Part of the process of exploration and development of an oil field consists of the drilling operations for oil and gas wells. Particularly for deep water and ultra deep water wells, the operation requires the control of a very exible structure which is subjected to complex boundary conditions such as the nonlinear interactions between drill bit and rock formation and between the drill-string and borehole wall. Concerning this complexity the stick-slip phenomenon is a major component, related to the torsional vibration and it can excite both axial and lateral vibrations. That may cause premature failure of drill-string components. So, the reduction and avoidance of stickslip oscillations are very valuable items in terms of savings and exploration time. With these intentions, this study has the main goal of confronting the torsional vibration problem using a real-time robust control strategy. The approach is obtained following some steps such as: Open-loop analysis of the drilling system considering a top-drive actuator and the drill-string system; Design of a novel controller using different angular velocity setpoints in a closed-loop system; Control of the torsional vibration considering the nonlinearity due to friction interaction in the wall and in the donwhole system; valuate a non-stop control system while drilling; Verification by numerical simulations. In this presentation the theoretical basis behind the drilling system will be given, as well examples of numerical results providing a stable and satisfactory controlled drilling operation.