ℒ1 adaptive controller for a rotary steerable system

The downhole directional steering system captures mechanical connections and interactions between different parts. Due to the spatial delays, parametric uncertainties and modeling inaccuracies in the system, the closed-loop stability and robust performance are challenging problems to address. Towards this goal, the current paper presents an ℒ₁ adaptive controller which drives the output of the system, i.e. the borehole propagation angle, according to the operator´s commands in the presence of uncertainties and disturbances. Specifically, the paper considers the Explicit Force, Finitely Sharp, Zero Mass (EFFSZM) model with spatial delays in the state. The closed-loop system response is shown to have uniform transient performance bounds with respect to a bounded reference system. The performance bounds can be improved by increasing the adaptation rate. The predictable response to the commands is demonstrated in simulations.