Super twisting control of torsional vibration in non-minimum phase nonlinear drill string system

In this paper, a second order sliding mode control law for regulation of rotational speed in a non-minimum phase drill string system is proposed. In this regard, first, the nonlinear dynamic model of a drill string which is in contact with non-Newtonian mud is conducted. Next, a super twisting sliding mode control is designed that ensures the asymptotic regulation of output during sliding motion in a finite time and stable zero dynamics. It is shown that the proposed super twisting controller is capable of adjusting the output on a desired value by generating a proper sliding surface in a finite time. The convergence of the proposed controller for the dynamic model with a higher number of mode shapes is also investigated, and it is found that by increasing the number of obtained modes, the desired output needs less computation time with more accuracy.