On the geometry of stability regions of Smith predictors subject to delay uncertainty
Identifieur interne : 002674 ( Istex/Corpus ); précédent : 002673; suivant : 002675On the geometry of stability regions of Smith predictors subject to delay uncertainty
Auteurs : Constantin-Irinel Morrescu ; Silviu-Iulian Niculescu ; Keqin GuSource :
- IMA Journal of Mathematical Control and Information [ 0265-0754 ] ; 2006-11-20.
Abstract
In this paper, we present a geometric method for describing the effects of the delay-induced uncertainty on the stability of a standard Smith predictor control scheme. The method consists of deriving the stability crossing curves in the parameter space defined by the nominal delay and delay uncertainty, respectively. More precisely, we start by computing the crossing set, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their complete classification, including also the explicit characterization of the directions in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. Several illustrative examples are also included.
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DOI: 10.1093/imamci/dnl032
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The method consists of deriving the stability crossing curves in the parameter space defined by the nominal delay and delay uncertainty, respectively. More precisely, we start by computing the crossing set, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their complete classification, including also the explicit characterization of the directions in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. 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Email: <email>Silviu.Niculescu@lss.supelec.fr</email>. On leave from HeuDiaSyC (UMR CNRS 6599), Université de Technologie de Compiègne, Centre de Recherche de Royallieu, BP 20529, 60205, Compiègne, France</corresp><corresp id="cor3"><label>§</label>Email: <email>kgu@siue.edu</email></corresp></author-notes><pub-date pub-type="epub-ppub"><month>9</month><year>2007</year></pub-date><pub-date pub-type="epub"><day>20</day><month>11</month><year>2006</year></pub-date><volume>24</volume><issue>3</issue><fpage>411</fpage><lpage>423</lpage><history><date date-type="received"><day>4</day><month>5</month><year>2006</year></date><date date-type="accepted"><day>13</day><month>9</month><year>2006</year></date></history><permissions><copyright-statement>© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.</copyright-statement><copyright-year>2007</copyright-year></permissions><abstract><p>In this paper, we present a geometric method for describing the effects of the ‘delay-induced uncertainty’ on the stability of a standard Smith predictor control scheme. The method consists of deriving the ‘stability crossing curves’ in the parameter space defined by the ‘nominal delay’ and ‘delay uncertainty’, respectively. More precisely, we start by computing the ‘crossing set’, which consists of all frequencies corresponding to all points on the stability crossing curve, and next we give their ‘complete classification’, including also the explicit characterization of the ‘directions’ in which the zeros cross the imaginary axis. This approach complements existing algebraic stability tests, and it allows some new insights in the stability analysis of such control schemes. Several illustrative examples are also included.</p></abstract><kwd-group><kwd>delay stability</kwd><kwd>robustness</kwd><kwd>Smith predictor</kwd></kwd-group></article-meta></front></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>On the geometry of stability regions of Smith predictors subject to delay uncertainty</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>On the geometry of stability regions of Smith predictors subject to delay uncertainty</title></titleInfo><name type="personal"><namePart type="given">Constantin-Irinel</namePart><namePart type="family">Morrescu</namePart><affiliation>HeuDiaSyC (UMR CNRS 6599), Universit de Technologie de Compigne, Centre de Recherche de Royallieu, BP 20529, 60205 Compigne, France and Department of Mathematics, University Politehnica of Bucharest, Romania</affiliation><affiliation>E-mail: constantin.morarescu@math.pub.ro</affiliation></name><name type="personal"><namePart type="given">Silviu-Iulian</namePart><namePart type="family">Niculescu</namePart><affiliation>Laboratoire de Signaux et Systmes (L2S), Suplec, 3, rue Joliot Curie, 91190 Gif-sur-Yvette, France</affiliation><affiliation>E-mail: Silviu.Niculescu@lss.supelec.fr</affiliation></name><name type="personal"><namePart type="given">Keqin</namePart><namePart type="family">Gu</namePart><affiliation>Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1805, USA</affiliation><affiliation>E-mail: kgu@siue.edu</affiliation></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article"></genre><subject><topic>Articles</topic></subject><originInfo><publisher>Oxford University Press</publisher><dateIssued encoding="w3cdtf">2006-11-20</dateIssued><dateCreated encoding="w3cdtf">2006-11-20</dateCreated><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType></physicalDescription><abstract>In this paper, we present a geometric method for describing the effects of the delay-induced uncertainty on the stability of a standard Smith predictor control scheme. 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