MC 6460

## Speaker

Jean Auriol | University of Calgary

## Title

Operating methods for the robust control of hyperbolic systems and application to directional drilling.

## Abstract

Linear hyperbolic systems naturally arise when modeling industrial processes for which the dynamics involve a transport phenomenon (related applications include electric transmission lines, traffic flow, oil well drilling…). These systems are the source of complex control and engineering problems (mostly due to the transport phenomena and the presence of destabilizing terms), which have impact in terms of environmental safety and economical feasibility. In this presentation, we develop operating methods for the control of such hyperbolic systems. More precisely, using a backstepping approach combined with a rewrite of the system as a difference equation, we design an explicit control law (and the corresponding dual observer) that guarantees the robust output feedback stabilization of a system of two hyperbolic PDEs. The proposed control law introduces three degrees of freedom (by means of tuning parameters) that enable a trade-off between performance and robustness, between disturbance rejection and sensitivity to noise. The proposed approach can be extended to higher dimensional systems and networks interconnected systems. Finally, we conclude this presentation by considering the problem of toolface control for directional drilling operations with the bit off-bottom. The torsional dynamics of such a system can be modeled as a non-linear hyperbolic system for which a robust backstepping-based state-observer is designed to monitor at all times the torque and the RPM. Using these estimations, we design an algorithm that controls the toolface orientation. The different algorithms are tested against real field data.