Abstract
To address security issues in oilwell drillstring system, the drilling operation handling which is in generally not autonomous but ensured by an operator may be drill bit destructive or fatal for the machine. In drilling process, the drillstring control at the right speed is not sufficient and a rate of fluid mud is necessary. This paper studies coupling between torsional vibrations, as a wave equation, the drillstring slider displacement, and the fluid flow distribution. The design consists to couple the fluid behavior ODE and the drillstring torsional vibration phenomena PDE. In presence of damping in the wave equation, we show only a PDE-ODE system stability. Further, investigation of the wave equation without damping term coupled with the fluid dynamics is reduced to a difference equation, and the designed controller leads to an asymptotic stability of the torsional variable, the downhole pressure, and the annulus pressure. Simulation results are presented to illustrate the PDE-ODE coupled system stability.