{"id":"https://openalex.org/W4317535280","doi":"https://doi.org/10.1177/01423312221127742","title":"Design of PI <sup>\u03bb</sup> -PD <sup>\u03bc</sup> controller for high-order systems based on model order reduction using BB-BC and time moment matching","display_name":"Design of PI <sup>\u03bb</sup> -PD <sup>\u03bc</sup> controller for high-order systems based on model order reduction using BB-BC and time moment matching","publication_year":2023,"publication_date":"2023-01-20","ids":{"openalex":"https://openalex.org/W4317535280","doi":"https://doi.org/10.1177/01423312221127742"},"language":"en","primary_location":{"id":"doi:10.1177/01423312221127742","is_oa":false,"landing_page_url":"https://doi.org/10.1177/01423312221127742","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","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/A5002933238","display_name":"Min Zheng","orcid":"https://orcid.org/0000-0003-1123-0306"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Zheng","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, China","Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, China","institution_ids":["https://openalex.org/I113940042"]},{"raw_affiliation_string":"Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032941294","display_name":"Peike Li","orcid":"https://orcid.org/0000-0003-1809-2137"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Peike Li","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, China"],"raw_orcid":"https://orcid.org/0000-0002-0632-2786","affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100414577","display_name":"Quan Liu","orcid":"https://orcid.org/0000-0002-9036-0290"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Quan Liu","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017723132","display_name":"Haisheng Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haisheng Lin","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":null,"apc_paid":null,"fwci":0.4907,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.61015073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"47","issue":"15","first_page":"3098","last_page":"3110"},"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":0.9952999949455261,"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":0.9825000166893005,"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/pid-controller","display_name":"PID controller","score":0.7163521647453308},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5818456411361694},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5440163016319275},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.5376914739608765},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5367988348007202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5340251922607422},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5023722648620605},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.4202347695827484},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3446069061756134},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33709508180618286},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2401968240737915},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23072519898414612},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13393518328666687},{"id":"https://openalex.org/keywords/temperature-control","display_name":"Temperature control","score":0.10175517201423645},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08070829510688782}],"concepts":[{"id":"https://openalex.org/C47116090","wikidata":"https://www.wikidata.org/wiki/Q716829","display_name":"PID controller","level":3,"score":0.7163521647453308},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5818456411361694},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5440163016319275},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5376914739608765},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5367988348007202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5340251922607422},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5023722648620605},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.4202347695827484},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3446069061756134},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33709508180618286},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2401968240737915},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23072519898414612},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13393518328666687},{"id":"https://openalex.org/C536315585","wikidata":"https://www.wikidata.org/wiki/Q7698332","display_name":"Temperature control","level":2,"score":0.10175517201423645},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08070829510688782},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1177/01423312221127742","is_oa":false,"landing_page_url":"https://doi.org/10.1177/01423312221127742","pdf_url":null,"source":{"id":"https://openalex.org/S24148485","display_name":"Transactions of the Institute of Measurement and Control","issn_l":"0142-3312","issn":["0142-3312","1477-0369"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Transactions of the Institute of Measurement and Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W138440741","https://openalex.org/W1972947796","https://openalex.org/W1973779450","https://openalex.org/W1984762043","https://openalex.org/W2004898970","https://openalex.org/W2033268024","https://openalex.org/W2062648096","https://openalex.org/W2066935185","https://openalex.org/W2084735697","https://openalex.org/W2090884011","https://openalex.org/W2132728101","https://openalex.org/W2134978220","https://openalex.org/W2139336218","https://openalex.org/W2211802523","https://openalex.org/W2309803304","https://openalex.org/W2551636533","https://openalex.org/W2584139399","https://openalex.org/W2588274445","https://openalex.org/W2735632318","https://openalex.org/W2765451990","https://openalex.org/W2790260102","https://openalex.org/W2791038025","https://openalex.org/W2809087494","https://openalex.org/W2874523342","https://openalex.org/W2955918317","https://openalex.org/W2995266622","https://openalex.org/W3038923201","https://openalex.org/W3040252179","https://openalex.org/W3092075392","https://openalex.org/W3158167909","https://openalex.org/W3177753206","https://openalex.org/W3197542727","https://openalex.org/W3208405023","https://openalex.org/W4240200017"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2002388147","https://openalex.org/W3098928304","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W2394883510","https://openalex.org/W1864774435","https://openalex.org/W2023324176","https://openalex.org/W2161271931","https://openalex.org/W2900563273"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3,18],"practical":[4],"fractional":[5,156],"proportional\u2013integral":[6],"and":[7,17,39,56,83,117,141,176,189,198],"proportional\u2013derivative":[8],"(PI":[9],"\u03bb":[10,71,110,158],"-PD":[11,72,159],"\u03bc":[12,73,121,160],")":[13],"controller":[14,74,111,122],"tuning":[15],"method":[16,21,44,90,163,188],"model":[19,178],"reduction":[20,179],"are":[22,45,148],"proposed":[23],"for":[24],"high-order":[25,53],"systems":[26],"with":[27,144],"or":[28],"without":[29],"time":[30,41,196],"delay.":[31],"First,":[32],"the":[33,40,49,52,57,65,79,84,95,99,103,107,118,131,138,142,155,170,174,177,183],"Big":[34],"Bang\u2013Big":[35],"Crunch":[36],"(BB-BC)":[37],"algorithm":[38,133,167,191],"moment":[42,186],"matching":[43,187],"used":[46,135],"to":[47,78,93,136],"reduce":[48],"order":[50],"of":[51,68,173,185],"system":[54,60],"function,":[55],"approximate":[58],"low-order":[59],"function":[61],"is":[62,75,91,112,123,134,192],"obtained.":[63,149],"Second,":[64],"parameter":[66,161],"region":[67,101],"fractional-order":[69,108,119],"PI":[70,109,157],"obtained":[76],"according":[77],"D":[80],"partition":[81],"method,":[82,116],"improved":[85],"weighted":[86],"geometric":[87],"center":[88],"(WGC)":[89],"introduced":[92],"select":[94],"special":[96],"points":[97],"in":[98,194],"stable":[100],"as":[102],"control":[104,139,146,171],"parameters.":[105],"Then,":[106],"discretized":[113,124],"by":[114,125],"Muir":[115],"PD":[120],"continued":[126],"fraction":[127],"expansion":[128],"(CFE).":[129],"Finally,":[130],"BB-BC":[132,166,190],"optimize":[137],"parameters,":[140],"parameters":[143],"better":[145],"performance":[147,172],"The":[150],"simulation":[151],"results":[152],"show":[153],"that":[154],"setting":[162],"based":[164,181],"on":[165,182],"can":[168],"improve":[169],"system,":[175],"scheme":[180],"combination":[184],"effective":[193],"both":[195],"domain":[197,200],"frequency":[199],"analysis.":[201]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}