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.

Automated summary

This paper proposes a second order sliding mode control law for regulation of rotational speed in a non-minimum phase drill string system. The nonlinear dynamic model of a drill string in contact with non-Newtonian mud is conducted. The results show that the proposed super twisting controller is capable of adjusting the output to a desired value during sliding motion, and increasing the number of mode shapes improves computation accuracy.