The concept of dynamics and control implies the combination of dynamic analysis and control synthesis. It is essential to gain an insight into the dynamics of a nonlinear system with uncertainty if any new control strategy is designed to utilize nonlinearity. However, the new control strategy to be proposed must be robust enough so that any unexpected small disturbances will not alter the desired target of control. Such a concept is calling more attention to the modelling and simplification of dynamic systems subject to uncertain environment, the fine analysis and robust design of controlled dynamic systems based on either good understanding of nonlinear phenomena or artificial intelligence, the combination of passive control, active control and semi-active control, as well as the interaction among sensors, controllers and actuators.
Author(s): H.Y. Hu, E. Kreuzer
Series: IUTAM Bookseries 2
Edition: 1
Publisher: Springer
Year: 2007
Language: English
Pages: 424
Contents ......Page 6
Preface ......Page 10
Opening Address ......Page 17
Welcome Address ......Page 20
Part 1 System Modeling With Uncertainty ......Page 24
1. Introduction ......Page 25
2. Modeling Of Seat-occupant System ......Page 27
2.1 Quasi-static Foam Behavior ......Page 28
2.2 Modeling Of Interfacial Forces ......Page 30
2.3 Equations Of Motion ......Page 31
3. Solutions For Static Equilibrium ......Page 32
4. Numerical Results And Discussion ......Page 33
References ......Page 34
1. Introduction ......Page 35
2.1 Polynomial Chaos Expansion ......Page 36
2.2 Restoring Force Identification ......Page 37
2.3 Polynomial Chaos Representation Of Stochastic Inputs ......Page 38
2.4 Polynomial Chaos Representation Of Stochastic Outputs ......Page 39
3. Application To Sdof Duffing Oscillator ......Page 40
4. Summary And Conclusions ......Page 45
References ......Page 46
1. Introduction ......Page 47
2. Modeling Of The System ......Page 48
2.2 Environmental Model ......Page 49
3. Simulation Concept ......Page 52
4. Results ......Page 53
5. Conclusions ......Page 55
Refere Nces ......Page 56
1. Introduction ......Page 57
Impacts In Multibody Systems ......Page 58
3. Numerical Models ......Page 60
4. Essential Parameters For The Coefficient Of Restitution ......Page 61
5.1 Comparison Of Numerical Models ......Page 63
5.2 Experimental Validation ......Page 64
5.3 Analysis Of The Coefficient Of Restitution ......Page 66
References ......Page 67
Part 2 System Dynamics With Uncertainty ......Page 69
1. Introduction ......Page 70
2. Subset Simulation Method ......Page 72
2.1 Procedure ......Page 73
2.2 Data-mining Using Markov Chain Samples ......Page 74
Illustrative Applications ......Page 75
4. Recent Developments ......Page 77
References ......Page 78
1. Introduction ......Page 80
2.1 Trajectory Tubes To Impulsive Systems ......Page 82
2.2 Systems With State Constraints ......Page 84
3. Linear Impulsive Systems With Ellipsoidal Constraints ......Page 85
Acknowledgements ......Page 88
Refere Nces ......Page 89
1. Introduction ......Page 90
2.1 Random Dynamical Systems ......Page 92
2.2 Generation Of Rds From Differential Equations ......Page 94
2.3 Invariant And Stationary Measures ......Page 95
3.1 Markov Operators ......Page 96
3.2 Approximation Of The Markov Operators ......Page 97
3.3 Approximation Of Stationary Densities ......Page 98
4. Numerical Example ......Page 99
5. Conclusions ......Page 100
References ......Page 101
1. Introduction ......Page 102
2. Dynamical Model Of The System ......Page 103
3. Result And Discussion ......Page 105
Acknowledgements ......Page 109
A2. Some Diagrams Of The Undisturbed Case ......Page 110
References ......Page 111
1. Introduction ......Page 112
2. The Spectral Analysis For A Linear Filter System ......Page 113
3. Formulation ......Page 114
4. Asymptotical Analysis ......Page 115
5. Expansion Of Invariant Measure ......Page 117
Asymptotic Expansion For Top Lyapunov Exponent ......Page 120
References ......Page 121
1. Dimensionless Set-up Of The Problem ......Page 122
2. Nonstationary Polynomial Moments ......Page 124
