Accurate control of weight-on-bit (WOB) in oil and gas drilling plays an important role in achieving high rates of penetration (ROP) and minimizing drillstring vibrations. In this paper, we propose a nonlinear, stochastic model of downhole WOB, and provide a framework for estimation, and control of the proposed model. We focus on real-time estimation of modeling and measurement uncertainties, and use these estimates to adapt the controller characteristics accordingly. The presented methodology is simulated for various scenarios, and benchmarked against existing control techniques in the industry.

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