Set IP 112
3.3.3 Data Set IPN 114
3.4 Effect of System Directionality 114
3.5 Containment Metric 116
4 Conclusions 117
References 118
Robust Estimation for Automatic ControllerTuning with Application to Active Noise Control 119
1 Introduction 119
2 Approach to Automatic Controller Tuning 120
2.1 Simultaneous Perturbation of Plant and Controller 120
2.2 Disturbance Model 122
2.3 Overview of REACT 122
3 REACT Algorithm 123
3.1 Defining an Error Function 123
3.2 Derivation of Algorithm 124
4 Stability and Convergence of the Tuning Algorithm 125
4.1 Stability of the Feedback System 125
4.2 Convergence of the Tuning Algorithm 127
5 Application to ANC 132
5.1 Description of System 132
5.2 Identification of Plant Model 133
5.3 Experimental Results 133
6 Conclusions 135
References 135
Identification of Parameters in Large ScalePhysical Model Structures, for the Purpose ofModel-Based Operations 137
1 Introduction 138
2 Identifiability - the starting point 139
3 Testing local identifiability in identification 141
3.1 Introduction 141
3.2 Analyzing local identifiability in q 141
3.3 Approximating the identifiable parameter space 142
4 Parameter scaling in identifiability 144
5 Relation with controllability and observability 145
6 Cost function minimization in identification 146
7 A Bayesian approach 148
8 Structural identifiability 150
9 Examples 151
10 Conclusions 153
References 154
Part III_Applications in Motion Control Systemsand Industrial Process Control 156
Recovering Data from Cracked Optical Discsusing Hankel Iterative Learning Control 157
1 Introduction 157
2 Experimental setup 160
2.1 Optical storage principle 160
2.2 Cracked disc 161
2.3 Motion system 162
3 Hankel ILC 164
3.1 System formulation 164
3.2 Hankel ILC control framework 166
3.2.1 Convergence 167
3.2.2 Performance 167
3.3 Hankel ILC control design 168
4 Implementation aspects 169
4.1 Trial-varying setpoint variations 169
4.2 Dealing with the DEFO 169
4.3 State transformation to physical coordinates 170
4.4 Resulting Hankel ILC scheme 172
5 Experimental results 173
6 Conclusions 173
References 175
Advances in Data-driven Optimization ofParametric and Non-parametric FeedforwardControl Designs with Industrial Applications 177
1 Introduction 177
2 Data-driven Feedforward Control Optimization 179
2.1 Objective Function 180
2.2 Optimization Algorithm 180
2.2.1 Convergence 182
2.2.2 Implementation 183
3 Parametric Feedforward Control Optimization for a WaferStage Application 183
3.1 Feedforward Controller Parameterization 184
3.2 Experimental Results 186
4 Non-parametric Feedforward Control Optimization for aDigital Light Projection Application 186
4.1 Feedforward Controller Parameterization 188
4.2 Non-parametric Feedforward Control Optimization and ILC 188
4.3 ILC Design for UHP Lamp Current Control 189
4.4 Experimental Results 190
5 Conclusions 192
References 192
Incremental Identification of Hybrid Models ofDynamic Process Systems 195
1 Introduction 196
2 Hybrid models 197
3 Model identification strategies 197
3.1 Incremental model development and refinement 198
3.2 Incremental model identification 199
3.3 An assessment of incremental identification 200
4 Incremental identification of a hybrid semi-batch reactor 201
4.1 Reactor model 201
4.2 Incremental identification approach for the hybrid semi-batchreactor example 202
4.3 Simulated isothermal reaction system 202
4.4 Experimental data 203
4.5 Various modeling scenarios 204
4.6 Validation of the hybrid reactor model 206
5 Incremental identification of generally structured hybridmodels 207
6 Conclusions 211
References 211
Front Controllability in Two-Phase PorousMedia Flow 213
1 Introduction 214
2 Front dynamics 214
3 Analytical solution 218
4 Numerical approximation 218
5 Controllability 220
5.1 Pressures and velocities at the front 220
5.2 Position of the front 223
6 Front control 224
7 Concluding remarks 225
Nomenclature 225
Appendix: Analytical expressions 227
References 228
Part IV_Appendix 230
PhD Supervision by Okko H. Bosgra 231
Delft University of Technology 231
Wageningen University and Research Centre 233
Eindhoven University of Technology 233
Okko H. Bosgra,Bibliographic Record 235
Journal Papers, Book Chapters and Book Reviews 235
Conference Papers 238
Index 245