Torsional Vibration Suppression with Boundary Impulsive Conditions in Rotary Drilling System

This paper presents a nonlinear control scheme to stabilize the problem of torsional vibration suppression with boundary impulsive conditions. A new nonlinear dynamical system is developed. Based on semi-group theory, we prove the well-posednes of the proposed system. In the model development, nonlinearities that arise due to dry friction and loss of contact is considered. Therefore, the impulsive system stability analysis is carried out by using Lyapunov theory and a comparison method. Numerical simulations show the relevance of our result for impulsive system.