Reduced order proportional integral compensator for disturbance suppression in oil well drill-strings

This paper considers stick-slip motion of the bit on the bottom hole assembly (BHA) in oil wells. This is a complex problem where the torques exerted on the drill bit are a function of the drilling speed, that is a state variable, which makes the disturbance a state dependent one leading to a nonlinear dynamic formulation. What makes the problem more complicated is the absence of the real-time measurements of drill bit speed and the disturbance torque acting on the bit. In this work, we have bypassed this problem by designing a novel reduced order observer to estimate the state variables, which cannot be sensed directly. In conjunction with this observer a feedback controller has been used to control the speed of the drill bit while at the same time reducing the effect of the disturbance torque by an integral action. Simulation studies show a strong potential for the practical applicability of this approach.