An Active Suppression Method Considering Input Time-Delay for Stick-Slip Vibration in the Drilling Procedure

This paper uses the wave equation to explain the torsional motion of the drill-string system. Solving the wave equation with the D'Alembert method, a neutral time-delay model of the drill-string system is obtained. The disturbance input, caused by the bit-rock interaction, is given consideration, and an equivalent-input-disturbance (EID) based controller is designed to mitigate the disturbance in the established model. In the actual drilling procedure, the system input time-delay increases as the length of the drill columns increases. If the influence of system input time-delay in the drilling procedure is ignored, it will most likely lead to the drill-string system instability and cause serious consequences. The essential contribution of this paper is the incorporation of input time-delay into the EID based control structure. Considering the system's input time-delay, the proposed model is more practical and has significant implications for stick-slip vibration assessment and control in drilling procedures.