{"id":"https://openalex.org/W2127627747","doi":"https://doi.org/10.1109/etfa.2009.5347160","title":"A proposal for optimal tuning of fractional order proportional integral-proportional derivative PI<sup>α</sup>-PD<sup>ß</sup> controllers","display_name":"A proposal for optimal tuning of fractional order proportional integral-proportional derivative PI<sup>α</sup>-PD<sup>ß</sup> controllers","publication_year":2009,"publication_date":"2009-09-01","ids":{"openalex":"https://openalex.org/W2127627747","doi":"https://doi.org/10.1109/etfa.2009.5347160","mag":"2127627747"},"language":"en","primary_location":{"id":"doi:10.1109/etfa.2009.5347160","is_oa":false,"landing_page_url":"https://doi.org/10.1109/etfa.2009.5347160","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Conference on Emerging Technologies & Factory Automation","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020909358","display_name":"K. Bettou","orcid":null},"institutions":[{"id":"https://openalex.org/I125485651","display_name":"University Fr\u00e8res Mentouri Constantine 1","ror":"https://ror.org/017wv6808","country_code":"DZ","type":"education","lineage":["https://openalex.org/I125485651"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Bettou Khalfa","raw_affiliation_strings":["D\u00e9partement d'Electronique, Universit\u00e9 Mentouri Constantine, Algeria","D\u00e9partement d'Electronique, Universit\u00e9 Mentouri de Constantine, Route Ain El-bey, 25000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'Electronique, Universit\u00e9 Mentouri Constantine, Algeria","institution_ids":["https://openalex.org/I125485651"]},{"raw_affiliation_string":"D\u00e9partement d'Electronique, Universit\u00e9 Mentouri de Constantine, Route Ain El-bey, 25000, Algeria","institution_ids":["https://openalex.org/I125485651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084014354","display_name":"Abdelfatah Charef","orcid":"https://orcid.org/0000-0002-4429-5192"},"institutions":[{"id":"https://openalex.org/I125485651","display_name":"University Fr\u00e8res Mentouri Constantine 1","ror":"https://ror.org/017wv6808","country_code":"DZ","type":"education","lineage":["https://openalex.org/I125485651"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Abdelfatah Charef","raw_affiliation_strings":["D\u00e9partement d'Electronique, Universit\u00e9 Mentouri Constantine, Algeria","D\u00e9partement d'Electronique, Universit\u00e9 Mentouri de Constantine, Route Ain El-bey, 25000, Algeria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement d'Electronique, Universit\u00e9 Mentouri Constantine, Algeria","institution_ids":["https://openalex.org/I125485651"]},{"raw_affiliation_string":"D\u00e9partement d'Electronique, Universit\u00e9 Mentouri de Constantine, Route Ain El-bey, 25000, Algeria","institution_ids":["https://openalex.org/I125485651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072043206","display_name":"Blas M. Vinagre","orcid":"https://orcid.org/0000-0001-5039-0738"},"institutions":[{"id":"https://openalex.org/I80606768","display_name":"Universidad de Extremadura","ror":"https://ror.org/0174shg90","country_code":"ES","type":"education","lineage":["https://openalex.org/I80606768"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Blas M. Vinagre","raw_affiliation_strings":["Department of Electrical, Electronic and Automation Engineering, University of Extremadura, Badajoz, Spain","Dept. of Electrical, Electronic and Automation Engineering, University of Extremadura, Avda. De Elvas, s/n. 06071 Badajos, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical, Electronic and Automation Engineering, University of Extremadura, Badajoz, Spain","institution_ids":["https://openalex.org/I80606768"]},{"raw_affiliation_string":"Dept. of Electrical, Electronic and Automation Engineering, University of Extremadura, Avda. De Elvas, s/n. 06071 Badajos, Spain","institution_ids":["https://openalex.org/I80606768"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.602,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.6380746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"135","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11081","display_name":"Advanced Control Systems Design","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9760000109672546,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pi","display_name":"Pi","score":0.5043584108352661},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4455137550830841},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.43812352418899536},{"id":"https://openalex.org/keywords/pid-controller","display_name":"PID controller","score":0.4300727844238281},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4269031882286072},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3020066022872925},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29862457513809204},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2974932789802551},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.0970328152179718}],"concepts":[{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.5043584108352661},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4455137550830841},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.43812352418899536},{"id":"https://openalex.org/C47116090","wikidata":"https://www.wikidata.org/wiki/Q716829","display_name":"PID controller","level":3,"score":0.4300727844238281},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4269031882286072},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3020066022872925},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29862457513809204},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2974932789802551},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0970328152179718},{"id":"https://openalex.org/C536315585","wikidata":"https://www.wikidata.org/wiki/Q7698332","display_name":"Temperature control","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/etfa.2009.5347160","is_oa":false,"landing_page_url":"https://doi.org/10.1109/etfa.2009.5347160","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 IEEE Conference on Emerging Technologies & Factory Automation","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W55790716","https://openalex.org/W806633968","https://openalex.org/W1480944004","https://openalex.org/W1533106049","https://openalex.org/W1969313263","https://openalex.org/W2118043890","https://openalex.org/W2126535736","https://openalex.org/W2142610074","https://openalex.org/W2155572235","https://openalex.org/W2183809567","https://openalex.org/W2283952362","https://openalex.org/W6628737827"],"related_works":["https://openalex.org/W2030762054","https://openalex.org/W3157618815","https://openalex.org/W2401345448","https://openalex.org/W255820224","https://openalex.org/W2002388147","https://openalex.org/W2278807000","https://openalex.org/W2964228179","https://openalex.org/W2628590989","https://openalex.org/W3098928304","https://openalex.org/W2742629407"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"propose":[4],"a":[5,31,34,46,86],"fractional":[6,70,121],"PI\u03b1-PD\u03b2controller":[7],"that":[8,108],"tuned":[9],"with":[10,85],"integral":[11,18,80,91],"performance":[12,117],"criterion.":[13],"The":[14,51,90],"orders":[15,111],"of":[16,33,59,68,101,118],"the":[17,57,65,69,72,78,105,119],"and":[19,23,110],"derivative":[20],"parts,":[21],"\u03b1":[22],"\u03b2,":[24],"respectively,":[25],"are":[26,103],"fractional.":[27],"This":[28,38],"controller":[29,49],"is":[30,54,75,93],"generalization":[32],"conventional":[35,47],"PI-PD":[36,48],"controller.":[37],"expansion":[39],"could":[40],"provide":[41],"much":[42],"more":[43],"flexibility":[44],"than":[45],"design.":[50],"tuning":[52],"method":[53,74],"based":[55,76],"on":[56,77],"solution":[58],"an":[60],"optimization":[61,112],"problem.":[62],"For":[63],"setting":[64],"six":[66],"parameters":[67],"PI\u03b1-PD\u03b2controller,":[71],"proposed":[73,120],"minimum":[79,87],"squared":[81],"error":[82],"(ISE)":[83],"criterion":[84,92],"control":[88],"effort.":[89],"calculated":[94],"by":[95],"using":[96],"Hall-Sartaurius":[97],"method.":[98],"Two":[99],"cases":[100],"study":[102],"given;":[104],"results":[106],"demonstrate":[107],"gains":[109],"leads":[113],"to":[114],"better":[115],"transient":[116],"PI\u03b1-PD\u03b2control":[122],"structure.":[123]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}