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This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole (NOPTD-I) models. The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data. In the study, step responses of NOPTD-I models are numerically calculated according to two fundamental methods, which are Mittag-Leffler (ML) function and Grunwald\u2013Letnikov (GL) definition. Particle swarm optimization (PSO) algorithm is used to perform data fitting. Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data. An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances. <\/jats:p>","DOI":"10.1142\/s1793962319410113","type":"journal-article","created":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T04:47:43Z","timestamp":1545886063000},"page":"1941011","source":"Crossref","is-referenced-by-count":39,"title":["Time-domain identification of One Noninteger Order Plus Time Delay models from step response measurements"],"prefix":"10.1142","volume":"10","author":[{"given":"Baris Baykant","family":"Alagoz","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Inonu University, Malatya, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aleksei","family":"Tepljakov","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Tallinn University of Technology, Tallinn, Estonia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdullah","family":"Ates","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Inonu University, Malatya, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eduard","family":"Petlenkov","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Tallinn University of Technology, Tallinn, Estonia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Celaleddin","family":"Yeroglu","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Inonu University, Malatya, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2019,2,18]]},"reference":[{"key":"S1793962319410113BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/3516.491407"},{"key":"S1793962319410113BIB002","volume-title":"Modern Control Engineering","volume":"4","author":"Ogata K.","year":"2002"},{"key":"S1793962319410113BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/S0959-1524(02)00062-8"},{"key":"S1793962319410113BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jprocont.2004.01.002"},{"key":"S1793962319410113BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2006.02.020"},{"key":"S1793962319410113BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.reffit.2016.11.009"},{"key":"S1793962319410113BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/9.739144"},{"key":"S1793962319410113BIB009","first-page":"1814","volume":"75","author":"Nakagawa M.","year":"1992","journal-title":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences"},{"key":"S1793962319410113BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.isatra.2011.02.003"},{"key":"S1793962319410113BIB012","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2010.0718"},{"key":"S1793962319410113BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-52950-9"},{"key":"S1793962319410113BIB015","volume-title":"Fractional Differential Equations of Mathematics in Science and Engineering","volume":"198","author":"Podlubny I.","year":"1999"},{"key":"S1793962319410113BIB016","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/807034"},{"key":"S1793962319410113BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10930-5"},{"key":"S1793962319410113BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijleo.2017.04.010"},{"key":"S1793962319410113BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S0218126608004162"},{"key":"S1793962319410113BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpowsour.2013.01.094"},{"key":"S1793962319410113BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.068"},{"key":"S1793962319410113BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.01.014"},{"issue":"2","key":"S1793962319410113BIB025","first-page":"225","volume":"89","author":"Dorcak L.","year":"2013","journal-title":"Int. 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