Stabilization of an Axially Moving Elastic Tape Under an External Disturbance
This paper considers the stabilization problem of a hybrid system consisting of a linear Euler-Bernoulli beam equation, which describes the motion of a tape moving axially between two sets of rollers, where the mass of the left rollers is taken into account and subject to an external disturbance. Th...
Gespeichert in:
| Veröffentlicht in: | Acta applicandae mathematicae 2022-02, Vol.177 (1), Article 12 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | 1 |
| container_start_page | |
| container_title | Acta applicandae mathematicae |
| container_volume | 177 |
| creator | Aouragh, My Driss Nahli, Mohamed |
| description | This paper considers the stabilization problem of a hybrid system consisting of a linear Euler-Bernoulli beam equation, which describes the motion of a tape moving axially between two sets of rollers, where the mass of the left rollers is taken into account and subject to an external disturbance. The objective of this work is to propose a nonlinear feedback control law to cancel the effect of the uniformly bounded external disturbance located at the left rollers. The well-posedness of the system is proved by the nonlinear maximal-monotone operators theory and the variational principle. Moreover, the exponential stability is established by the Lyapunov approach. Finally, the article concludes by presenting some numerical simulations to illustrate the validity of the theoretical results. |
| doi_str_mv | 10.1007/s10440-022-00473-2 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2628404607</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2628404607</sourcerecordid><originalsourceid>FETCH-LOGICAL-c319t-42f6ceaf04139915e34d397e9ad56ba2065a479655d418df1715bf76d2156a03</originalsourceid><addsrcrecordid>eNp9kEtLAzEURoMoWKt_wFXAdfTm3SxLrQ9ocWFdh8xMUlLGmZpMpfXXO3UEd67u5pyPy0HomsItBdB3mYIQQIAxAiA0J-wEjajUjBjg6hSNgCpNJkDNObrIeQMA3Cg1QsvXzhWxjl-ui22D24Bdg6f76Or6gJftZ2zWeF673MUSr9zW47em8ukIzfedT42r8X3M3S4Vrin9JToLrs7-6veO0ephvpo9kcXL4_NsuiAlp6YjggVVehdAUG4MlZ6LihvtjaukKhwDJZ3QRklZCTqpAtVUFkGrilGpHPAxuhlmt6n92Pnc2U27O_6SLVNsIkAo0D3FBqpMbc7JB7tN8d2lg6Vgj9XsUM321exPNct6iQ9S7uFm7dPf9D_WN_ORbio</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2628404607</pqid></control><display><type>article</type><title>Stabilization of an Axially Moving Elastic Tape Under an External Disturbance</title><source>SpringerLink Journals - AutoHoldings</source><creator>Aouragh, My Driss ; Nahli, Mohamed</creator><creatorcontrib>Aouragh, My Driss ; Nahli, Mohamed</creatorcontrib><description>This paper considers the stabilization problem of a hybrid system consisting of a linear Euler-Bernoulli beam equation, which describes the motion of a tape moving axially between two sets of rollers, where the mass of the left rollers is taken into account and subject to an external disturbance. The objective of this work is to propose a nonlinear feedback control law to cancel the effect of the uniformly bounded external disturbance located at the left rollers. The well-posedness of the system is proved by the nonlinear maximal-monotone operators theory and the variational principle. Moreover, the exponential stability is established by the Lyapunov approach. Finally, the article concludes by presenting some numerical simulations to illustrate the validity of the theoretical results.</description><identifier>ISSN: 0167-8019</identifier><identifier>EISSN: 1572-9036</identifier><identifier>DOI: 10.1007/s10440-022-00473-2</identifier><language>eng</language><publisher>Dordrecht: Springer Netherlands</publisher><subject>Applications of Mathematics ; Calculus of Variations and Optimal Control; Optimization ; Closed loop systems ; Computational Mathematics and Numerical Analysis ; Euler-Bernoulli beams ; Feedback control ; Hybrid systems ; Laboratories ; Mathematics ; Mathematics and Statistics ; Nonlinear control ; Nonlinear feedback ; Partial Differential Equations ; Probability Theory and Stochastic Processes ; Rollers ; Stabilization</subject><ispartof>Acta applicandae mathematicae, 2022-02, Vol.177 (1), Article 12</ispartof><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2022</rights><rights>The Author(s), under exclusive licence to Springer Nature B.V. 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-42f6ceaf04139915e34d397e9ad56ba2065a479655d418df1715bf76d2156a03</citedby><cites>FETCH-LOGICAL-c319t-42f6ceaf04139915e34d397e9ad56ba2065a479655d418df1715bf76d2156a03</cites><orcidid>0000-0002-3078-4294</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10440-022-00473-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10440-022-00473-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Aouragh, My Driss</creatorcontrib><creatorcontrib>Nahli, Mohamed</creatorcontrib><title>Stabilization of an Axially Moving Elastic Tape Under an External Disturbance</title><title>Acta applicandae mathematicae</title><addtitle>Acta Appl Math</addtitle><description>This paper considers the stabilization problem of a hybrid system consisting of a linear Euler-Bernoulli beam equation, which describes the motion of a tape moving axially between two sets of rollers, where the mass of the left rollers is taken into account and subject to an external disturbance. The objective of this work is to propose a nonlinear feedback control law to cancel the effect of the uniformly bounded external disturbance located at the left rollers. The well-posedness of the system is proved by the nonlinear maximal-monotone operators theory and the variational principle. Moreover, the exponential stability is established by the Lyapunov approach. Finally, the article concludes by presenting some numerical simulations to illustrate the validity of the theoretical results.