Non-linear control of torsional and bending vibrations of oilwell drillstrings

Drillstring dynamics is highly non-linear in nature and its model can only be described by a set of non-linear differential equations. In addition to this complexity, the drillstring dynamics are not linearly controllable and thus linear control methods are not suitable for suppressing the coupled torsional and lateral vibrations of a rotating drillstring. In this paper a non-linear dynamic inversion control design method is used to suppress the lateral and the torsional vibrations of a non-linear drillstring. It was found that the designed controller is effective in suppressing the torsional vibrations and reducing the lateral vibrations significantly.