{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T23:07:56Z","timestamp":1760828876709},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,4]]},"abstract":"<jats:p> Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open loop transfer function. However, these contours have been built using nonband-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. Also presented are how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response, and how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers. <\/jats:p>","DOI":"10.1142\/s0218127412300133","type":"journal-article","created":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T11:14:38Z","timestamp":1331723678000},"page":"1230013","source":"Crossref","is-referenced-by-count":16,"title":["STABILITY OF CLOSED LOOP FRACTIONAL ORDER SYSTEMS AND DEFINITION OF DAMPING CONTOURS FOR THE DESIGN OF CONTROLLERS"],"prefix":"10.1142","volume":"22","author":[{"given":"PATRICK","family":"LANUSSE","sequence":"first","affiliation":[{"name":"University of Bordeaux, IMS Laboratory \u2013 UMR 5218 CNRS, Talence, 33405, France"}]},{"given":"ALAIN","family":"OUSTALOUP","sequence":"additional","affiliation":[{"name":"University of Bordeaux, IMS Laboratory \u2013 UMR 5218 CNRS, Talence, 33405, France"}]},{"given":"VALERIE","family":"POMMIER-BUDINGER","sequence":"additional","affiliation":[{"name":"ISAE, DMIA Department, Toulouse, 31055, France"}]}],"member":"219","published-online":{"date-parts":[[2012,5,23]]},"reference":[{"key":"rf3","volume-title":"Network Analysis and Feedback Amplifier Design","author":"Bode H. W.","year":"1945"},{"key":"rf4","first-page":"1375","volume":"14","author":"Cervera J.","journal-title":"J. Vib. Contr."},{"key":"rf5","volume-title":"Linear Control System Analysis and Design, Conventional and Modern","author":"D'Azzo J. J.","year":"1995"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1080\/00207177208932261"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1080\/00207179108953619"},{"key":"rf8","volume-title":"Quantitative Feedback Design Theory \u2014 QFT","author":"Horowitz I. M.","year":"1993"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cej.2008.09.041"},{"key":"rf17","volume-title":"Syst\u00e8mes Asservis Lin\u00e9aires d'ordre Fractionnaire","author":"Oustaloup A.","year":"1983"},{"key":"rf18","volume-title":"La Commande CRONE","author":"Oustaloup A.","year":"1991"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/S0947-3580(95)70014-0"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1109\/81.817385"},{"key":"rf23","first-page":"1","volume":"6","author":"Oustaloup A.","journal-title":"Fract. Cal. Appl. Anal."},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1016\/S0967-0661(01)00154-X"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.3166\/jesa.40.211-232"},{"key":"rf28","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016531915706"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412300133","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:23:17Z","timestamp":1565094197000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412300133"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4]]},"references-count":15,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,5,23]]},"published-print":{"date-parts":[[2012,4]]}},"alternative-id":["10.1142\/S0218127412300133"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412300133","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,4]]}}}