The control of drilling vibrations: A coupled PDE-ODE modeling approach
Belem Saldivar; Sabine Mondié; Juan Carlos Avila Vilchis
International Journal of Applied Mathematics and Computer Science (2016)
- Volume: 26, Issue: 2, page 335-349
- ISSN: 1641-876X
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topBelem Saldivar, Sabine Mondié, and Juan Carlos Avila Vilchis. "The control of drilling vibrations: A coupled PDE-ODE modeling approach." International Journal of Applied Mathematics and Computer Science 26.2 (2016): 335-349. <http://eudml.org/doc/280113>.
@article{BelemSaldivar2016,
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.},
author = {Belem Saldivar, Sabine Mondié, Juan Carlos Avila Vilchis},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {drilling vibrations; LMI approach; ultimate boundedness; coupled wave-ODE system},
language = {eng},
number = {2},
pages = {335-349},
title = {The control of drilling vibrations: A coupled PDE-ODE modeling approach},
url = {http://eudml.org/doc/280113},
volume = {26},
year = {2016},
}
TY - JOUR
AU - Belem Saldivar
AU - Sabine Mondié
AU - Juan Carlos Avila Vilchis
TI - The control of drilling vibrations: A coupled PDE-ODE modeling approach
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 2
SP - 335
EP - 349
AB - 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.
LA - eng
KW - drilling vibrations; LMI approach; ultimate boundedness; coupled wave-ODE system
UR - http://eudml.org/doc/280113
ER -
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