3. Stability Of Stationary Processes ......Page 127
4. Evaluation Of Top Lyapunov Exponents ......Page 130
5. Summary And Conclusion ......Page 132
References ......Page 133
1. Introduction ......Page 134
2. Uncertainties Induced By Boundary Crisis And Effect Of Noise To Wada Basin Boundaries ......Page 136
3. Control Uncertainty In Duffing Equation ......Page 139
References ......Page 141
1. Introduction ......Page 142
2. How To Approximate The Invariant Manifolds ......Page 143
3. Basin Erosion Of Duffing Oscillator Under Deterministic Excitation ......Page 144
Basin Erosion Of Duffing Oscillator Under Stochastic Noise ......Page 148
5. Conclusions ......Page 150
References ......Page 151
Part 3 Nonlinear Dynamics ......Page 152
1. Introduction ......Page 153
2. Direct Problem ......Page 157
Inverse Problem ......Page 158
4. Random Fractals ......Page 160
References ......Page 162
1. Introduction ......Page 163
2. Ray Theory ......Page 164
3. Stability ......Page 167
4. Transitions ......Page 169
References ......Page 172
1. Introduction ......Page 173
2. Gea Equation For Deterministic Systems ......Page 174
3.1 Free Oscillation Of A Nonlinear Suspension System ......Page 175
3.2 Forced Oscillation – Nonlinear Suspension System ......Page 179
4. Conclusions ......Page 181
References ......Page 182
1. Introduction ......Page 183
2. Bifurcation Of Single-sided Constraint ......Page 184
3. Bifurcation Of Double-sided Constraint ......Page 185
4. Periodic Bifurcations Of Non-smooth Systems ......Page 187
5. Conclusions ......Page 191
References ......Page 192
1. Introduction ......Page 193
2.1 Typical Equations Of Motion Of Rotor System ......Page 194
2.2 Introduction Of Complex Coordinate And Separation Of Forward And Backward Whirling Modes ......Page 196
2.3 Application Of The Method Of Multiple Scales To Rotor Dynamics ......Page 197
2.4 Production Of Backward Whirling Mode Due To Nonlinearity And Gravity Effect ......Page 199
3. Experiment ......Page 201
References ......Page 202
1. Introduction ......Page 203
2. Dynamical Model Of Spur Gear Pair ......Page 204
3. Computation Scheme For The Periodic Solutions By Ihbm ......Page 205
4. Results And Analysis ......Page 208
References ......Page 212
1. Introduction ......Page 213
2. The Transcription Of The Optimal Control Problem Into A Nlp ......Page 216
2.1 Description Of The Algorithm ......Page 218
3. Numerical Example ......Page 219
4. Discussions And Conclusions ......Page 220
References ......Page 222
Part 4 Dynamics Of High-dimensional Systems ......Page 223
1. Introduction ......Page 224
2. Experimental Rig ......Page 225
3. Mathematical Modelling ......Page 226
4. Numerical Prediction And Experimental Observation ......Page 228
5. Concluding Remarks ......Page 232
References ......Page 233
1. Introduction ......Page 234
1.2 Micro-scale Cantilever Arrays ......Page 235
2.1 Simulation Profile ......Page 237
2.2 Array Model ......Page 238
2.3 Analytical Profile ......Page 239
3. Results And Discussion ......Page 241
Acknowledgements ......Page 242
References ......Page 243
1. Introduction ......Page 244
2. Problem Formulations ......Page 245
3. Multi-scale Analysis ......Page 246
Steady-state Response ......Page 248
5. Stability ......Page 250
7. Conclusions ......Page 252
References ......Page 253
1. Introduction ......Page 254
2. Statement Of The Problem ......Page 255
3. Relative Motion ......Page 256
4. Dry Friction: Two-phase Motion ......Page 258
5. Dry Friction: Three-phase Motion ......Page 259
6. Generalizations And Experiments ......Page 260
7. Nonlinear Resistance ......Page 261
References ......Page 263
1. Introduction ......Page 264
2. Mechanical Model ......Page 265
3. Linear Modal Characteristics ......Page 266
4. Nonlinear Modal Characteristics ......Page 268
Concluding Remarks ......Page 271
References ......Page 273
1. Introduction ......Page 274
2. Mechanical Model And Modal Expansion ......Page 276
3. Homoclinic Orbits (unperturbed System) ......Page 277
3.1 A Hierarchy Of Roms ......Page 278
4. Homoclinic Bifurcations (perturbed System) ......Page 280
