{"id":"https://openalex.org/W4415087993","doi":"https://doi.org/10.48550/arxiv.2509.11235","title":"Comparing Model-based Control Strategies for a Quadruple Tank System: Decentralized PID, LMPC, and NMPC","display_name":"Comparing Model-based Control Strategies for a Quadruple Tank System: Decentralized PID, LMPC, and NMPC","publication_year":2025,"publication_date":"2025-09-14","ids":{"openalex":"https://openalex.org/W4415087993","doi":"https://doi.org/10.48550/arxiv.2509.11235"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.11235","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.11235","pdf_url":"https://arxiv.org/pdf/2509.11235","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.11235","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104282193","display_name":"Anders Hilmar Damm Christensen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Christensen, Anders H. D.","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ritschel, Tobias K. S.","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Ritschel, Tobias K. S.","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009781632","display_name":"Jan Lorenz Svensen","orcid":"https://orcid.org/0000-0001-9185-7605","observed_orcids":["https://orcid.org/0000-0001-9185-7605"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Svensen, Jan Lorenz","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048119227","display_name":"Steen H\u00f8rsholt","orcid":"https://orcid.org/0000-0001-9624-5026","observed_orcids":["https://orcid.org/0000-0001-9624-5026"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"H\u00f8rsholt, Steen","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083214789","display_name":"Jakob Kj\u00f8bsted Huusom","orcid":"https://orcid.org/0000-0002-1367-7235","observed_orcids":["https://orcid.org/0000-0002-1367-7235"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Huusom, Jakob Kj\u00f8bsted","raw_affiliation_strings":["- control ApS , DK-7400 Herning , Denmark","Department of Chemical and Biochemical Engineering , Technical University of Denmark , S\u00f8ltofts Plads 228A , Kgs. Lyngby , DK-2800 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"- control ApS , DK-7400 Herning , Denmark","institution_ids":[]},{"raw_affiliation_string":"Department of Chemical and Biochemical Engineering , Technical University of Denmark , S\u00f8ltofts Plads 228A , Kgs. Lyngby , DK-2800 , Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050946774","display_name":"John Bagterp J\u00f8rgensen","orcid":"https://orcid.org/0000-0001-9799-2808","observed_orcids":["https://orcid.org/0000-0001-9799-2808"]},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"J\u00f8rgensen, John Bagterp","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science , Technical University of Denmark , Matematiktorvet , Building 303B , Kgs. Lyngby , DK-2800 , Denmark","institution_ids":["https://openalex.org/I96673099"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9994999766349792,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9994999766349792,"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":9.999999747378752e-05,"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/T11236","display_name":"Control Systems and Identification","score":0.0,"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/quadruple-tank-system","display_name":"four-tank system","score":0.9959999918937683},{"id":"https://openalex.org/keywords/decentralized-pid-control","display_name":"decentralized PID control","score":0.8769999742507935},{"id":"https://openalex.org/keywords/linear-model-predictive-control","display_name":"linear model predictive control","score":0.9810000061988831},{"id":"https://openalex.org/keywords/nonlinear-model-predictive-control","display_name":"nonlinear model predictive control","score":1.0},{"id":"https://openalex.org/keywords/parameter-estimation","display_name":"parameter estimation","score":0.6320000290870667},{"id":"https://openalex.org/keywords/setpoint-tracking","display_name":"reference tracking","score":0.7559999823570251},{"id":"https://openalex.org/keywords/disturbance-rejection","display_name":"disturbance rejection","score":0.996999979019165},{"id":"https://openalex.org/keywords/controller-performance-comparison","display_name":"controller performance comparison","score":0.6370000243186951}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.8598999977111816},{"id":"https://openalex.org/C47116090","wikidata":"https://www.wikidata.org/wiki/Q716829","display_name":"PID controller","level":3,"score":0.7041000127792358},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.6570000052452087},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6417999863624573},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.6262000203132629},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.524399995803833},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.511900007724762},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4699999988079071},{"id":"https://openalex.org/C28427503","wikidata":"https://www.wikidata.org/wiki/Q13580300","display_name":"Internal