{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T17:15:42Z","timestamp":1776446142066,"version":"3.51.2"},"reference-count":0,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"2","license":[{"start":{"date-parts":[[2016,6,1]],"date-time":"2016-06-01T00:00:00Z","timestamp":1464739200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats: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.<\/jats:p>","DOI":"10.1515\/amcs-2016-0024","type":"journal-article","created":{"date-parts":[[2016,7,6]],"date-time":"2016-07-06T10:03:24Z","timestamp":1467799404000},"page":"335-349","source":"Crossref","is-referenced-by-count":39,"title":["The control of drilling vibrations: A coupled PDE-ODE modeling approach"],"prefix":"10.61822","volume":"26","author":[{"given":"Belem","family":"Saldivar","sequence":"first","affiliation":[{"name":"Faculty of Engineering Autonomous University of the State of Mexico, Instituto Literario No. 100 Ote., 50130 Toluca, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sabine","family":"Mondi\u00e9","sequence":"additional","affiliation":[{"name":"Department of Automatic Control CINVESTAV-IPN, Av. IPN No. 2508, Col. San Pedro Zacatenco, C.P. 07360, M\u00e9xico D.F., Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Carlos","family":"\u00c1vila Vilchis","sequence":"additional","affiliation":[{"name":"Faculty of Engineering Autonomous University of the State of Mexico, Instituto Literario No. 100 Ote., 50130 Toluca, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2016,7,2]]},"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/26\/2\/article-p335.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/amcs-2016-0024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,15]],"date-time":"2024-05-15T22:57:08Z","timestamp":1715813828000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.sciendo.com\/article\/10.1515\/amcs-2016-0024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2016,7,2]]},"published-print":{"date-parts":[[2016,6,1]]}},"alternative-id":["10.1515\/amcs-2016-0024"],"URL":"https:\/\/doi.org\/10.1515\/amcs-2016-0024","relation":{},"ISSN":["2083-8492"],"issn-type":[{"value":"2083-8492","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,1]]}}}