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ArticleOriginal scientific text

Title

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

Authors 1, 2, 1

Affiliations

  1. Faculty of Engineering, Autonomous University of the State of Mexico, Instituto Literario No. 100 Ote., 50130 Toluca, Mexico
  2. Department of Automatic Control, CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, C.P. 07360, México D.F., Mexico

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.

Keywords

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

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Additional information

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

International Journal of Applied Mathematics and Computer Science
2016/26/2
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Pages:
335-349
Main language of publication
English
Published
2016

DOI: 10.1515/amcs-2016-0024

Exact and natural sciences