Boundary observer design for hyperbolic PDE in rotary drilling systems

It is well known that vibrations in oilwell system affect the drilling directions and may be inherent for drilling systems. Further, the environment complexity requires a minimum number of sensor variables. In this paper, for an oilwell drilling system, we present an adaptive observer design for a second-order Partial Differential Equation (PDE) with the usually neglected damping term. The design relies on the top boundary measurements only. From the Lyapunov theory and the backstepping technique, we develop an observer based control law for the one dimension wave PDE. We show an exponentially vibration stability of the partially equipped oilwell drilling system. The simulation results confirm the effectiveness of the proposed PDE observer based controller.