Mohammadpour / Grigoriadis Efficient Modeling and Control of Large-Scale Systems

1. Auflage 2010
ISBN: 978-1-4419-5757-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 335 Seiten

Complexity and dynamic order of controlled engineering systems is constantly increasing. Complex large scale systems (where 'large' reflects the system's order and not necessarily its physical size) appear in many engineering fields, such as micro-electromechanics, manufacturing, aerospace, civil engineering and power engineering. Modeling of these systems often result in very high-order models imposing great challenges to the analysis, design and control problems. 'Efficient Modeling and Control of Large-Scale Systems' compiles state-of-the-art contributions on recent analytical and computational methods for addressing model reduction, performance analysis and feedback control design for such systems. Also addressed at length are new theoretical developments, novel computational approaches and illustrative applications to various fields, along with: - An interdisciplinary focus emphasizing methods and approaches that can be commonly applied in various engineering fields -Examinations of applications in various fields including micro-electromechanical systems (MEMS), manufacturing processes, power networks, traffic control 'Efficient Modeling and Control of Large-Scale Systems' is an ideal volume for engineers and researchers working in the fields of control and dynamic systems.

Autoren/Hrsg.

Mohammadpour, Javad

Grigoriadis, Karolos M.

Inhaltsverzeichnis

1;Foreword;6
2;Preface;8
3;Contents;12
4;List of Contributors;18
5;Part I Model Reduction, Large-Scale System Modelingand Applications;22
5.1;Interpolatory Model Reduction of Large-Scale Dynamical Systems;23
5.1.1;1 Introduction;23
5.1.2;2 Problem Setting;24
5.1.2.1;2.1 The General Interpolation Framework;26
5.1.2.2;2.2 Model Reduction via Projection;28
5.1.2.3;2.3 Interpolatory Projections;30
5.1.2.4;2.4 Error Measures;34
5.1.3;3 Interpolatory Optimal H2 Approximation;38
5.1.3.1;3.1 An Algorithm for Interpolatory Optimal H2 Model Reduction;41
5.1.3.2;3.2 Numerical Results for IRKA;42
5.1.4;4 Interpolatory Passivity Preserving Model Reduction;45
5.1.4.1;4.1 An Example of Passivity Preserving Model Reduction;47
5.1.5;5 Structure-Preserving Model Reduction Using Generalized Coprime Factorizations;50
5.1.5.1;5.1 A Numerical Example: Driven Cavity Flow;53
5.1.5.2;5.2 Second-Order Dynamical Systems;55
5.1.6;6 Model Reduction of Parametric Systems;57
5.1.6.1;6.1 Numerical Example;60
5.1.7;7 Model Reduction from Measurements;61
5.1.7.1;7.1 Motivation: S-Parameters;61
5.1.7.2;7.2 The Loewner Matrix Pair and Constructionof Interpolants;62
5.1.7.2.1;7.2.1 The General Case;66
5.1.7.3;7.3 Loewner and Pick Matrices;66
5.1.7.4;7.4 Examples;67
5.1.7.4.1;7.4.1 A Simple Low-order Example;67
5.1.7.4.2;7.4.2 Coupled Mechanical System;69
5.1.7.4.3;7.4.3 Four-pole Band-pass Filter;72
5.1.8;8 Conclusions;73
5.1.9;References;73
5.2;Efficient Model Reduction for the Control of Large-Scale Systems;79
5.2.1;1 Introduction;79
5.2.2;2 Spectral Decomposition;80
5.2.3;3 Simultaneous Gradient Error Reduction;82
5.2.4;4 Balancing;84
5.2.4.1;4.1 Techniques Not Requiring Balancing;86
5.2.4.2;4.2 Balancing Over A Disk;88
5.2.5;5 Example: Large-Scale System Application;89
5.2.6;References;91
5.3;Dynamics of Tensegrity Systems;93
5.3.1;1 Introduction and Motivation;93
5.3.2;2 Dynamics of a Single Rigid Rod;94
5.3.2.1;2.1 Nodes as Functions of the Configuration;96
5.3.2.2;2.2 String Forces;97
5.3.2.3;2.3 Generalized Forces and Torques;98
5.3.2.4;2.4 Equations of Motion;98
5.3.3;3 Class 1 Tensegrity Systems;99
