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.
Author(s): Ji Wang, Miroslav Krstić
Series: Princeton Series in Applied Mathematics, 73
Publisher: Princeton University Press
Year: 2022
Language: English
Pages: 512
City: Princeton
Cover
Contents
1. Introduction
1.1 String-Actuated Mechanisms
1.2 Hyperbolic PDE-ODE Systems
1.3 “Sandwich” PDEs
1.4 Advanced Boundary Control of Hyperbolic PDEs
1.5 Notes
I. Applications
2. Single-Cable Mining Elevators
2.1 Modeling
2.2 State-Feedback for Vibration Suppression
2.3 Observer and Output-Feedback Controller Using Cage Sensing
2.4 Stability Analysis
2.5 Simulation Test in a Single-Cable Mining Elevator
2.6 Appendix
2.7 Notes
3. Dual-Cable Elevators
3.1 Dual-Cable Mining Elevator Dynamics and Reformulation
3.2 Observer for Cable Tension
3.3 Controller for Cable Tension Oscillation Suppression and Cage Balance
3.4 Stability Analysis
3.5 Simulation Test for a Dual-Cable Mining Elevator
3.6 Appendix
3.7 Notes
4. Elevators with Disturbances
4.1 Problem Formulation
4.2 Disturbance Estimator
4.3 Observer of Cable-and-Cage State
4.4 Control Design for Rejection of Disturbances at the Cage
4.5 Simulation for a Disturbed Elevator
4.6 Appendix
4.7 Notes
5. Elevators with Flexible Guides
5.1 Description of Flexible Guides and Generalized Model
5.2 Observer for Distributed States of the Cable
5.3 Adaptive Disturbance Cancellation and Stabilization
5.4 Adaptive Update Laws
5.5 Control Law and Stability Analysis
5.6 Simulation for a Flexible-Guide Elevator
5.7 Appendix
5.8 Notes
6. Deep-Sea Construction
6.1 Modeling Process and Linearization
6.2 Basic Control Design Using Full States
6.3 Observer for Two-Dimensional Oscillations of the Cable
6.4 Controller with Collocated Boundary Sensing
6.5 Simulation for a Deep-Sea Construction System
6.6 Appendix
6.7 Notes
7. Deep-Sea Construction with Event-Triggered Delay Compensation
7.1 Problem Formulation
7.2 Observer Design Using Delayed Measurement
7.3 Delay-Compensated Output-Feedback Controller
7.4 Event-Triggering Mechanism
7.5 Stability Analysis
7.6 Simulation for Deep-Sea Construction with Sensor Delay
7.7 Appendix
7.8 Notes
8. Offshore Rotary Oil Drilling
8.1 Description of Oil-Drilling Models
8.2 Adaptive Update Laws for Unknown Coefficients
8.3 Output-Feedback Control Design
8.4 Stability Analysis
8.5 Simulation for OffShore Oil Drilling
8.6 Notes
II. Generalizations
9. Basic Control of Sandwich Hyperbolic PDEs
9.1 Problem Formulation
9.2 Backstepping for the PDE-ODE Cascade
9.3 Backstepping for the Input ODE
9.4 Controller and Stability Analysis
9.5 Boundedness and Exponential Convergence of the Controller
9.6 Extension to ODEs of Arbitrary Order
9.7 Simulation
9.8 Appendix
9.9 Notes
10. Delay-Compensated Control of Sandwich Hyperbolic Systems
10.1 Problem Formulation
10.2 Observer Design
10.3 Output-Feedback Control Design
10.4 Stability Analysis of the Closed-Loop System
10.5 Application in Deep-Sea Construction
10.6 Appendix
10.7 Notes
11. Event-Triggered Control of Sandwich Hyperbolic PDEs
11.1 Problem Formulation
11.2 Observer
11.3 Continuous-in-Time Control Law
11.4 Event-Triggering Mechanism
11.5 Stability Analysis of the Event-Based Closed-Loop System
11.6 Application in the Mining Cable Elevator
11.7 Appendix
11.8 Notes
12. Sandwich Hyperbolic PDEs with Nonlinearities
12.1 Problem Formulation
12.2 State-Feedback Control Design
12.3 Observer Design and Stability Analysis
12.4 Stability of the Output-Feedback Closed-Loop System
12.5 Simulation
12.6 Appendix
12.7 Notes
III. Adaptive Control of Hyperbolic PDE-ODE Systems
13. Adaptive Event-Triggered Control of Hyperbolic PDEs
13.1 Problem Formulation
13.2 Observer
13.3 Adaptive Continuous-in-Time Control Design
13.4 Event-Triggering Mechanism
13.5 Stability Analysis of the Closed-Loop System
13.6 Application in the Flexible-Guide Mining Cable Elevator
13.7 Appendix
13.8 Notes
14. Adaptive Control with Regulation-Triggered Parameter Estimation of Hyperbolic PDEs
14.1 Problem Formulation
14.2 Nominal Control Design
14.3 Regulation-Triggered Adaptive Control
14.4 Main Result
14.5 Simulation
14.6 Appendix
14.7 Notes
15. Adaptive Control of Hyperbolic PDEs with Piecewise-Constant Inputs and Identification
15.1 Problem Formulation
15.2 Nominal Control Design
15.3 Event-Triggered Control Design with Piecewise-Constant Parameter Identification
15.4 Main Result
15.5 Application in the Mining Cable Elevator
15.6 Appendix
15.7 Notes
Bibliography
Index
