Adaptive event-triggered PDE control for load-moving cable systems

• Published in: Automatica (Oxford) Vol. 129; p. 109637
• Main Authors: Wang, Ji, Krstic, Miroslav
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2021
• Subjects: Adaptive control; Backstepping; Cable elevators; Event-triggered control; Hyperbolic PDEs; Backstepping; Cable elevators; Hyperbolic PDEs; Event-triggered control; Adaptive control
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2021.109637

Motivated by lateral vibration suppression of a mining cable elevator, which is a load-moving cable system, where the load moves along a viscoelastic guideway whose stiffness and damping coefficients are unknown, we present event-triggered adaptive output-feedback boundary control design of a hyperbolic PDE–ODE coupled system using the measurements at the PDE actuated boundary and the ODE, where the PDE subsystem is a class of 2 × 2 coupled hyperbolic PDEs with spatially-varying coefficients and on a time-varying domain, and a high uncertainty exist in the system matrix of the ODE subsystem at the uncontrolled boundary of the PDE. A continuous-in-time observer-based adaptive backstepping control law is designed where the control gains can be self-tuned to adjust the system matrix of the ODE into a given target system matrix, based on which an observer-based dynamic event-triggering mechanism is built and the existence of a minimal dwell-time is proved. The asymptotic stability of the overall adaptive event-based output-feedback closed-loop system is proved via Lyapunov analysis. In numerical simulation, the performance of the proposed controller is verified in lateral vibration suppression of a mining cable elevator.