Recursive dynamics interconnection framework applied to angular velocity control of drilling systems

In this paper, we apply a recursive dynamics interconnection framework to achieve reliable angular velocity control of a multi-sectional drilling device with the bit off-bottom. The proposed model describing the torsional motion of the drill string takes into account the Coulomb friction between the drill string and the borehole. It has been field validated. Compensating the effects of these Coulomb side forces is necessary to avoid stick-slip oscillations. More precisely, the torsional motion of each section of the drilling pipe is modeled by a wave equation (with some non-linear terms corresponding to the Coulomb friction), while the dynamics of the top-drive and Bottom Hole Assembly are modeled by ordinary differential equations. The reference trajectory tracking problem for the drill string is solved by considering each section independently. The Coulomb side forces are seen as disturbances acting on each section of the drill string. These disturbances do not depend on time, providing there is enough energy in the system (i.e., that we have overcome the static friction). We propose here a switching-mode controller: using first a classical PI controller (with poor performance), we break the static friction. Then, the disturbance terms that correspond to the Coulomb friction terms can be estimated and compensated. The trajectory tracking is guaranteed using a recursive control procedure. The performances of the controller are illustrated through simulations using various field scenarios.