Limits of Controller Performance in the Heave Disturbance Attenuation Problem

The periodic heave movement of a floating drilling rig is transferred to an elastic pipe suspended in a drilling well. The pipe oscillates up and down in the well with the period of the heave motion pushing the mud in the well and exciting pressure fluctuations in the mud in the pipe. These dynamics are described by six coupled first-order linear partial differential equations of hyperbolic type. By using the Laplace transform, the system is solved in the frequency domain and the resulting irrational transfer functions, from the periodic heave disturbance and the controlled choke flow to the distributed pressure in the annulus around the pipe, are found for different boundary conditions. We show that the response can be improved by choosing an impedance matched boundary condition which can be achieved without the use of active control. We also derive the response when a theoretical `perfect feed-forward control law´, which yields full attenuation of the effect of the disturbance at a single point in the well-annulus, is applied. The limitations of this `perfect point control´ when considering an extended section of the well is shown.