</description><subject>Applications of Mathematics</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Closed loop systems</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Euler-Bernoulli beams</subject><subject>Feedback control</subject><subject>Hybrid systems</subject><subject>Laboratories</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear control</subject><subject>Nonlinear feedback</subject><subject>Partial Differential Equations</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Rollers</subject><subject>Stabilization</subject><issn>0167-8019</issn><issn>1572-9036</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp9kEtLAzEURoMoWKt_wFXAdfTm3SxLrQ9ocWFdh8xMUlLGmZpMpfXXO3UEd67u5pyPy0HomsItBdB3mYIQQIAxAiA0J-wEjajUjBjg6hSNgCpNJkDNObrIeQMA3Cg1QsvXzhWxjl-ui22D24Bdg6f76Or6gJftZ2zWeF673MUSr9zW47em8ukIzfedT42r8X3M3S4Vrin9JToLrs7-6veO0ephvpo9kcXL4_NsuiAlp6YjggVVehdAUG4MlZ6LihvtjaukKhwDJZ3QRklZCTqpAtVUFkGrilGpHPAxuhlmt6n92Pnc2U27O_6SLVNsIkAo0D3FBqpMbc7JB7tN8d2lg6Vgj9XsUM321exPNct6iQ9S7uFm7dPf9D_WN_ORbio</recordid><startdate>20220201</startdate><enddate>20220201</enddate><creator>Aouragh, My Driss</creator><creator>Nahli, Mohamed</creator><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><orcidid>https://orcid.org/0000-0002-3078-4294</orcidid></search><sort><creationdate>20220201</creationdate><title>Stabilization of an Axially Moving Elastic Tape Under an External Disturbance</title><author>Aouragh, My Driss ; Nahli, Mohamed</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-42f6ceaf04139915e34d397e9ad56ba2065a479655d418df1715bf76d2156a03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Applications of Mathematics</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Closed loop systems</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Euler-Bernoulli beams</topic><topic>Feedback control</topic><topic>Hybrid systems</topic><topic>Laboratories</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear control</topic><topic>Nonlinear feedback</topic><topic>Partial Differential Equations</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Rollers</topic><topic>Stabilization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Aouragh, My Driss</creatorcontrib><creatorcontrib>Nahli, Mohamed</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Database (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>One Business (ProQuest)</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>ProQuest Central Basic</collection><jtitle>Acta applicandae mathematicae</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Aouragh, My Driss</au><au>Nahli, Mohamed</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stabilization of an Axially Moving Elastic Tape Under an External Disturbance</atitle><jtitle>Acta applicandae mathematicae</jtitle><stitle>Acta Appl Math</stitle><date>2022-02-01</date><risdate>2022</risdate><volume>177</volume><issue>1</issue><artnum>12</artnum><issn>0167-8019</issn><eissn>1572-9036</eissn><abstract>This paper considers the stabilization problem of a hybrid system consisting of a linear Euler-Bernoulli beam equation, which describes the motion of a tape moving axially between two sets of rollers, where the mass of the left rollers is taken into account and subject to an external disturbance. The objective of this work is to propose a nonlinear feedback control law to cancel the effect of the uniformly bounded external disturbance located at the left rollers. The well-posedness of the system is proved by the nonlinear maximal-monotone operators theory and the variational principle. Moreover, the exponential stability is established by the Lyapunov approach. Finally, the article concludes by presenting some numerical simulations to illustrate the validity of the theoretical results.</abstract><cop>Dordrecht</cop><pub>Springer Netherlands</pub><doi>10.1007/s10440-022-00473-2</doi><orcidid>https://orcid.org/0000-0002-3078-4294</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0167-8019 |
| ispartof | Acta applicandae mathematicae, 2022-02, Vol.177 (1), Article 12 |
| issn | 0167-8019 1572-9036 |
| language | eng |
| recordid | cdi_proquest_journals_2628404607 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Calculus of Variations and Optimal Control Optimization Closed loop systems Computational Mathematics and Numerical Analysis Euler-Bernoulli beams Feedback control Hybrid systems Laboratories Mathematics Mathematics and Statistics Nonlinear control Nonlinear feedback Partial Differential Equations Probability Theory and Stochastic Processes Rollers Stabilization |
| title | Stabilization of an Axially Moving Elastic Tape Under an External Disturbance |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-29T11%3A40%3A01IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stabilization%20of%20an%20Axially%20Moving%20Elastic%20Tape%20Under%20an%20External%20Disturbance&rft.jtitle=Acta%20applicandae%20mathematicae&rft.au=Aouragh,%20My%20Driss&rft.date=2022-02-01&rft.volume=177&rft.issue=1&rft.artnum=12&rft.issn=0167-8019&rft.eissn=1572-9036&rft_id=info:doi/10.1007/s10440-022-00473-2&rft_dat=%3Cproquest_cross%3E2628404607%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2628404607&rft_id=info:pmid/&rfr_iscdi=true |