{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T16:57:45Z","timestamp":1756573065023},"reference-count":42,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Abstract and Applied Analysis"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.<\/jats:p>","DOI":"10.1155\/2013\/102068","type":"journal-article","created":{"date-parts":[[2013,6,20]],"date-time":"2013-06-20T17:19:46Z","timestamp":1371748786000},"page":"1-14","source":"Crossref","is-referenced-by-count":9,"title":["Root Locus Practical Sketching Rules for Fractional-Order Systems"],"prefix":"10.1155","volume":"2013","author":[{"given":"Ant\u00f3nio M.","family":"Lopes","sequence":"first","affiliation":[{"name":"Institute of Mechanical Engineering, UISPA, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"given":"J. A.","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Polytechnic of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida 431, 4200-072 Porto, Portugal"}]}],"member":"98","reference":[{"issue":"1","key":"1","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1109\/T-AIEE.1948.5059708","volume":"67","year":"1948","journal-title":"Transactions of the American Institute of Electrical Engineers"},{"issue":"1","key":"2","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1109\/T-AIEE.1950.5060121","volume":"69","year":"1950","journal-title":"Transactions of the American Institute of Electrical Engineers"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1137\/1012002"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1109\/13.925815"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1137\/0902032"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012991222620"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1051\/proc:1998004"},{"issue":"3","key":"10","first-page":"269","volume":"12","year":"2009","journal-title":"Fractional Calculus & Applied Analysis"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2008.08.001"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1155\/2008\/528934"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2011.01.020"},{"key":"14","year":"1993"},{"key":"15","year":"1993"},{"key":"16","volume":"198","year":"1999"},{"key":"17","series-title":"North-Holland Mathematics Studies","year":"2006"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2"},{"key":"19","year":"1991"},{"key":"20","year":"2008"},{"key":"21","year":"2006"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1142\/9781848163300"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-335-0"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.05.027"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/BF00206239"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2009.2033738"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9581-1"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1109\/TBCAS.2010.2077636"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(00)00255-7"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9680-z"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1109\/TBME.2008.2007807"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-009-9590-0"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/971641"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.11.007"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.01.021"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2005.08.033"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/40\/24\/003"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1016\/0967-0661(96)00109-8"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1002\/cta.453"},{"key":"40","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.10.054"},{"key":"41","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijhydene.2009.11.103"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-012-0495-y"},{"key":"43","year":"2011"},{"key":"44","year":"1961"}],"container-title":["Abstract and Applied Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2013\/102068.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2013\/102068.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/aaa\/2013\/102068.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T11:00:25Z","timestamp":1498042825000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/aaa\/2013\/102068\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":42,"alternative-id":["102068","102068"],"URL":"https:\/\/doi.org\/10.1155\/2013\/102068","relation":{},"ISSN":["1085-3375","1687-0409"],"issn-type":[{"value":"1085-3375","type":"print"},{"value":"1687-0409","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}