This paper introduces a robust observer-based output feedback control strategy that enables the generation of complex three-dimensional borehole trajectories created by directional drilling systems, while avoiding undesired transient behavior. The model-based controller relies on a set of nonlinear delay differential equations describing the borehole evolution. Herein, only local orientation measurements of the bottom hole assembly of the drilling system are employed. Controller and observer gains are synthesized by optimizing the location of the rightmost pole of the closed-loop dynamics, using a spectral approach for delay differential equations. Moreover, the strategy is extended to cope with the uncertainty of key system parameters in the directional drilling process. The effectiveness of the designed controller is tested in an illustrative benchmark study.

Directional drilling systems generate complex curved boreholes in the earth's crust for the exploration and harvesting of oil, gas and geothermal energy. In practice, boreholes drilled with such systems often show instability-induced borehole spiraling, which negatively affects the borehole quality and increases drag losses while drilling. This paper presents a dynamic state-feedback controller design approach for the stable generation of complex, three-dimensional borehole geometries, while avoiding undesired borehole spiraling. The design is based on a model for three-dimensional borehole propagation in terms of nonlinear delay differential equations. After casting the problem of borehole propagation into a tracking problem, it is shown that complex, three-dimensional borehole geometries can be asymptotically stabilized with the proposed controller. The effectiveness of the proposed approach is evidenced in an illustrative benchmark study.