H∞ control for suppressing stick-slip in oil well drillstrings

We show, applying the linear H_∞ control design technique, that the suppression of stick-slip oscillations and transient behavior can be largely improved over a PD-like control system currently applied in oil well drilling. Using rough knowledge (e.g. size and induced oscillation frequency) of the friction disturbance, the appropriate choice of dynamic weighting functions can make the closed loop system robust toward the substantial uncertainty in the knowledge of the nonlinear friction. After an introduction to drilling engineering and a description of the drilling system, a condensed analysis of the stick-slip phenomenon in drillstrings and a brief history of control solutions for the drillstring problem are given, and H_∞ control solutions for allied systems are described. Then, the general principles of linear H_∞ control design are sketched. Subsequently, the H_∞ control design technique is applied to design a controller for the system under study. Next, the improved closed-loop behavior toward stick-slip oscillations is shown in simulations and experiments. Conclusions with respect to the results are drawn