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E-raamat: PDE Control of String-Actuated Motion

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PDE Control of String-Actuated MotionSuurem pilt
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New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevators

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.

Arvustused

"[ PDE Control of String-Actuated Motion] is what the metaphor applied mathematics is all about. In this field, there is often a gap between pretension and reality, a mismatch between mathematical rigor and engineering objectives. This book is a nice counterexample!"---Guenter Leugering, SIAM Review

List of Figures
ix
List of Tables
xv
Preface xvii
1 Introduction
1(8)
1.1 String-Actuated Mechanisms
1(2)
1.2 Hyperbolic PDE-ODE Systems
3(2)
1.3 "Sandwich" PDEs
5(1)
1.4 Advanced Boundary Control of Hyperbolic PDEs
5(3)
1.5 Notes
8(1)
I Applications
9(222)
2 Single-Cable Mining Elevators
11(23)
2.1 Modeling
11(4)
2.2 State-Feedback for Vibration Suppression
15(3)
2.3 Observer and Output-Feedback Controller Using Cage Sensing
18(3)
2.4 Stability Analysis
21(5)
2.5 Simulation Test in a Single-Cable Mining Elevator
26(5)
2.6 Appendix
31(2)
2.7 Notes
33(1)
3 Dual-Cable Elevators
34(30)
3.1 Dual-Cable Mining Elevator Dynamics and Reformulation
34(4)
3.2 Observer for Cable Tension
38(5)
3.3 Controller for Cable Tension Oscillation Suppression and Cage Balance
43(3)
3.4 Stability Analysis
46(3)
3.5 Simulation Test for a Dual-Cable Mining Elevator
49(5)
3.6 Appendix
54(9)
3.7 Notes
63(1)
4 Elevators with Disturbances
64(31)
4.1 Problem Formulation
64(3)
4.2 Disturbance Estimator
67(4)
4.3 Observer of Cable-and-Cage State
71(2)
4.4 Control Design for Rejection of Disturbances at the Cage
73(7)
4.5 Simulation for a Disturbed Elevator
80(4)
4.6 Appendix
84(9)
4.7 Notes
93(2)
5 Elevators with Flexible Guides
95(35)
5.1 Description of Flexible Guides and Generalized Model
95(4)
5.2 Observer for Distributed States of the Cable
99(3)
5.3 Adaptive Disturbance Cancellation and Stabilization
102(6)
5.4 Adaptive Update Laws
108(2)
5.5 Control Law and Stability Analysis
110(7)
5.6 Simulation for a Flexible-Guide Elevator
117(4)
5.7 Appendix
121(8)
5.8 Notes
129(1)
6 Deep-Sea Construction
130(40)
6.1 Modeling Process and Linearization
131(10)
6.2 Basic Control Design Using Full States
141(8)
6.3 Observer for Two-Dimensional Oscillations of the Cable
149(8)
6.4 Controller with Collocated Boundary Sensing
157(1)
6.5 Simulation for a Deep-Sea Construction System
158(6)
6.6 Appendix
164(4)
6.7 Notes
168(2)
7 Deep-Sea Construction with Event-Triggered Delay Compensation
170(32)
7.1 Problem Formulation
170(5)
7.2 Observer Design Using Delayed Measurement
175(6)
7.3 Delay-Compensated Output-Feedback Controller
181(2)
7.4 Event-Triggering Mechanism
183(7)
7.5 Stability Analysis
190(3)
7.6 Simulation for Deep-Sea Construction with Sensor Delay
193(5)
7.7 Appendix
198(3)
7.8 Notes
201(1)
8 Offshore Rotary Oil Drilling
202(29)
8.1 Description of Oil-Drilling Models
203(3)
8.2 Adaptive Update Laws for Unknown Coefficients
206(2)
8.3 Output-Feedback Control Design
208(7)
8.4 Stability Analysis
