Observer Design for a Wellbore Drilling System With Downhole Measurement Feedback

The increasingly complex oil and gas wellbore condition and the need of drilling in more challenging downhole environments motivate rising research on the drilling control system based on real-time state feedback or measurements from the bottom of the wellbore. However, due to the complex downhole condition and cost-viability, mud pulse telemetry is normally used in this industry to transmit the downhole measurements to the surface, which can cause a large data communication delay as a result of its low bandwidth and slow mud pulse transmission. Since the major drilling control is on the surface, an observer is required to estimate the real-time states of the drilling dynamics as well as the downhole condition, based on the delayed downhole measurement. In this study, we first construct a drilling system dynamics model with coupled axial and torsional dynamics. Then, with the existence of a large output measurement delay, two chain-observer design strategies are introduced for the case of slowly varying control inputs and that of fast-varying control inputs, respectively. The effectiveness of the proposed observer design methods is shown through numerical results.