<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell drilling system. The model considered consists of a wave equation coupled to an ordinary differential equation (ODE) through a nonlinear function describing the rock-bit interaction. We propose a systematic method to design feedback controllers guaranteeing ultimate boundedness of the system trajectories and leading consequently to the suppression of harmful dynamics. The proposal of a Lyapunov-Krasovskii functional provides stability conditions stated in terms of the solution of a set of linear and bilinear matrix inequalities (LMIs, BMIs). Numerical simulations illustrate the efficiency of the obtained control laws.</p></abstract>

The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell drilling system. The model considered consists of a wave equation coupled to an ordinary differential equation (ODE) through a nonlinear function describing the rock-bit interaction. We propose a systematic method to design feedback controllers guaranteeing ultimate boundedness of the system trajectories and leading consequently to the suppression of harmful dynamics. The proposal of a Lyapunov-Krasovskii functional provides stability conditions stated in terms of the solution of a set of linear and bilinear matrix inequalities (LMIs, BMIs). Numerical simulations illustrate the efficiency of the obtained control laws.

The control of drilling vibrations: A coupled PDE-ODE modeling approach

Faculty of Engineering Autonomous University of the State of Mexico, Instituto Literario No. 100 Ote., 50130 Toluca, Mexico

Department of Automatic Control CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, C.P. 07360, México D.F., Mexico

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"The control of drilling vibrations: A coupled PDE-ODE modeling approach"}

The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell drilling system. The model...

The control of drilling vibrations: A coupled PDE-ODE modeling approach

Published Online: Jul 02, 2016

Page range: 335 - 349

Received: Apr 04, 2015

Accepted: Dec 02, 2015

DOI: https://doi.org/10.1515/amcs-2016-0024

Keywords
drilling vibrations, LMI approach, ultimate boundedness, coupled wave-ODE system

© by Belem Saldivar

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The control of drilling vibrations: A coupled PDE-ODE modeling approach

Published Online: Jul 02, 2016

Page range: 335 - 349

Received: Apr 04, 2015

Accepted: Dec 02, 2015

DOI: https://doi.org/10.1515/amcs-2016-0024

Keywordsdrilling vibrations, LMI approach, ultimate boundedness, coupled wave-ODE system

© by Belem Saldivar

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
drilling vibrations, LMI approach, ultimate boundedness, coupled wave-ODE system