5.3.4;4 Class k Tensegrity Systems;102
5.3.4.1;4.1 A Class 2 Tensegrity Cable Model;102
5.3.5;5 Concluding Remarks;107
5.3.6;References;107
5.4;Modeling a Complex Aero-Engine Using Reduced Order Models;109
5.4.1;1 Introduction;109
5.4.2;2 Gas Turbine System;110
5.4.2.1;2.1 Nonlinear Static Model of Gas Turbine;111
5.4.2.2;2.2 Nonlinear Dynamic Model of Gas Turbine;112
5.4.3;3 Problem Formulation for Reduced Order Data Driven Modeling;113
5.4.3.1;3.1 Criterion Selection;114
5.4.3.2;3.2 Model Selection: EE vs. OE;116
5.4.3.2.1;3.2.1 Equation Error (EE) Model;117
5.4.3.2.2;3.2.2 Output Error (OE) Model;118
5.4.4;4 NLS for OE Parameter Identification;119
5.4.4.1;4.1 Calculation of bold0mu mumu equation V(k)/ and the Jacobian;120
5.4.4.2;4.2 Approximation of R(k) and the Hessian;121
5.4.5;5 Application and Results;124
5.4.5.1;5.1 First-Order Model;125
5.4.5.2;5.2 Second-Order Model;129
5.4.6;6 Summary;130
5.4.7;References;130
6;Part II Large-Scale Systems Control and Applications;132
6.1;Robust Control of Large-Scale Systems: Efficient Selection of Inputs and Outputs;133
6.1.1;1 Introduction;133
6.1.2;2 Preliminaries and Problem Formulation;135
6.1.2.1;2.1 Background on Sum-of-Squares;136
6.1.3;3 Robust Controllability Degree;137
6.1.3.1;3.1 Special Case: A Polytopic Region;142
6.1.3.2;3.2 Comparison with Existing Results;146
6.1.4;4 Numerical Example;147
6.1.5;5 Summary;150
6.1.6;References;150
6.2;Decentralized Output-Feedback Control of Large-Scale Interconnected Systems via Dynamic High-Gain Scaling;153
6.2.1;1 Introduction;153
6.2.2;2 Decentralized Control Based on The Adaptive Dual Dynamic High-Gain Scaling Paradigm;155
6.2.2.1;2.1 Assumptions;155
6.2.2.2;2.2 Observer and Controller Designs;158
6.2.2.3;2.3 Stability Analysis;159
6.2.3;3 Generalized Scaling: Application to Decentralized Control;169
6.2.3.1;3.1 Assumptions;170
6.2.3.2;3.2 Observer Design;172
6.2.3.3;3.3 Controller Design;173
6.2.3.4;3.4 Stability Analysis;176
6.2.4;References;182
6.3;Decentralized Output Feedback Guaranteed Cost Control of Uncertain Markovian Jump Large-Scale Systems: Local Mode Dependent Control Approach;184
6.3.1;1 Introduction;184
6.3.2;2 Problem Formulation;187
6.3.3;3 Guaranteed Cost Controller Design;190
6.3.3.1;3.1 Design Methodology;190
6.3.3.2;3.2 Design of Global Mode Dependent Controllers;193
6.3.3.3;3.3 The Main Result: Design of Local Mode Dependent Controllers;197
6.3.3.4;3.4 Design Procedure;199
6.3.4;4 An Illustrative Example;200
6.3.5;5 Conclusions;203
6.3.6;Appendix 1;204
6.3.7;Appendix 2;211
6.3.8;References;212
6.4;Consensus Based Multi-Agent Control Algorithms;214
6.4.1;1 Introduction;214
6.4.2;2 Problem Formulation;216
6.4.3;3 Consensus at the Control Input Level;217
6.4.3.1;3.1 Algorithms Derived from the Local Dynamic Output Feedback Control Laws;217
6.4.3.2;3.2 Algorithms Derived from the Local Static Feedback Control Laws;222
6.4.4;4 Consensus at the State Estimation Level;224
6.4.5;5 Consensus Based Decentralized Control of UAV Formations;227
6.4.5.1;5.1 Formation Model;227
6.4.5.2;5.2 Global LQ Optimal State Feedback;229
6.4.5.3;5.3 Decentralized State Estimation;230
6.4.5.4;5.4 Experiments;232
6.4.6;References;234
6.5;Graph-Theoretic Methods for Networked Dynamic Systems: Heterogeneity and H2 Performance;236
6.5.1;1 Introduction;236
6.5.1.1;1.1 Preliminaries and Notations;238
6.5.2;2 Canonical Models of Networked Dynamic Systems;241
6.5.3;3 Analysis and Graph-Theoretic Performance Bounds;246
6.5.3.1;3.1 Observability and Controllability of NDS;246
6.5.3.2;3.2 Graph-Theoretic Bounds on NDS Performance;249
6.5.4;4 Topology Design for NDS;258
