Design and comparison of passive and active control methods in absorbing torsional vibrations of a vertical drilling string with time delay

In oil drilling systems, vibrations are one of the main sources of economic losses. In this paper, a non-linear continuous model with time delay for the vertical drilling string is proposed to study the torsional vibrations of the drilling string. The Karnopp friction model is used to simulate the stick-slip phenomenon in the interaction between the ground and the drill. In the following, two different methods for reducing torsional vibrations and controlling the stick-slip phenomenon of the drilling string are investigated. In the first method, the effect of changing the system parameters on reducing the torsional vibrations is investigated. In the second method, the torsional vibrations of the drill string are controlled using the pole placement method. In this way, corresponding to the desired response of the system, with the search of parameters space, the appropriate location of the closed-loop poles of the system is found. With the designed control system, it is observed that the torsional vibrations are absorbed and the stick-slip phenomenon is damped.