Quasi-bilinear modelling and control of directional drilling

A quasi-bilinear proportional-plus-integral (QBPI) controller is proposed for the attitude control of directional drilling tools for the oil and gas industry; and it is designed based on the proposed quasi-bilinear model of the directional drilling tool. The quasi-bilinear model accurately depicts the nonlinear characteristics of the directional drilling tool to a greater extent than the existing linear model, thus extends the scope of appropriate performance. The proposed QBPI control system is an LTI system and it is shown to be exponentially stable. The proposed QBPI controller outstandingly diminishes the deleterious impact of disturbances and measurement delay regarding to performance and stability of the directional drilling tool, and it yields invariant azimuth responses. Drilling cycle scheme which captures the drilling cycle and toolface actuator dynamics of the directional drilling tool, is developed. The servo-velocity and servo-position loops of the toolface servo-control architecture are proven to be robustly stable using Kharitonov's Theorem.