Advanced Structural Dynamics and Active Control of Structures

By: Wodek Gawronski

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Hardcover | 22 April 2004

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424 Pages

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20.32 x 15.24 x 1.91

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Science is for those who learn; poetry for those who know. -Joseph Roux This book is a continuation of my previous book, Dynamics and Control of Structures [44]. The expanded book includes three additional chapters and an additional appendix: Chapter 3, "Special Models"; Chapter 8, "Modal Actuators and Sensors"; and Chapter 9, "System Identification. " Other chapters have been significantly revised and supplemented with new topics, including discrete-time models of structures, limited-time and -frequency grammians and reduction, almo- balanced modal models, simultaneous placement of sensors and actuators, and structural damage detection. The appendices have also been updated and expanded. Appendix A consists of thirteen new Matlab programs. Appendix B is a new addition and includes eleven Matlab programs that solve examples from each chapter. In Appendix C model data are given. Several books on structural dynamics and control have been published. Meirovitch's textbook [108] covers methods of structural dynamics (virtual work, d'Alambert's principle, Hamilton's principle, Lagrange's and Hamilton's equations, and modal analysis of structures) and control (pole placement methods, LQG design, and modal control). Ewins's book [33] presents methods of modal testing of structures. Natke's book [111] on structural identification also contains excellent material on structural dynamics. Fuller, Elliot, and Nelson [40] cover problems of structural active control and structural acoustic control.

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"The monograph presents advanced structural dynamics and active control of structures. ... The monograph is well written and readable ... . The text can be used in graduate courses on structural dynamics and control. The book is an up-to-date authoritative reference supplied with numerous illustrative examples which will be useful to graduate students, professionals, researchers and practitioners in the field." (Lubomir Bakule, Zentralblatt MATH, Vol. 1064, 2005)

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Automatic Control Engineering Robotics Materials Science Mechanics of Solids Science Physics Classical Mathematics