5.2 Optimizing The Temporal Shape Of The Excitation ......Page 282
References ......Page 283
1. Introduction ......Page 284
2. Mechanical Model With One Degree Of Freedom ......Page 285
3. Continuous Infinite Dimensional System ......Page 288
References ......Page 293
1. Introduction ......Page 294
2. Equations Of Motion And Perturbation Analysis ......Page 296
4. Dissipative Perturbations ......Page 299
5. The K-pulse Melnikov Function ......Page 300
7. Conclusions ......Page 302
References ......Page 303
Part 5 Control Of Nonlinear Dynamic Systems ......Page 304
1. Introduction ......Page 305
2. Statement Of The Problem ......Page 307
3. Synthesis Of Control ......Page 308
4. The Computer Simulation Results ......Page 311
5. Comparison With Time-optimal Control ......Page 313
References ......Page 314
1. Introduction ......Page 315
2. Physical Model ......Page 316
3.1 Boundary Value Problem ......Page 317
4. Vibration Suppression Concept ......Page 320
4.1 Model Reduction ......Page 321
4.3 Full State Observer ......Page 322
4.4 Telescopic Operations With Clearance ......Page 323
References ......Page 324
1. Introduction ......Page 325
2. Problem Formulation ......Page 327
2.1 Algebraic Non-linear Equations ......Page 329
3. Results ......Page 330
Acknowledgements ......Page 333
Refere Nces ......Page 334
1. Introduction ......Page 335
2. Model For Aeroservoelastic System ......Page 336
3. Model Of Servo ......Page 338
4. Design Of Robust Controllers ......Page 339
5. Numerical Simulations ......Page 341
6. Wind Tunnel Tests ......Page 342
References ......Page 344
1. Introduction ......Page 345
2. The Model ......Page 346
3. Synchronization, Periodization And Beating Of The Oscillations ......Page 347
References ......Page 350
1. Intruduction ......Page 351
2. Noise-induced Synchronization ......Page 352
2.1 Noise-induced Complete Synchronization ......Page 353
2.2 Noise-induced Phase Synchronization ......Page 354
3.1 Noise-enhanced Complete Synchronization ......Page 355
4. Spatial Patterns In A Square-lattice Hh Neuronal Systems ......Page 357
References ......Page 359
Part 6 Dynamics Of Time-delay Systems ......Page 361
1. Introduction ......Page 362
2. Averaged Equations Of The Generalized System ......Page 363
3. Stability And Response Analysis For The Steady-state Moments ......Page 365
3.1 Case I: Additive Gaussian White Noise ......Page 366
3.2 Case Ii: Multiplicative Gaussian White Noise ......Page 367
References ......Page 370
1. Introduction ......Page 372
2. Overview Of Act-and-wait Control For Discrete-time Systems ......Page 373
2.2 Act-and-wait Controller ......Page 374
3. Case Study: 1 Dof Pd Position Control ......Page 375
3.1 Stability Analysis ......Page 376
3.2 Stability Charts, Optimal Control Gains ......Page 377
Acknowledgements ......Page 380
Refere Nces ......Page 381
1. Introduction ......Page 382
2. Regenerative Turning Dynamics ......Page 383
3. Finite-dimensional Reduction Using Galerkin Projection ......Page 386
4. Global Bifurcation Structure Of Turning ......Page 387
Amplitudes At Turning Points ......Page 389
5. Concluding Remarks ......Page 390
References ......Page 391
1. Introduction ......Page 392
2.1 The Case Of T=t ......Page 394
2.2 The Case Of T2.3 The Case Of T3. An Illustrative Example ......Page 398
3.2 The Stability Of The Edge Quasi-polynomials ......Page 400
References ......Page 401
1. Introduction ......Page 402
2. Delay-induced Double Hopf Bifurcation With Non-resonance ......Page 403
3. Center Manifold Reduction ......Page 404
4. Classification Of Dynamical Behaviors ......Page 406
5. Quantitative Computation ......Page 408
6. Conclusions ......Page 410
References ......Page 411
1. Introduction ......Page 412
2. The Stochastic Averaging Method For Quasi Integrable Hamiltonian Systems With Time-delayed Feedback Control ......Page 413
The Largest Lyapunov Exponent And Asymptotic Lyapunov Stability With Probability One ......Page 416
4. Effects Of Time-delay In Feedback Control On Stability And Response ......Page 417
Refere Nces ......Page 421
Author Index ......Page 422
