Abstract
The paper considers oilwell drilling operations and, in particular, the problem of minimizing drilling vibrations. We develop a stabilizing controller for a one dimension wave PDE with damping term that describes the drillstring torsional system. The drillstring system stability is studied via the Lyapunov theory and the control steps are deduced from a PDE backstepping approach. As a result, exponential vibration suppression is obtained in presence of stick-slip friction due to the drill-bit and the soil interactions. The torsional vibration rejection is shown through the developed simulation results. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.