Title Details

Kazuto Seto was born in 1938. He graduated from a doctoral course in Engineering at Tokyo Metropolitan University in 1971 and received a Dr. Eng. degree from Tokyo Metropolitan University in the Same Year. He worked as an associate professor and professor in the Department of Mechanical Engineering,National Defense Academy from 1973 until 1993. From 1993, he worked as a professor in the Department of Mechanical Engineering, Nihon University. He retired in 2007 and is now president of Seto-Vibration Control Laboratory. He retired in 2007 and is now president of Society of Mechanical Engineers (JSME) and a fellow of IE Australia. He was given JSME Awards for his research in 1984 and 1989, and the Dynamics, Measurement and Control Award from JSME in 1994 and 1996. His research interests in the areas of structural vibration control, system modeling and identification, motion and vibration control for multistructural systems with multi-controlled modes.

About the Authors xi

Preface xiii

Acknowledgements xv

1 Active Damping 1

1.1 Introduction 1

1.1.1 Why Suppress Vibrations? 1

1.1.2 How can Vibrations be Reduced? 2

1.2 Structural Control 2

1.3 Plant Description 3

1.3.1 Error Budget 4

1.4 Equations of Structural Dynamics 6

1.4.1 Equation of Motion Including Seismic Excitation 6

1.4.2 Modal Coordinates 8

1.4.3 Support Reaction, Dynamic Mass 10

1.4.4 Dynamic Flexibility Matrix 12

1.5 Collocated Control System 15

1.5.1 Transmission Zeros and Constrained System 18

1.5.2 Nearly Collocated Control System 20

1.5.3 Non-Collocated Control Systems 21

1.6 Active Damping with Collocated System 24

1.6.1 Lead Control 25

1.6.2 Direct Velocity Feedback 29

1.6.3 Positive Position Feedback 31

1.6.4 Integral Force Feedback 35

1.6.5 Duality between The Lead and IFF Controllers 44

1.7 Decentralized Control with Collocated Pairs 46

1.7.1 Cross-Talk 46

1.7.2 Transmission Zeros (Case 1) 47

1.7.3 Transmission Zeros (Case 2) 52

References 55

2 Active Isolation 57

2.1 Introduction 57

2.2 Relaxation Isolator 60

2.2.1 Electromagnetic Realization 62

2.3 Sky-hook Damper 64

2.4 Force Feedback 66

2.5 Six-Axis Isolator 69

2.5.1 Decentralized Control 73

2.5.2 Leg Design 76

2.5.3 Model of the Isolator 80

2.5.4 Six-Axis Transmissibility 82

2.6 Vehicle Active Suspension 89

2.6.1 Quarter-Car Model 91

2.7 Semi-Active Suspension 106

2.7.1 Semi-Active Devices 106

2.7.2 Narrow-Band Disturbance 107

2.7.3 Quarter-Car Semi-Active Suspension 108

References 113

3 A Comparison of Passive, Active and Hybrid Control 117

3.1 Introduction 117

3.2 System Description 119

3.3 The Dynamic Vibration Absorber 120

3.3.1 Single-d.o.f. Oscillator 120

3.3.2 Multiple-d.o.f. System 123

3.3.3 Shear Frame Example 124

3.4 Active Mass Damper 126

3.5 Hybrid Control 131

3.6 Shear Control 133

3.7 Force Actuator, Displacement Sensor 135

3.7.1 Direct Velocity Feedback 136

3.7.2 First-Order Positive Position Feedback 137

3.7.3 Comparison of the DVF and the PPF 138

3.8 Displacement Actuator, Force Sensor 140

3.8.1 Comparison of the IFF and the DVF 142

References 144

4 Vibration Control Methods and Devices 147

4.1 Introduction 147

4.2 Classification of Vibration Control Methods 148

4.3 Construction of Active Dynamic Absorber 151

4.4 Control Devices forWind Excitation Control in Civil Structures 154

4.5 Real Towers Using the Connected Control Method 156