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Paperback

Published: 26th May 2011

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Series Preface	p. vii
Preface	p. ix
List of Symbols	p. xix
Introduction to Structures	p. 1
Examples	p. 1
A Simple Structure	p. 1
A 2D Truss	p. 2
A 3D Truss	p. 2
A Beam	p. 3
The Deep Space Network Antenna	p. 3
The International Space Station Structure	p. 6
Definition	p. 6
Properties	p. 7
Standard Models	p. 13
Models of a Linear System	p. 14
State-Space Representation	p. 14
Transfer Function	p. 15
Second-Order Structural Models	p. 16
Nodal Models	p. 16
Modal Models	p. 17
State-Space Structural Models	p. 29
Nodal Models	p. 29
Models in Modal Coordinates	p. 31
Modal Models	p. 35
Special Models	p. 41
Models with Rigid-Body Modes	p. 41
Models with Accelerometers	p. 45
State-Space Representation	p. 45
Second-Order Representation	p. 48
Transfer Function	p. 49
Models with Actuators	p. 50
Model with Proof-Mass Actuators	p. 50
Model with Inertial Actuators	p. 53
Models with Small Nonproportional Damping	p. 54
Generalized Model	p. 58
State-Space Representation	p. 59
Transfer Function	p. 59
Discrete-Time Models	p. 60
State-Space Representation	p. 61
Transfer Function	p. 63
Controllability and Observability	p. 65
Definition and Properties	p. 65
Continuous-Time Systems	p. 66
Discrete-Time Systems	p. 68
Relationship Between Continuous- and Discrete-Time Grammians	p. 69
Balanced Representation	p. 71
Balanced Structures with Rigid-Body Modes	p. 73
Input and Output Gains	p. 74
Controllability and Observability of a Structural Modal Model	p. 76
Diagonally Dominant Grammians	p. 76
Closed-Form Grammians	p. 79
Approximately Balanced Structure in Modal Coordinates	p. 80
Controllability and Observability of a Second-Order Modal Model	p. 85
Grammians	p. 85
Approximately Balanced Structure in Modal Coordinates	p. 87
Three Ways to Compute Hankel Singular Values	p. 91
Controllability and Observability of the Discrete-Time Structural Model	p. 91
Time-Limited Grammians	p. 94
Frequency-Limited Grammians	p. 99
Time- and Frequency-Limited Grammians	p. 103
Discrete-Time Grammians in Limited-Time and -Frequency Range	p. 107
Norms	p. 109
Norms of the Continuous-Time Systems	p. 109
The H₂ Norm	p. 109
The H_∞ Norm	p. 111
The Hankel Norm	p. 112
Norms of the Discrete-Time Systems	p. 113
The H₂ Norm	p. 113
The H_∞ Norm	p. 114
The Hankel Norm	p. 114
Norms of a Single Mode	p. 115
The H₂ Norm	p. 115
The H_∞ Norm	p. 117
The Hankel Norm	p. 118
Norm Comparison	p. 119
Norms of a Structure	p. 120
The H₂ Norm	p. 121
The H_∞ Norm	p. 121
The Hankel Norm	p. 123
Norms of a Structure with a Filter	p. 124
The H₂ Norm	p. 124
The H_∞ Norm	p. 126
The Hankel Norm	p. 127
Norms of a Structure with Actuators and Sensors	p. 127
The H₂ Norm	p. 128
The H_∞ Norm	p. 130
The Hankel Norm	p. 132
Norms of a Generalized Structure	p. 135
Norms of the Discrete-Time Structures	p. 137
The H₂ Norm	p. 138
The H_∞ Norm	p. 139
The Hankel Norm	p. 140
Norm Comparison	p. 140
Model Reduction	p. 143
Reduction Through Truncation	p. 143
Reduction Errors	p. 145
H₂ Model Reduction	p. 145
H_∞ and Hankel Model Reduction	p. 146
Reduction in the Finite-Time and -Frequency Intervals	p. 147
Reduction in the Finite-Time Interval	p. 148
Reduction in the Finite-Frequency Interval	p. 150
Reduction in the Finite-Time and -Frequency Intervals	p. 151
Structures with Rigid-Body Modes	p. 155
Structures with Actuators and Sensors	p. 159
Actuators and Sensors in a Cascade Connection	p. 159
Structure with Accelerometers	p. 161
Structure with Proof-Mass Actuators	p. 162
Structure with Inertial Actuators	p. 165
Actuator and Sensor Placement	p. 167
Problem Statement	p. 168
Additive Property of Modal Norms	p. 168
The H₂ Norm	p. 169
The H_∞ and Hankel Norms	p. 169
Placement Indices and Matrices	p. 170
H₂ Placement Indices and Matrices	p. 170
H_∞ and Hankel Placement Indices and Matrices	p. 172
Actuator/Sensor Indices and Modal Indices	p. 173
Placement for Large Structures	p. 180
Actuator Placement Strategy	p. 182
Sensor Placement Strategy	p. 182
Placement for a Generalized Structure	p. 187
Structural Testing and Control	p. 187
