Robust μ-synthesis controllers for suppressing stick-slip induced vibrations in oil well drill strings

Stick-slip friction is a major cause of drill-string failure. This paper addresses the problem of suppressing stick-slip induced oscillations in oil well drill strings using a control design technique known as μ-synthesis. This technique allows for the inclusion of modeling errors in the control design process in terms of uncertainty weights. The dynamic model of the drill string with stick-slip friction is highly nonlinear and has to be linearized around an operating point in order to use μ-synthesis. The difference between the linear and nonlinear models is characterized in terms of uncertainty weights and included in the control design process. The designed controllers are robust to uncertainty in the dynamic model, spillover, actuator uncertainty, and noise. Two controllers were designed using μ-synthesis and the simulation results are presented and discussed here. The first controller assumes no measurement delay; however, the second controller includes a sensor time delay in the measurements. Both controllers are robust and performed well.