{"id":"https://openalex.org/W3111388643","doi":"https://doi.org/10.1109/tac.2020.3030860","title":"Characterizing PID Controllers for Linear Time-Delay Systems: A Parameter-Space Approach","display_name":"Characterizing PID Controllers for Linear Time-Delay Systems: A Parameter-Space Approach","publication_year":2020,"publication_date":"2020-10-13","ids":{"openalex":"https://openalex.org/W3111388643","doi":"https://doi.org/10.1109/tac.2020.3030860","mag":"3111388643"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.3030860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3030860","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03075462","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100704690","display_name":"Xu-Guang Li","orcid":"https://orcid.org/0000-0003-1739-5371"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu-Guang Li","raw_affiliation_strings":["State Key Laboratory of Synthetical Automation for Process Industries, and School of Information Science and Engineering, Northeastern University, Shenyang, China","Northeastern University [Shenyang] (3-11, Wenhua Road, Heping District, Shenyang 110819 - China)"],"raw_orcid":"https://orcid.org/0000-0003-1739-5371","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries, and School of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Northeastern University [Shenyang] (3-11, Wenhua Road, Heping District, Shenyang 110819 - China)","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058754609","display_name":"Silviu\u2010Iulian Niculescu","orcid":"https://orcid.org/0000-0002-3444-2566"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Silviu-Iulian Niculescu","raw_affiliation_strings":["Laboratoire des Signaux et Syst\u00e8mes (L2S, UMR CNRS 8506), CNRS-CentraleSup\u00e9lec-Universit\u00e9 Paris-Sud, Gif-Sur-Yvette, France","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","DISCO - Dynamical Interconnected Systems in COmplex Environments (CentraleSupelec 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex - France)"],"raw_orcid":"https://orcid.org/0000-0002-3444-2566","affiliations":[{"raw_affiliation_string":"Laboratoire des Signaux et Syst\u00e8mes (L2S, UMR CNRS 8506), CNRS-CentraleSup\u00e9lec-Universit\u00e9 Paris-Sud, Gif-Sur-Yvette, France","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]},{"raw_affiliation_string":"DISCO - Dynamical Interconnected Systems in COmplex Environments (CentraleSupelec 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex - France)","institution_ids":["https://openalex.org/I4210107720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101894334","display_name":"Junxiu Chen","orcid":"https://orcid.org/0000-0003-4350-8990"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun-Xiu Chen","raw_affiliation_strings":["State Key Laboratory of Synthetical Automation for Process Industries, and School of Information Science and Engineering, Northeastern University, Shenyang, China","Northeastern University [Shenyang] (3-11, Wenhua Road, Heping District, Shenyang 110819 - China)"],"raw_orcid":"https://orcid.org/0000-0003-4350-8990","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries, and School of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Northeastern University [Shenyang] (3-11, Wenhua Road, Heping District, Shenyang 110819 - China)","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042520521","display_name":"Tianyou Chai","orcid":"https://orcid.org/0000-0002-4623-1483"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianyou Chai","raw_affiliation_strings":["State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China","Northeastern University [Shenyang] (3-11, Wenhua Road, Heping District, Shenyang 110819 - China)"],"raw_orcid":"https://orcid.org/0000-0002-4623-1483","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]},{"raw_affiliation_string":"Northeastern University [Shenyang] (3-11, Wenhua Road, Heping District, Shenyang 110819 - China)","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2386,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.87650917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"66","issue":"10","first_page":"4499","last_page":"4513"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987000226974487,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9987000226974487,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9927999973297119,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.989300012588501,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6408051252365112},{"id":"https://openalex.org/keywords/pid-controller","display_name":"PID controller","score":0.5691090822219849},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4820588529109955},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42518821358680725},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39197424054145813},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38506096601486206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32607734203338623},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2893578112125397},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.20471274852752686},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11706757545471191}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6408051252365112},{"id":"https://openalex.org/C47116090","wikidata":"https://www.wikidata.org/wiki/Q716829","display_name":"PID