{"id":"https://openalex.org/W2149754660","doi":"https://doi.org/10.1109/tcst.2009.2019120","title":"A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments","display_name":"A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments","publication_year":2009,"publication_date":"2009-07-01","ids":{"openalex":"https://openalex.org/W2149754660","doi":"https://doi.org/10.1109/tcst.2009.2019120","mag":"2149754660"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2009.2019120","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2009.2019120","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control Systems Technology","raw_type":"journal-article"},"type":"article","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/A5113688511","display_name":"HongSheng Li","orcid":null},"institutions":[{"id":"https://openalex.org/I2799736854","display_name":"Nanjing Institute of Technology","ror":"https://ror.org/00n6txq60","country_code":"CN","type":"education","lineage":["https://openalex.org/I2799736854"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"HongSheng Li","raw_affiliation_strings":["Department of Automation Engineering, Nanjing Institute of Technology, Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation Engineering, Nanjing Institute of Technology, Jiangsu, China","institution_ids":["https://openalex.org/I2799736854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057127971","display_name":"Ying Luo","orcid":"https://orcid.org/0000-0002-7006-2122"},"institutions":[{"id":"https://openalex.org/I121980950","display_name":"Utah State University","ror":"https://ror.org/00h6set76","country_code":"US","type":"education","lineage":["https://openalex.org/I121980950"]},{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Ying Luo","raw_affiliation_strings":["Department of Automation Science and Engineering, South China University of Technology, Guangzhou, China","Department of Electrical and Computer Engineering, Utah State University, Logan, UT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automation Science and Engineering, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Utah State University, Logan, UT, USA","institution_ids":["https://openalex.org/I121980950"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100715957","display_name":"YangQuan Chen","orcid":"https://orcid.org/0000-0002-7422-5988"},"institutions":[{"id":"https://openalex.org/I121980950","display_name":"Utah State University","ror":"https://ror.org/00h6set76","country_code":"US","type":"education","lineage":["https://openalex.org/I121980950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"YangQuan Chen","raw_affiliation_strings":["Electrical and Computer Engineering Department, Utah State University, Logan, UT, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, Utah State University, Logan, UT, USA","institution_ids":["https://openalex.org/I121980950"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":56.3069,"has_fulltext":false,"cited_by_count":405,"citation_normalized_percentile":{"value":0.99912908,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"18","issue":"2","first_page":"516","last_page":"520"},"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9879999756813049,"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":0.9846000075340271,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5578135251998901},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5136403441429138},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45290854573249817},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38183414936065674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37941139936447144},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32998162508010864}],"concepts":[{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5578135251998901},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5136403441429138},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45290854573249817},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38183414936065674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37941139936447144},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32998162508010864},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"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/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/tcst.2009.2019120","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2009.2019120","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control Systems Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","score":0.5600000023841858,"id":"https://metadata.un.org/sdg/9"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W203939894","https://openalex.org/W1553338987","https://openalex.org/W1969313263","https://openalex.org/W2051939057","https://openalex.org/W2066260126","https://openalex.org/W2125443829","https://openalex.org/W2142174241","https://openalex.org/W2148453544","https://openalex.org/W2168882942","https://openalex.org/W2177300559","https://openalex.org/W2322341491","https://openalex.org/W2477921776","https://openalex.org/W2623692599","https://openalex.org/W2980070341"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"In":[0,54],"recent":[1],"years,":[2],"it":[3],"is":[4,71,107,114,126,139],"remarkable":[5],"to":[6,14,128,143],"see":[7],"the":[8,15,87,99,105,110,117,123,137,151],"increasing":[9],"number":[10],"of":[11,19,28,50,76],"studies":[12],"related":[13],"theory":[16],"and":[17,30,40,65,92,97,141,146,159],"application":[18],"fractional":[20,44,62],"order":[21,45,63],"controller":[22,70,83],"(FOC),":[23],"speciallyPI\u00bfD\u00bfcontroller,":[24],"in":[25,136],"many":[26],"areas":[27],"science":[29],"engineering.":[31],"Research":[32],"activities":[33],"are":[34,95],"focused":[35],"on":[36],"developing":[37],"new":[38,58],"analysis":[39],"design":[41,133],"methods":[42],"for":[43,61,73],"controllers":[46],"as":[47],"an":[48],"extension":[49],"classical":[51],"control":[52],"theory.":[53],"this":[55],"paper,":[56],"a":[57,74],"tuning":[59],"method":[60,134],"proportional":[64],"derivative":[66,101],"(PD\u00bf)":[67],"or":[68],"FO-PD":[69,82],"proposed":[72,135],"class":[75],"typical":[77],"second-order":[78],"plants.":[79],"The":[80,131],"tuned":[81],"can":[84,154],"ensure":[85],"that":[86,150],"given":[88,118],"gain":[89,119,129],"crossover":[90,120],"frequency":[91,106],"phase":[93,100,111],"margin":[94],"fulfilled,":[96],"furthermore,":[98],"w.":[102],"r.":[103],"t.":[104],"zero,":[108],"i.e.,":[109],"Bode":[112],"plot":[113],"flat":[115],"at":[116],"frequency.":[121],"Consequently,":[122],"closed-loop":[124,152],"system":[125,153],"robust":[127],"variations.":[130],"FOC":[132],"paper":[138],"practical":[140],"simple":[142],"apply.":[144],"Simulation":[145],"experimental":[147],"results":[148],"show":[149],"achieve":[155],"favorable":[156],"dynamic":[157],"performance":[158],"robustness.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":29},{"year":2020,"cited_by_count":34},{"year":2019,"cited_by_count":28},{"year":2018,"cited_by_count":42},{"year":2017,"cited_by_count":33},{"year":2016,"cited_by_count":27},{"year":2015,"cited_by_count":32},{"year":2014,"cited_by_count":28},{"year":2013,"cited_by_count":24},{"year":2012,"cited_by_count":35}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}