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Abstract. 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. General Introduction Oilwell drilling and test-rig model overviewThe actual organizational model of oil and gas industry is no longer sustainable with oil prices below $50 a barrel. Christopher et al. (2016) [1] describes what they call the "potentially game-changing disruptions that may lead oil and gas companies to rethink their operating models fundamentally". Then, to address the industry challenges, this paper focuses its efforts on modelling conventional drilling operations using a reduced scale set-up model.Briefly, the drilling process involves rock failure by a rotating drill bit. To rotate this drill bit from the top-end position (surface), the drilling rig's power source is used to turn a rotary table. A mechanism, consisting of master bushing and kelly is used to transmit the rotation from the rotary table (or top drive) to the drill string. The drill string is the subsurface component through which torque is transmitted from the surface to the bottom of the drilling system (downhole). It consists of connected lengths of drill pipes, the bottom hole assembly (BHA), and the drill bit. The BHA is the portion of the drill string between the drill pipe and the drill bit. It is made up, primarily, of drill collars (DC) and heavy weight drill pipe (HWDP).Previous studies have identified three types of vibrations that may occur during drilling operations: Torsional, Lateral and Axial, as cited in [2][3][4].In order to reproduce the phenomena inherent to the torsional vibrations present in the rotating drilling system e-mail: leopereiradias@yahoo.com.br e-mail: bruno.cayres@cefet-rj.br e-mail: hans@puc-rio.br a reduced-scale test rig set-up model (shown in Fig. 1) was developed at the PUC-Rio Dynamics and Vibration Laboratory. The set-up model consists of an electrical and a mechanical subsystems. Electrical subsystem represents the drilling rig's power source and the rotary table (or top drive), while the mechanical system represents the drill pipes, BHA and drill bit.The test rig consists of three degrees of freedom: disc 1 (R1), disc 2 (R2) and the DC-motor inertia. Also, it contains an electric ...

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