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

Belem Saldivar; Sabine Mondié; Juan Carlos Ávila Vilchis

doi:10.1515/amcs-2016-0024

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

International Journal of Applied Mathematics and Computer Science

Volume 26 (2016): Issue 2 (June 2016)

By: Belem Saldivar, Sabine Mondié and Juan Carlos Ávila Vilchis

Open Access

|Jul 2016

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.

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Articles in this issue

DOI: https://doi.org/10.1515/amcs-2016-0024 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X

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Language: English

Page range: 335 - 349

Submitted on: Apr 4, 2015

Accepted on: Dec 2, 2015

Published on: Jul 2, 2016

Published by: University of Zielona Góra

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

drilling vibrations,

LMI approach,

ultimate boundedness,

coupled wave-ODE system

Related subjects:

Mathematics,

Applied mathematics

© 2016 Belem Saldivar, Sabine Mondié, Juan Carlos Ávila Vilchis, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 26 (2016): Issue 2 (June 2016)