{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:22:00Z","timestamp":1760242920495,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,11,12]],"date-time":"2016-11-12T00:00:00Z","timestamp":1478908800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The paper presents a fractional order model of a heating process and a comparison of fractional and standard PI controllers in its closed loop system. Preliminarily, an enhanced fractional order model for the heating process on non-continuous materials has been identified through a fitting algorithm on experimental data. Experimentation has been carried out on a finite length beam filled with three non-continuous materials (air, styrofoam, metal buckshots) in order to identify a model in the frequency domain and to obtain a relationship between the fractional order of the heating process and the different materials\u2019 properties. A comparison between the experimental model and the theoretical one has been performed, proving a significant enhancement of the fitting performances. Moreover the obtained modelling results confirm the fractional nature of the heating processes when diffusion occurs in non-continuous composite materials, and they show how the model\u2019s fractional order can be used as a characteristic parameter for non-continuous materials with different composition and structure. Finally, three different kinds of controllers have been applied and compared in order to keep constant the beam temperature constant at a fixed length.<\/jats:p>","DOI":"10.3390\/e18110398","type":"journal-article","created":{"date-parts":[[2016,11,14]],"date-time":"2016-11-14T11:39:50Z","timestamp":1479123590000},"page":"398","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Fractional-Order Identification and Control of Heating Processes with Non-Continuous Materials"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9574-7187","authenticated-orcid":false,"given":"Riccardo","family":"Caponetto","sequence":"first","affiliation":[{"name":"Department of Electrical, Electronic and Information Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesca","family":"Sapuppo","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Information Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincenzo","family":"Tomasello","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronic and Information Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guido","family":"Maione","sequence":"additional","affiliation":[{"name":"Department of Electrical and Information Engineering, Politecnico di Bari, Via Amendola 126\/b, 70126 Bari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paolo","family":"Lino","sequence":"additional","affiliation":[{"name":"Department of Electrical and Information Engineering, Politecnico di Bari, Via Amendola 126\/b, 70126 Bari, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,12]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_2","unstructured":"Oldham, K.B., and Spanier, J. (2006). 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