Prediction-based control of linear input-delay system subject to state-dependent state delay – Application to suppression of mechanical vibrations in drilling

In this paper, we consider linear dynamics subject to a distributed state-dependent delay and a pointwise input-delay. We propose a prediction-based controller which exponentially stabilizes the plant. The controller design is based on a backstepping approach where delays are reformulated as hyperbolic transport PDEs. Infinity-norm stability analysis of the corresponding closed-loop system is addressed. We show that this result is of interest to suppress mechanical vibrations arising in drilling facilities, which have been attributed recently to a coupling between torsional and vertical displacement involving an implicit state delay equation. Numerical simulations illustrate the merits of our controller in this context.