Adaptive observer design under low data rate transmission with applications to oil well drill-string

In oil well drilling operations, one of the important problem to deal with is represented by the necessity of suppressing harmful stick-slip oscillations. A control law named D-OSKIL mechanism uses the weight-on-the-bit force as a control variable to extinguish limit cycles. It uses the value of the bit angular velocity that is found through an unknown parameter observer by means of the measure of the table rotary angular speed. To improve this former estimation, we add the measurement of the angular velocity of the bit that, due to the technological constraints, arrives delayed. This new design leads us to the analysis of a time-varying delay system.