215(7)
8.5 Simulation for Offshore Oil Drilling
222(7)
8.6 Notes
229(2)
II Generalizations
231(144)
9 Basic Control of Sandwich Hyperbolic PDEs
233(40)
9.1 Problem Formulation
233(1)
9.2 Backstepping for the PDE-ODE Cascade
234(4)
9.3 Backstepping for the Input ODE
238(1)
9.4 Controller and Stability Analysis
239(5)
9.5 Boundedness and Exponential Convergence of the Controller
244(11)
9.6 Extension to ODEs of Arbitrary Order
255(10)
9.7 Simulation
265(3)
9.8 Appendix
268(4)
9.9 Notes
272(1)
10 Delay-Compensated Control of Sandwich Hyperbolic Systems
273(37)
10.1 Problem Formulation
273(3)
10.2 Observer Design
276(11)
10.3 Output-Feedback Control Design
287(8)
10.4 Stability Analysis of the Closed-Loop System
295(2)
10.5 Application in Deep-Sea Construction
297(8)
10.6 Appendix
305(4)
10.7 Notes
309(1)
11 Event-Triggered Control of Sandwich Hyperbolic PDEs
310(31)
11.1 Problem Formulation
310(2)
11.2 Observer
312(3)
11.3 Continuous-in-Time Control Law
315(5)
11.4 Event-Triggering Mechanism
320(6)
11.5 Stability Analysis of the Event-Based Closed-Loop System
326(6)
11.6 Application in the Mining Cable Elevator
332(6)
11.7 Appendix
338(2)
11.8 Notes
340(1)
12 Sandwich Hyperbolic PDEs with Nonlinearities
341(34)
12.1 Problem Formulation
341(1)
12.2 State-Feedback Control Design
342(7)
12.3 Observer Design and Stability Analysis
349(7)
12.4 Stability of the Output-Feedback Closed-Loop System
356(3)
12.5 Simulation
359(3)
12.6 Appendix
362(11)
12.7 Notes
373(2)
III Adaptive Control of Hyperbolic PDE-ODE Systems
375(98)
13 Adaptive Event-Triggered Control of Hyperbolic PDEs
377(28)
13.1 Problem Formulation
377(2)
13.2 Observer
379(2)
13.3 Adaptive Continuous-in-Time Control Design
381(4)
13.4 Event-Triggering Mechanism
385(3)
13.5 Stability Analysis of the Closed-Loop System
388(5)
13.6 Application in the Flexible-Guide Mining Cable Elevator
393(6)
13.7 Appendix
399(4)
13.8 Notes
403(2)
14 Adaptive Control with Regulation-Triggered Parameter Estimation of Hyperbolic PDEs
405(34)
14.1 Problem Formulation
405(3)
14.2 Nominal Control Design
408(2)
14.3 Regulation-Triggered Adaptive Control
410(8)
14.4 Main Result
418(7)
14.5 Simulation
425(3)
14.6 Appendix
428(10)
14.7 Notes
438(1)
15 Adaptive Control of Hyperbolic PDEs with Piecewise-Constant Inputs and Identification
439(34)
15.1 Problem Formulation
439(2)
15.2 Nominal Control Design
441(1)
15.3 Event-Triggered Control Design with Piecewise-Constant Parameter Identification
442(7)
15.4 Main Result
449(10)
15.5 Application in the Mining Cable Elevator
459(5)
15.6 Appendix
464(7)
15.7 Notes
471(2)
Bibliography 473(14)
Index 487
Ji Wang is associate professor in the Department of Automation at Xiamen University, China, and a former postdoctoral scholar at the University of California, San Diego. Miroslav Krstic is Distinguished Professor at the University of California, San Diego, where he also serves as senior associate vice chancellor for research. He is a recipient of the Bellman, Reid, and Oldenburger awards, and is the coauthor of many books, including Delay-Adaptive Linear Control and Adaptive Control of Parabolic PDEs (both Princeton).
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