Delay-Compensated Control of Sandwiched ODE-PDE-ODE Hyperbolic Systems for Oil Drilling and Disaster Relief

TL;DR

This paper develops a delay-compensated output-feedback boundary control for complex ODE-PDE-ODE hyperbolic systems, with applications in oil drilling and disaster relief, ensuring stability and reducing oscillations.

Contribution

It introduces a novel control design using backstepping and frequency-domain methods for sandwiched hyperbolic PDEs with delayed measurements, applicable to real-world engineering problems.

Findings

The control stabilizes the coupled ODE-PDE-ODE system.

Simulation shows reduced cable oscillations in oil drilling vessel.

Control maintains stability under certain disturbances.

Abstract

Motivated by engineering applications of subsea installation by deepwater construction vessels in oil drilling, and of aid delivery by unmanned aerial vehicles in disaster relief, we develop output-feedback boundary control of heterodirectional coupled hyperbolic PDEs sandwiched between two ODEs, where the measurement is the output state of one ODE and suffers a time delay. After rewriting the time-delay dynamics as a transport PDE of which the left boundary connects with the sandwiched system, a state observer is built to estimate the states of the overall system of ODE-heterodirectional coupled hyperbolic PDEs-ODE-transport PDE using the right boundary state of the last transport PDE. An observer-based output-feedback controller acting at the first ODE is designed to stabilize the overall system using backstepping transformations and frequency-domain designs. The exponential stability results of the closed-loop system, boundedness and exponential convergence of the control input are proved. The obtained theoretical result is applied to control of a deepwater oil drilling construction vessel as a simulation case, where the simulation results show the proposed control design reduces cable oscillations and places the oil drilling equipment to be installed in the target area on the sea floor. Performance deterioration under extreme and unmodeled disturbances is also illustrated.