Abstract
A model describing the flow and pressure fluctuations in the bore-hole due to drillstring movement has been presented. It consists of a pair of coupled nonlinear partial differential equations modelling the distributed pressure and flow in the well, and a superposition of multiple sine waves for the disturbance. Considering only top-side flow and pressure as measurements, it is shown that the model can be represented by a linear time invariant finite-dimensional system with output delay. This result is achieved by linearization and de-coupling using Riemann invariants. An infinite-dimensional observer is designed that estimates the disturbance, and the estimate is used in a controller that rejects the effect of the disturbance on the down-hole pressure. A model reduction technique based on the Laguerre series representation of the transfer function is used to derive a finite-dimensional, rational transfer function for the controller. The performance of the full-order and reduced-order controllers are compared in simulations, which show satisfactory attenuation of the heave disturbance for both controllers.
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