4.6 Application of Active Dynamic Absorber for Controlling Vibration of Single-d.o.f. Systems 158

4.6.1 Equations of Motion and State Equation 159

4.6.2 Representation of a Non-Dimensional State Equation 160

4.6.3 Control System Design 162

4.6.4 Similarity Law between Dimensional and Non-dimensional System 163

4.6.5 Analysis of Vibration Control Effect 165

4.6.6 Experiment 173

4.7 Remarks 175

References 176

5 Reduced-Order Model for Structural Control 179

5.1 Introduction 179

5.2 Modeling of Distributed Structures 180

5.2.1 Equation of Motion for Distributed Structures 180

5.2.2 Conventional Modeling of Structures 181

5.3 Spillover 183

5.4 The Lumped Modeling Method 185

5.4.1 A Key Idea for Deriving a Reduced-Order Model 185

5.4.2 Relationship Between Physical and Modal Coordinate Systems 187

5.4.3 Modification of Normalized Modal Matrix 188

5.5 Method of Equivalent Mass Estimation 190

5.5.1 Meaning of Equivalent Mass 190

5.5.2 Eigenvector Method 191

5.5.3 Mass Response Method 193

5.6 Modeling of Tower-like Structure 197

5.6.1 Two-d.o.f. Model 197

5.6.2 Dimension and Dynamic Characteristics of the Tower-Like Structure 198

5.6.3 Calculation of Parameters of Two-d.o.f. Model 201

5.6.4 Comparison between the Distributed Parameter and Two-d.o.f. Systems 203

5.7 Modeling of Plate Structures 203

5.7.1 Dimensions of a Plate Structure 203

5.7.2 Three-d.o.f. Model 206

5.7.3 Calculation of Parameters of the Three-d.o.f. Model 207

5.7.4 Comparison between Real System and Three-d.o.f. Systems 208

5.8 Modeling of a Bridge Tower 209

5.8.1 Dimensions of a Scaled Bridge Tower 209

5.8.2 Construction of a Four-d.o.f. Model 210

5.8.3 Calculation of Parameters of the Four-d.o.f. Model 212

5.8.4 Comparison between Real System and Four-d.o.f. Systems 213

5.9 Robust Vibration Control for Neglected Higher Modes 217

5.10 Conclusions 217

References 219

6 Active Control of Civil Structures 221

6.1 Introduction 221

6.2 Classification of Structural Control for Buildings 222

6.3 Modeling and Vibration Control for Tower Structures 222

6.3.1 One-d.o.f. Model 222

6.3.2 Two-d.o.f. Model for Tower-Like Structures and Its LQ Control 225

6.3.3 Three-d.o.f. Model for Broad Structures and Its H∞ Robust Control 228

6.3.4 Four-d.o.f. Model for Bridge Tower and Spillover Suppression Using Filtered LQ Control 239

6.4 Active Vibration Control of Multiple Buildings Connected with Active Control Bridges in Response to
Large Earthquakes 249

6.4.1 Construction of Four Model Buildings 249

6.4.2 Characteristics of the Tower Structures 251

6.4.3 Reduced-order Model of the Four Tower Structures Connected by Four Actuators 252

6.4.4 Control System Design 254

6.4.5 Simulated Results of Seismic Response Control 257

6.4.6 Experiment 259

6.5 Vibration Control for Real Triple Towers Using CCM 264

6.5.1 Outline of the Triple Towers 264

6.5.2 Modeling of Towers 265

6.5.3 Control System Design 266

6.5.4 Simulation of the Triple Towers Using CCM 269

6.5.5 Realization of the CCM 270

6.6 Vibration Control of Bridge Towers Using a Lumped Modeling Approach 274

6.6.1 Vibration Problem of Bridge Towers Under Construction 274

6.6.2 Controlled Object and Its Dynamic Characteristics 277

6.6.3 Five-d.o.f. Modeling of a Scaled Bridge Tower Structure with a Crane Tower 278

6.6.4 LQ Control System Design 278

6.6.5 Simulations 283

6.6.6 Experiments 283

6.6.7 H∞ Robust Control 286

6.7 Conclusion 290

References 291

Index 293