US Patent 8689906 Methods and apparatus for reducing stick-slip

A method and apparatus for estimating the instantaneous rotational speed of a bottom hole assembly at the lower end of a drill string. In one embodiment, a method includes driving the drill string by a drilling mechanism at the upper end of the drill string. A fundamental frequency of stick-slip oscillations suffered by the drill string is estimated. Variations in a drive torque of the drilling mechanism are determined. Known torsional compliance of the drill string is combined with the variations in the drive torque. An output signal representing the instantaneous rotational speed is provided.