Study of stick-slip suppression and robustness to parametric uncertainty in drill strings containing torsional vibration tool using sliding-mode control

Excessive stick-slip vibration of drill strings can cause inefficiency and unsafety of drilling operations. To suppress the stick-slip vibration that occurred during the downhole drilling process, a drill string torsional vibration system considering the torsional vibration tool has been proposed on the basis of the 4-degree of freedom lumped-parameter model. In the design of the model, the tool is approximated by a simple torsional pendulum that brings impact torque to the drill bit. Furthermore, two sliding mode controllers, U1 and U2, are used to suppress stick-slip vibrations while enabling the drill bit to track the desired angular velocity. Aiming at parameter uncertainty and system instability in the drilling operations, a parameter adaptation law is added to the sliding mode controller U2. Finally, the suppression effects of stick-slip and robustness of parametric uncertainty about the two proposed controllers are demonstrated and compared by simulation and field test results. This paper provides a reference for the suppression of stick-slip vibration and the further study of the complex dynamics of the drill string.