{"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","DISCO - Dynamical Interconnected Systems in COmplex Environments (CentraleSupelec 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex - France)","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 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":"DISCO - Dynamical Interconnected Systems in COmplex Environments (CentraleSupelec 3 rue Joliot-Curie 91192 Gif-sur-Yvette cedex - France)","institution_ids":["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"]}]},{"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":2.1259,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.86932908,"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":{"grobid_xml":false,"pdf":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":[2,33],"the":[3,13,19,34,55,58,76,90,93,99,111,124,127,178],"proportional-integral-derivative":[4],"(PID)":[5],"controller":[6,14,86],"design":[7],"for":[8,82,176],"linear":[9],"time-delay":[10],"systems.":[11],"All":[12],"gains":[15],"($k_P$,$k_I$,":[16],"and$k_D$)":[17],"and":[18,27,110,134],"delay":[20],"($\\tau$)":[21],"are":[22,31],"treated":[23],"as":[24,48,50,102],"free":[25,43],"parameters":[26],"no":[28],"particular":[29],"constraints":[30],"imposed":[32],"controlled":[35],"plants.":[36],"Such":[37],"a":[38,103,120,147,149,169,172],"problem":[39,79],"(involving":[40],"totally":[41],"four":[42],"parameters)":[44],"is":[45],"of":[46,57,95,123],"theoretical":[47],"well":[49],"practical":[51],"importance,":[52],"but,":[53],"to":[54,74],"best":[56],"authors\u2019":[59],"knowledge,":[60],"it":[61],"has":[62],"not":[63],"been":[64],"fully":[65],"explored.":[66],"First,":[67],"we":[68,166],"will":[69,161,167],"develop":[70],"an":[71],"algebraic":[72],"algorithm":[73],"solve":[75],"complete":[77,150],"stability":[78,113,179],"w.r.t.$\\tau$.":[80],"Consequently,":[81],"any":[83],"given":[84],"PID":[85],"vector$(k_P,":[87],"k_I,":[88,129,183],"k_D)$,":[89],"distribution":[91,125],"of${NU}(\\tau)$(${NU}(\\tau)$denotes":[92],"number":[94],"characteristic":[96,159],"roots":[97],"in":[98,181],"right-half":[100],"plane,":[101],"function":[104],"of$\\tau$)":[105],"can":[106,140],"be":[107,116,132,141,162],"accurately":[108],"obtained":[109],"exhaustive":[112],"range":[114],"of$\\tau$may":[115],"automatically":[117],"calculated.":[118],"Next,":[119],"global":[121],"understanding":[122],"of${NU}(\\tau)$over":[126],"whole$(k_P,":[128],"k_D)$-space":[130],"may":[131],"achieved":[133],"all":[135],"structural":[136],"changes":[137],"regarding":[138],"the${NU}(\\tau)$distribution":[139],"analytically":[142],"determined.":[143],"To":[144],"achieve":[145],"such":[146],"goal,":[148],"positive":[151],"real":[152],"root":[153],"classification":[154],"(for":[155],"some":[156],"appropriate":[157],"auxiliary":[158],"equation)":[160],"explicitly":[163],"proposed.":[164],"Finally,":[165],"give":[168],"new":[170,173],"methodology,":[171],"parameter-space":[174],"approach,":[175],"determining":[177],"set":[180],"the$(k_P,":[182],"k_D,":[184],"\\tau)$-space.":[185]},"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":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
