Active Control of Stick-Slip Torsional Vibrations of Drill-Strings using Non-Switching Sliding Mode Controller

Torsional vibrations of drill-strings are actively controlled using a non-switching sliding mode strategy. The controller is intended also to reject the effect of the interaction between the drill-bit and rock formation which induces non-linear stick-slip friction torque while tracking a desirable constant angular velocity of the drill-string. In order to demonstrate the merits of the proposed control algorithm, it is integrated with a simple two degrees-of-freedom model of the drill-string which is considered as a benchmark model for studying stick-slip induced torsional vibrations. Details of the development of the individual components making up the entire control action of the sliding mode controller (SMC) are presented. These components aim at rejecting the effect of the external disturbance of the stick-slip disturbance and tracking a reference angular velocity of the drill-string. Such development of the control action components is established using Lyapunov stability criterion. Numerical examples are presented to demonstrate the effectiveness of the SMC controller as influenced by the weight-on-bit (WOB), the drill-string rotational speed, and the main parameters of the controller. The stick-slip sensitivity (SSS) maps are developed to illustrate the performance characteristics of the active system for different operating conditions and important design parameters of the SMC. The presented active control approach is envisioned to present an invaluable and practical means for effectively mitigating the undesirable effects of stick-slip frictional disturbances on drill-stings.