Torsional stick-slip vibrations are a significant cause of drill string damage and failure. Using damping subs distributed along the drill string has been demonstrated in both simulations and laboratory experiments as a viable solution to reduce stick-slip in drilling. The effectiveness in mitigating stick-slip can be further improved through active control of the damping strength of one or several subs. This paper evaluates a control scheme, which relies only on local downhole measurements, for various operating conditions simulated with a drill string mechanics model. Damping subs with sleeves supported on bearings and incorporated eddy current brakes are installed along the drill string, adding viscous damping to the system to mitigate torsional vibrations. The damping amount is proportional to the relative rotational speed between the sleeve and the pipe, and therefore maximized when the sleeves are non-rotating. However, if the braking force surpasses the static friction holding the sleeve in place, the sleeve slips and reduces its braking abilities. To counteract this, an On-Off-based control scheme with proportional control (P-Off controller) is implemented at the level of each sub to manipulate the value of its damping coefficient. The Off condition is triggered when local measurements indicate slipping of the sleeve. Simulations of various drilling scenarios conducted with a coupled axial and torsional drill string model show that the P-Off controller can reduce stick-slip in the system in both off-bottom and on-bottom conditions. The results indicate that the average damping coefficient, and implicitly the torque added to the system, can be greatly reduced compared to a passive damping system, consisting of the same number and positioning of subs but with constant damping coefficients. Also, the settling time of the downhole rotational speed is significantly reduced compared to the passive system. The control scheme is decentralized as it relies only on local knowledge, such as pipe rotational speed inferred from an inertial measurement unit, to estimate the top drive revolutions per minute (RPM) setpoint. Therefore, communication with the surface or with neighboring subs is not a requirement for the control implementation. The controller also shows robustness against variations in the top drive RPM and noisy downhole measurements, which is important for a real-world application. The presented approach differs from existing downhole torsional vibration damping solutions, as it does not rely on a single tool placed inside or near the bottom-hole assembly, but on several subs distributed along the drill string, with their damping strength adjusted directly downhole in a decentralized manner.

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