6.5.4.1;4.1 H2 Topology Design for NDS Coupled at the Output;259
6.5.4.2;4.2 Sensor Placement with H2 Performance for NDS Coupled at the State;261
6.5.5;5 Concluding Remarks;263
6.5.6;References;264
6.6;A Novel Coordination Strategy for Multi-Agent Control Using Overlapping Subnetworks with Application to Power Systems;267
6.6.1;1 Introduction;267
6.6.1.1;1.1 Multi-Agent Control of Power Networks;268
6.6.1.2;1.2 Control of Subnetworks;269
6.6.1.3;1.3 Optimal Power Flow Control;271
6.6.1.4;1.4 Goal and Outline of This Chapter;272
6.6.2;2 Modeling of Network Characteristics and Control Objectives;272
6.6.2.1;2.1 Network Characteristics;272
6.6.2.2;2.2 Control Objectives;273
6.6.2.3;2.3 Definition of Subnetworks;273
6.6.3;3 Multi-Agent Control of Touching Subnetworks;274
6.6.3.1;3.1 Internal and External Nodes;274
6.6.3.2;3.2 Control Problem Formulation for One Agent;275
6.6.3.2.1;3.2.1 Prediction Model;276
6.6.3.2.2;3.2.2 Objectives;277
6.6.3.3;3.3 Control Scheme for Multiple Agents;278
6.6.4;4 Multi-Agent Control for Overlapping Subnetworks;279
6.6.4.1;4.1 Common Nodes;279
6.6.4.2;4.2 Control Problem Formulation for One Agent;280
6.6.4.2.1;4.2.1 Prediction Model;281
6.6.4.2.2;4.2.2 Objectives;282
6.6.4.3;4.3 Control Scheme for Multiple Agents;283
6.6.5;5 Application: Optimal Flow Control in Power Networks;284
6.6.5.1;5.1 Parameters of the Power Network;284
6.6.5.2;5.2 Steady-state Characteristics of Power Networks;284
6.6.5.2.1;5.2.1 Transmission Lines;286
6.6.5.2.2;5.2.2 Generators;287
6.6.5.2.3;5.2.3 Loads;287
6.6.5.2.4;5.2.4 FACTS Devices;288
6.6.5.2.5;5.2.5 Power Balance;288
6.6.5.3;5.3 Control Objectives;289
6.6.5.4;5.4 Setting Up the Control Problems;289
6.6.5.5;5.5 Simulations;290
6.6.5.5.1;5.5.1 Scenario 1: Control of SVCs;290
6.6.5.5.2;5.5.2 Scenario 2: Control of TCSCs;291
6.6.6;6 Conclusions and Future Research;293
6.6.7;References;293
6.7;Distributed Control Methods for Structured Large-Scale Systems;295
6.7.1;1 Introduction;295
6.7.2;2 Problem Statement;296
6.7.2.1;2.1 H2 Problem and Exact Solution;297
6.7.3;3 A Rational Laurent Operator Structure Preserving Iterative Approach to Distributed Control;298
6.7.3.1;3.1 L-Operator Sign Function;300
6.7.3.2;3.2 Definition;301
6.7.3.3;3.3 Convergence;301
6.7.3.4;3.4 Applications;302
6.7.3.5;3.5 Numerical Difficulties;303
6.7.3.6;3.6 Application to the Example Problem;304
6.7.4;4 Distributed Control Design for Decomposable Systems;304
6.7.4.1;4.1 General Description;305
6.7.4.2;4.2 Application to the Example Problem;308
6.7.4.2.1;4.2.1 Generalization to Infinite Dimensional Systems;308
6.7.4.2.2;4.2.2 The Platoon;309
6.7.5;5 Distributed LQR of Identical Systems;310
6.7.5.1;5.1 Special Properties of LQR for Dynamically Decoupled Systems;311
6.7.5.2;5.2 Application to the Example Problem;313
6.7.6;6 Numerical Results of the Car Platoon Benchmark Problem;315
6.7.7;7 Conclusions and Open Problems;317
6.7.8;References;318
6.8;Integrated Design of Large-Scale Collocated Structural System and Control Parameters Using a Norm Upper Bound Approach;320
6.8.1;1 Introduction;320
6.8.2;2 Symmetric Output Feedback Control of Collocated Systems;322
6.8.3;3 Upper Bounds on Collocated Structural System Norms;323
6.8.4;4 Integrated Damping and Control Design Using the Analytical Bound Approach;326
6.8.4.1;4.1 Integrated Design Based on an H Specification;326
6.8.4.2;4.2 Integrated Design Based on an H2 Specification;327
6.8.4.3;4.3 Integrated Design Based on a Mixed H2/H Specification;329
6.8.4.4;4.4 Decentralized Control Using the Norm Upper Bound Formulation;330
6.8.4.5;4.5 Additional Remarks;332
6.8.5;5 Simulation Results;332
6.8.6;6 Concluding Remarks;341
6.8.7;References;341
7;Index;344