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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 flexible 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. With these intentions, this paper has the main goal of confronting the torsional vibration problem over a test rig numerical model using a real-time conventional controller. The system contains two discs in which dry friction torques are applied. Therefore, the dynamical behaviour were analysed with and without controlling strategies.