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Overview
Control applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states. In PDE Control of String-Actuated Motion, Ji Wang and Miroslav Krstic develop control algorithms for these complex PDE-ODE systems evolving on time-varying domains.
Motivated by physical systems, the book’s algorithms are designed to operate, with rigorous mathematical guarantees, in the presence of real-world challenges, such as unknown parameters, unmeasured distributed states, environmental disturbances, delays, and event-triggered implementations. The book leverages the power of the PDE backstepping approach and expands its scope in many directions.
Filled with theoretical innovations and comprehensive in its coverage, PDE Control of String-Actuated Motion provides new design tools and mathematical techniques with far-reaching potential in adaptive control, delay systems, and event-triggered control.
Product Details
| ISBN-13: | 9780691233499 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 10/25/2022 |
| Series: | Princeton Series in Applied Mathematics , #73 |
| Pages: | 512 |
| Product dimensions: | 7.00(w) x 10.00(h) x (d) |
About the Author
Table of Contents
List of Figures ix
List of Tables xv
Preface xvii
1 Introduction 1
1.1 String-Actuated Mechanisms 1
1.2 Hyperbolic PDE-ODE Systems 3
1.3 "Sandwich" PDEs 5
1.4 Advanced Boundary Control of Hyperbolic PDEs 5
1.5 Notes 8
I Applications 9
2 Single-Cable Mining Elevators 11
2.1 Modeling 11
2.2 State-Feedback for Vibration Suppression 15
2.3 Observer and Output-Feedback Controller Using Cage Sensing 18
2.4 Stability Analysis 21
2.5 Simulation Test in a Single-Cable Mining Elevator 26
2.6 Appendix 31
2.7 Notes 33
3 Dual-Cable Elevators 34
3.1 Dual-Cable Mining Elevator Dynamics and Reformulation 34
3.2 Observer for Cable Tension 38
3.3 Controller for Cable Tension Oscillation Suppression and Cage Balance 43
3.4 Stability Analysis 46
3.5 Simulation Test for a Dual-Cable Mining Elevator 49
3.6 Appendix 54
3.7 Notes 63
4 Elevators with Disturbances 64
4.1 Problem Formulation 64
4.2 Disturbance Estimator 67
4.3 Observer of Cable-and-Cage State 71
4.4 Control Design for Rejection of Disturbances at the Cage 73
4.5 Simulation for a Disturbed Elevator 80
4.6 Appendix 84
4.7 Notes 93
5 Elevators with Flexible Guides 95
5.1 Description of Flexible Guides and Generalized Model 95
5.2 Observer for Distributed States of the Cable 99
5.3 Adaptive Disturbance Cancellation and Stabilization 102
5.4 Adaptive Update Laws 108
5.5 Control Law and Stability Analysis 110
5.6 Simulation for a Flexible-Guide Elevator 117
5.7 Appendix 121
5.8 Notes 129
6 Deep-Sea Construction 130
6.1 Modeling Process and Linearization 131
6.2 Basic Control Design Using Full States 141
6.3 Observer for Two-Dimensional Oscillations of the Cable 149
6.4 Controller with Collocated Boundary Sensing 157
6.5 Simulation for a Deep-Sea Construction System 158
6.6 Appendix 164
6.7 Notes 168
7 Deep-Sea Construction with Event-Triggered Delay Compensation 170
7.1 Problem Formulation 170
7.2 Observer Design Using Delayed Measurement 175
7.3 Delay-Compensated Output-Feedback Controller 181
7.4 Event-Triggering Mechanism 183
7.5 Stability Analysis 190
7.6 Simulation for Deep-Sea Construction with Sensor Delay 193
7.7 Appendix 198
7.8 Notes 201
8 Offshore Rotary Oil Drilling 202
8.1 Description of Oil-Drilling Models 203
8.2 Adaptive Update Laws for Unknown Coefficients 206
8.3 Output-Feedback Control Design 208
8.4 Stability Analysis 215
8.5 Simulation for Offshore Oil Drilling 222
8.6 Notes 229
II Generalizations 231
9 Basic Control of Sandwich Hyperbolic PDEs 233
9.1 Problem Formulation 233
9.2 Backsteppmg for the PDE-ODE Cascade 234
9.3 Backsteppmg for the Input ODE 238
9.4 Controller and Stability Analysis 239
9.5 Boundedness and Exponential Convergence of the Controller 244
9.6 Extension to ODEs of Arbitrary Order 255
9.7 Simulation 265
9.8 Appendix 268
9.9 Notes 272
10 Delay-Compensated Control of Sandwich Hyperbolic Systems 273
10.1 Problem Formulation 273
10.2 Observer Design 276
10.3 Output-Feedback Control Design 287
10.4 Stability Analysis of the Closed-Loop System 295
10.5 Application in Deep-Sea Construction 297
10.6 Appendix 305
10.7 Notes 309
11 Event-Triggered Control of Sandwich Hyperbolic PDEs 310
11.1 Problem Formulation 310
11.2 Observer 312
11.3 Continuous-in-Time Control Law 315
11.4 Event-Triggering Mechanism 320
11.5 Stability Analysis of the Event-Based Closed-Loop System 326
11.6 Application in the Mining Cable Elevator 332
11.7 Appendix 338
11.8 Notes 340
12 Sandwich Hyperbolic PDEs with Nonlinearities 341
12.1 Problem Formulation 341
12.2 State-Feedback Control Design 342
12.3 Observer Design and Stability Analysis 349
12.4 Stability of the Output-Feedback Closed-Loop System 356
12.5 Simulation 359
12.6 Appendix 362
12.7 Notes 373
III Adaptive Control of Hyperbolic PDE-ODE Systems 375
13 Adaptive Event-Triggered Control of Hyperbolic PDEs 377
13.1 Problem Formulation 377
13.2 Observer 379
13.3 Adaptive Continuous-in-Time Control Design 381
13.4 Event-Triggering Mechanism 385
13.5 Stability Analysis of the Closed-Loop System 388
13.6 Application in the Flexible-Guide Mining Cable Elevator 393
13.7 Appendix 399
13.8 Notes 403
14 Adaptive Control with Regulation-Triggered Parameter Estimation of Hyperbolic PDEs 405
14.1 Problem Formulation 405
14.2 Nominal Control Design 408
14.3 Regulation-Triggered Adaptive Control 410
14.4 Main Result 418
14.5 Simulation 425
14.6 Appendix 428
14.7 Notes 438
15 Adaptive Control of Hyperbolic PDEs with Piecewise-Constant Inputs and Identification 439
15.1 Problem Formulation 439
15.2 Nominal Control Design 441
15.3 Event-Triggered Control Design with Piecewise-Constant Parameter Identification 442
15.4 Main Result 449
15.5 Application in the Mining Cable Elevator 459
15.6 Appendix 464
15.7 Notes 471
Bibliography 473
Index 487
What People are Saying About This
“A valuable resource for control theorists and practitioners, this is the first book to deal with the emerging field of event-triggered control for PDEs. Easy to read and technically sound, it has an excellent balance between theory and applications, making the practical significance of the methods clear.”—Joachim Deutscher, Ulm University, Germany“To the best of my knowledge, this is the first book to deal with string-related dynamical systems, and it opens the door for perspectives and applications beyond the control of cable-driven systems. A very significant book.”—Christophe Prieur, CNRS, France