Suppression of axial-torsional vibrations in drilling system described by neutral-type delay differential equations

Vibrations in deep drilling systems lead to efficiency deterioration and may even cause the system failure. In this paper, a controller is designed aiming at mitigation of these vibrations, which is based on a neutral-type time delay model that represents distributed axial and torsional dynamics. First, the stability of the associated linearized dynamics is analyzed using a spectral approach. Furthermore, the open-loop system is shown to be stabilizable by state feedback which supports subsequent controller design. An optimization-based continuous pole placement technique has been employed to design a stabilizing controller, which mitigates steady-state drill-string vibrations. The effectiveness of the controller is shown in a representative case study