Rejecting heave-induced pressure oscillations in a semilinear hyperbolic well model

In this paper, we apply recent results on the output feedback control of 2×2 semilinear systems to the problem of rejecting heave-induced pressure oscillations in offshore drilling. The well is modeled as a transmission line with nonlinear friction, with both actuation and measurement restricted to one boundary. The heave motion is represented by disturbance terms entering both inside the domain and at the uncontrolled boundary. We construct an output feedback controller to track a reference pressure at one location in the well. The controller performance is demonstrated in simulations