Sensor and Actuator Properties	p. 189
Placement Indices and Matrices	p. 192
Placement of a Large Number of Sensors	p. 193
Simultaneous Placement of Actuators and Sensors	p. 197
Modal Actuators and Sensors	p. 203
Modal Actuators and Sensors Through Modal Transformations	p. 204
Modal Actuators	p. 204
Modal Sensors	p. 208
Modal Actuators and Sensors Through Grammian Adjustment	p. 213
System Identification	p. 219
Discrete-Time Systems	p. 220
Markov Parameters	p. 221
Identification Algorithm	p. 221
Determining Markov Parameters	p. 224
Examples	p. 226
A Simple Structure	p. 226
The 2D Truss	p. 230
The Deep Space Network Antenna	p. 232
Collocated Controllers	p. 235
A Low-Authority Controller	p. 236
Dissipative Controller	p. 237
Properties of Collocated Controllers	p. 239
Root-Locus of Collocated Controllers	p. 241
Collocated Controller Design Examples	p. 245
A Simple Structure	p. 245
The 2D Truss	p. 246
LQG Controllers	p. 249
Definition and Gains	p. 250
The Closed-Loop System	p. 253
The Balanced LQG Controller	p. 254
The Low-Authority LQG Controller	p. 255
Approximate Solutions of CARE and FARE	p. 257
Root-Locus	p. 260
Almost LQG-Balanced Modal Representation	p. 262
Three Ways to Compute LQG Singular Values	p. 264
The Tracking LQG Controller	p. 264
Frequency Weighting	p. 266
The Reduced-Order LQG Controller	p. 269
The Reduction Index	p. 269
The Reduction Technique	p. 271
Stability of the Reduced-Order Controller	p. 272
Performance of the Reduced-Order Controller	p. 274
Weights of Special Interest	p. 275
Controller Design Procedure	p. 276
Controller Design Examples	p. 277
A Simple Structure	p. 277
The 3D Truss	p. 279
The 3D Truss with Input Filter	p. 281
The Deep Space Network Antenna	p. 283
H_∞ and H₂ Controllers	p. 287
Definition and Gains	p. 288
The Closed-Loop System	p. 291
The Balanced H_∞ Controller	p. 292
The H₂ Controller	p. 294
Gains	p. 294
The Balanced H₂ Controller	p. 296
The Low-Authority H_∞ Controller	p. 296
Approximate Solutions of !CARE and !FARE	p. 298
Almost H_∞-Balanced Modal Representation	p. 300
Three Ways to Compute H_∞ Singular Values	p. 301
The Tracking H_m Controller	p. 301
Frequency Weighting	p. 301
The Reduced-Order H_∞ Controller	p. 304
The Reduction Index	p. 304
Closed-Loop Poles	p. 304
Controller Performance	p. 306
Controller Design Procedure	p. 307
Controller Design Examples	p. 308
A Simple Structure	p. 308
The 2D Truss	p. 310
Filter Implementation Example	p. 312
The Deep Space Network Antenna with Wind Disturbance Rejection Properties	p. 313
Appendices	p. 317
Matlab Functions	p. 319
Transformation from an Arbitrary State-Space Representation to the Modal 1 State-Space Representation	p. 320
Transformation from an Arbitrary State-Space Representation to the Modal 2 State-Space Representation	p. 322
Transformation from Modal Parameters to the Modal 1 State-Space Representation	p. 324
Transformation from Modal Parameters to the Modal 2 State-Space Representation	p. 325
Transformation from Nodal Parameters to the Modal 1 State-Space Representation	p. 326
Transformation from Nodal Parameters to the Modal 2 State-Space Representation	p. 328
Determination of the Modal 1 State-Space Representation and the Time- and Frequency-Limited Grammians	p. 329
Open-Loop Balanced Representation	p. 331
H₂ Norm of a Mode	p. 332
H_∞, Norm of a Mode	p. 333
Hankel Norm of a Mode	p. 333
LQG-Balanced Representation	p. 334
H_∞-Balanced Representation	p. 335
Matlab Examples	p. 337
Example 2.5	p. 337
Example 3.3	p. 341
Example 4.11	p. 342
Example 5.3	p. 344
Example 6.7	p. 347
Example 7.2	p. 348
Example 8.1	p. 353
Example 9.1	p. 356
Example 10.4.2	p. 359
Example 11.13.1	p. 361
Example 12.13.2	p. 365
Structural Parameters	p. 371
Mass and Stiffness Matrices of the 2D Truss	p. 371
Mass and Stiffness Matrices of the Clamped Beam Divided into 15 Finite Elements	p. 373
State-Space Representation of the Deep Space Network Antenna	p. 376
References	p. 379
Index
Table of Contents provided by Publisher. All Rights Reserved.

Advanced Structural Dynamics and Active Control of Structures

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