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. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.