Identification and control of stick-slip vibrations using Kalman estimator in oil-well drill strings

Excessive stick-slip vibrations of drill strings can cause premature component failures and inefficient drilling operations. Previous research works employ real-time measurements of all states of the drill string as feedback to the controllers to suppress such vibrations. While real-time measurements are readily available for components at the surface, only limited measurements are practically available for the downhole states. To address the requirement for downhole states, this paper proposes the utilization of Kalman estimator to estimate the downhole drill bit position and velocity based on the measurements at the surface. In the design of the estimator, the nonlinear downhole friction torque is approximated by a linear persistent disturbance model. A linear-quadratic-Gaussian (LQG) control strategy is then applied on the estimated states to mitigate the unwanted vibrations. Performance of this control scheme is investigated through numerical simulations where the dynamics of the drill string is modeled using a high fidelity lumped parameter model considering torsional stick-slip and lateral motions as well as a nonlinear friction model. The dynamic response from the high-fidelity model is demonstrated to have a close qualitative agreement with the stick-slip vibrations observed in field. The simulated results demonstrate the capability of the proposed Kalman estimator in identifying the stick-slip vibrations and estimating the downhole friction torque. The effectiveness of the proposed controller in avoiding such vibrations is also verified.