École Nationale Supérieure de
Techniques Avancées

Résumé

The coming work aims at presenting new results obtained in the field of control of oil drilling facilities. The theoretical part of our work is mainly based on backstepping controller design, a PDE-inspired technique developped a decade ago by Krstic and Smyshlyaev which allows to conduct Lyapunov stability analyses on a wide classe of dynamical systems. The main novelties of this work are to consider the presence of non-linear interactions between the driller and the rock and the main practical issues they generate(parts of the dynamics being too fast for the actuators to be exactly compensated and impossibility to carry out a prediction approach on the disturbances) in the backstepping controller design. In this framework,we generalized a stability result obtained in the linear case by Di Meglio & Bresch-Pietri to a more general Input to State Stability result in order to theoretically justify the controller design we perform. To this end,we first conveyed a precise analysis of the stick-slip limit cycle arising in the dynamics in order to include a well chosen averaged value in the controller design. Both these theoretical results and the physical peculiarities of the models of drilling systems we discuss are supported by figures obtained from a Matlab simulator which implementation is also exposed.