Drilling vibration reduction via attractive ellipsoid method

The oscillations occurring during the drilling process constitute a major problem to solve in the oil extraction industry. Drilling vibrations most frequently occurring in the field are torsional (stick-slip) and axial (bit-bounce). They may cause equipment failures which increase drilling operation costs. An important challenge to overcome is the modeling of drillstring dynamics and the design of effective controllers to reduce undesirable behavior. This paper introduces a neutral-type time-delay model that effectively describes the oscillatory behavior in the drilling system. It simplifies significantly the system analysis and simulation. The attractive ellipsoid method allows us develop an efficient strategy for the stabilizing controllers synthesis guaranteeing the elimination of drilling oscillations. In fact, this methodology can be applied to any system described by a time-delay equation subject to bounded disturbances. The effectiveness of this approach is validated through simulations.