controller","level":3,"score":0.5691090822219849},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4820588529109955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42518821358680725},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39197424054145813},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38506096601486206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32607734203338623},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2893578112125397},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.20471274852752686},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11706757545471191},{"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/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2020.3030860","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3030860","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03075462v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03075462","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2020, &#x27E8;10.1109/TAC.2020.3030860&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03075462v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03075462","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2020, &#x27E8;10.1109/TAC.2020.3030860&#x27E9;","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8830865568","display_name":null,"funder_award_id":"61733003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W610730700","https://openalex.org/W1506119886","https://openalex.org/W1965431946","https://openalex.org/W1974988149","https://openalex.org/W1977100588","https://openalex.org/W2015026446","https://openalex.org/W2020426469","https://openalex.org/W2038197536","https://openalex.org/W2090569656","https://openalex.org/W2095424008","https://openalex.org/W2098081686","https://openalex.org/W2099381337","https://openalex.org/W2100757047","https://openalex.org/W2116937896","https://openalex.org/W2123840888","https://openalex.org/W2142604267","https://openalex.org/W2153313182","https://openalex.org/W2160204261","https://openalex.org/W2170140261","https://openalex.org/W2283952362","https://openalex.org/W2344359354","https://openalex.org/W2402852366","https://openalex.org/W2470418570","https://openalex.org/W2500120077","https://openalex.org/W2506632866","https://openalex.org/W2521304522","https://openalex.org/W2558280960","https://openalex.org/W2560038821","https://openalex.org/W2793814012","https://openalex.org/W2842303777","https://openalex.org/W2904251574","https://openalex.org/W2963738556","https://openalex.org/W4231563473"],"related_works":["https://openalex.org/W2002388147","https://openalex.org/W3098928304","https://openalex.org/W2394883510","https://openalex.org/W2023324176","https://openalex.org/W2150958483","https://openalex.org/W2922503265","https://openalex.org/W3097920840","https://openalex.org/W2165013373","https://openalex.org/W3212795132","https://openalex.org/W2104103723"],"abstract_inverted_index":{"We":[0],"focus":[1],"on":[2,53],"the":[3,13,34,54,75,78,96,120,133,139,156,174,182,199,243,247],"proportional-integral-derivative":[4],"(PID)":[5],"controller":[6,14,111],"design":[7],"for":[8,107,241],"linear":[9],"time-delay":[10],"systems.":[11],"All":[12],"gains":[15],"(":[16,36,127],"<inline-formula":[17,22,28,37,101,113,123,128,146,161,177,184,200,248],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,23,29,38,102,114,124,129,147,162,178,185,201,249],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[19,24,30,39,103,115,125,130,148,163,179,186,202,250],"notation=\"LaTeX\">$k_P$</tex-math></inline-formula>":[20],",":[21,26,119],"notation=\"LaTeX\">$k_I$</tex-math></inline-formula>":[25],"and":[27,33,47,155,194],"notation=\"LaTeX\">$k_D$</tex-math></inline-formula>":[31],")":[32,41,150],"delay":[35],"notation=\"LaTeX\">$\\tau$</tex-math></inline-formula>":[40,104,149,164],"are":[42,51],"treated":[43],"as":[44,68,70,142],"free":[45,63],"parameters":[46],"no":[48],"particular":[49],"constraints":[50],"imposed":[52],"controlled":[55],"plants.":[56],"Such":[57],"a":[58,143,170,212,214,234,237],"problem":[59,99],"(involving":[60],"totally":[61],"four":[62],"parameters)":[64],"is":[65],"of":[66,77,122,135,145,160,173,176],"theoretical":[67],"well":[69],"practical":[71],"importance,":[72],"but,":[73],"to":[74,94],"best":[76],"authors\u2019":[79],"knowledge,":[80],"it":[81],"has":[82],"not":[83],"been":[84],"fully":[85],"explored.":[86],"First,":[87],"we":[88,231],"will":[89,226,232],"develop":[90],"an":[91],"algebraic":[92],"algorithm":[93],"solve":[95],"complete":[97,215],"stability":[98,158,244],"w.r.t.":[100],".":[105],"Consequently,":[106],"any":[108],"given":[109],"PID":[110],"vector":[112],"notation=\"LaTeX\">$(k_P,":[116,187,251],"k_I,":[117,188,252],"k_D)$</tex-math></inline-formula>":[118,189],"distribution":[121,175,204],"notation=\"LaTeX\">${NU}(\\tau)$</tex-math></inline-formula>":[126,131,180,203],"denotes":[132],"number":[134],"characteristic":[136,224],"roots":[137],"in":[138,246],"right-half":[140],"plane,":[141],"function":[144],"can":[151,205],"be":[152,166,192,206,227],"accurately":[153],"obtained":[154],"exhaustive":[157],"range":[159],"may":[165,191],"automatically":[167],"calculated.":[168],"Next,":[169],"global":[171],"understanding":[172],"over":[181],"whole":[183],"-space":[190],"achieved":[193],"all":[195],"structural":[196],"changes":[197],"regarding":[198],"analytically":[207],"determined.":[208],"To":[209],"achieve":[210],"such":[211],"goal,":[213],"positive":[216],"real":[217],"root":[218],"classification":[219],"(for":[220],"some":[221],"appropriate":[222],"auxiliary":[223],"equation)":[225],"explicitly":[228],"proposed.":[229],"Finally,":[230],"give":[233],"new":[235,238],"methodology,":[236],"parameter-space":[239],"approach,":[240],"determining":[242],"set":[245],"k_D,":[253],"\\tau)$</tex-math></inline-formula>":[254],"-space.":[255]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}