Smith Predictor Based Sliding Mode Control for Torsional Vibration Control of Drillstring with Input Delay

This paper presents a smith predictor based sliding mode controller to eliminate torsional vibrations in oil well drillstrings. The drillstring model is considered as a torsional pendulum with four degrees-of-freedom. The control objective of the system is tracking desired angular velocity without stick-slip oscillations. The main purpose of this paper is to design a controller dealing with both input delay and uncertainty in the nonlinear bit-rock interaction appropriately. For robustness in the presence of parameter uncertainty in drillstring model a sliding mode controller is proposed. However, smith predictive control method is used to deal with input delay. Asymptotic stability of the system and reference angular velocity tracking is proved by the Lyapunov method. Simulation results confirm that, the designed controller is robust in the presence of parametric uncertainties while preventing torsional vibrations in the drillstring, under input delay.