To enable access to unconventional reservoirs of oil and (shale-) gas, geothermal energy and minerals, complex curved boreholes need to be drilled in the earth's crust. Directional drilling techniques, incorporating down-hole robotic actuation systems called rotary steerable systems, are used to generate these curved boreholes. In practice, however, boreholes drilled with such systems often show instability-induced borehole spiraling, which negatively affects the borehole quality and increases drag losses while drilling. As a basis for controller synthesis, we present a directional drilling model in terms of delay differential equations. Next, the problem of curved well-bore generation is formulated as a tracking problem and a model-based robust control strategy is developed, solving this tracking problem while guaranteeing the prevention of borehole spiraling. The effectiveness of the proposed approach is illustrated by representative case studies for the generation of curved boreholes.

This paper proposes feedback control strategies for the mitigation of torsional stick-slip oscillations in drilling systems using drag bits. Herein, we employ a model for the coupled axial-torsional drill-string dynamics in combination with a rate-independent bit-rock interaction law including both cutting and frictional effects. Using a singular perturbation and averaging approach, we show that the dynamics of this model generate an apparent velocity-weakening effect in the torque-on-bit, explaining the onset of torsional stick-slip vibrations. Based on this dynamic analysis, the (decoupled) torsional dynamics can be described by a delay-differential equation with a state-dependent delay. Using this model, we propose both state-and output-feedback control strategies for the mitigation of torsional stick-slip oscillations, where the latter strategy uses surface measurements only. The effectiveness of the proposed approaches is shown in a simulation study.