model","level":3,"score":0.43939998745918274},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.38589999079704285},{"id":"https://openalex.org/C205875254","wikidata":"https://www.wikidata.org/wiki/Q17156857","display_name":"Decentralised system","level":3,"score":0.38040000200271606},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.2736999988555908},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.27239999175071716},{"id":"https://openalex.org/C2984755018","wikidata":"https://www.wikidata.org/wiki/Q17118374","display_name":"Nonlinear model","level":3,"score":0.2662000060081482},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C9628104","wikidata":"https://www.wikidata.org/wiki/Q788009","display_name":"Autonomous system (mathematics)","level":2,"score":0.2639000117778778},{"id":"https://openalex.org/C154586513","wikidata":"https://www.wikidata.org/wiki/Q4420972","display_name":"Tracking system","level":3,"score":0.25859999656677246},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25119999051094055},{"id":"https://openalex.org/C2780440489","wikidata":"https://www.wikidata.org/wiki/Q5227278","display_name":"Data-driven","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.11235","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.11235","pdf_url":"https://arxiv.org/pdf/2509.11235","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2509.11235","doi":"https://doi.org/10.48550/arxiv.2509.11235","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.11235","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2509.11235","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.11235","pdf_url":"https://arxiv.org/pdf/2509.11235","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G389380988","display_name":"Innovations to accelerate vaccine development and manufacture","funder_award_id":"101007799","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4742250757","display_name":null,"funder_award_id":"00001B","funder_id":"https://openalex.org/F4320313796","funder_display_name":"Innovationsfonden"},{"id":"https://openalex.org/G5176001544","display_name":null,"funder_award_id":"IMI2/EU/EFPIA","funder_id":"https://openalex.org/F4320314178","funder_display_name":"European Federation of Pharmaceutical Industries and Associations"},{"id":"https://openalex.org/G637844082","display_name":null,"funder_award_id":"64021-7009","funder_id":"https://openalex.org/F4320331736","funder_display_name":"Energiteknologisk udviklings- og demonstrationsprogram"},{"id":"https://openalex.org/G7405828554","display_name":null,"funder_award_id":"1150-00001B","funder_id":"https://openalex.org/F4320313796","funder_display_name":"Innovationsfonden"}],"funders":[{"id":"https://openalex.org/F4320313796","display_name":"Innovationsfonden","ror":"https://ror.org/00daj4111"},{"id":"https://openalex.org/F4320314178","display_name":"European Federation of Pharmaceutical Industries and Associations","ror":"https://ror.org/00g1x4v36"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320325128","display_name":"Energistyrelsen","ror":"https://ror.org/03wtazd67"},{"id":"https://openalex.org/F4320331736","display_name":"Energiteknologisk udviklings- og demonstrationsprogram","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415087993.pdf","grobid_xml":"https://content.openalex.org/works/W4415087993.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W2794219647","https://openalex.org/W4317717860","https://openalex.org/W4416649563"],"related_works":["https://openalex.org/W7030361292","https://openalex.org/W2921012380","https://openalex.org/W3166215322","https://openalex.org/W2610507889","https://openalex.org/W7096192411","https://openalex.org/W4206310995","https://openalex.org/W7075674206","https://openalex.org/W2974608380","https://openalex.org/W2981986980","https://openalex.org/W4385955457"],"abstract_inverted_index":{"This":[0],"paper":[1],"compares":[2],"the":[3,40,68,74,81,86,91,105,112,117,126,130,135,147,153,158,171,178,186,193,206,214,223,227],"performance":[4,136],"of":[5,39,80,104,139,144,185,195,205,229,235],"a":[6,11,18,26,36,52,61,77,231],"decentralized":[7,87,159,179],"proportional-integral-derivative":[8],"(PID)":[9],"controller,":[10],"linear":[12],"model":[13,20,94],"predictive":[14,21],"controller":[15,22,89,118],"(LMPC),":[16],"and":[17,107,129,142,152,209],"nonlinear":[19,54,70],"(NMPC)":[23],"applied":[24],"to":[25,191,222],"quadruple":[27],"tank":[28],"system":[29,162],"(QTS).":[30],"We":[31,84,115,133,198],"present":[32],"experimental":[33],"data":[34],"from":[35,111],"physical":[37,127],"setup":[38,128],"QTS":[41,48],"as":[42,44,51],"well":[43],"simulation":[45,203],"results.":[46],"The":[47,65,98,150,182],"is":[49,188],"modeled":[50],"stochastic":[53,69],"continuous-discrete-time":[55,71],"system,":[56],"with":[57,208],"parameters":[58],"estimated":[59],"using":[60,90,124],"maximum-likelihood":[62],"prediction-error-method":[63],"(ML-PEM).":[64],"NMPC":[66,154,215],"applies":[67],"model,":[72],"while":[73],"LMPC":[75,151,224],"uses":[76],"linearized":[78,113],"version":[79],"same":[82],"model.":[83,114],"tune":[85],"PID":[88,160,180],"simple":[92],"internal":[93],"control":[95,161],"(SIMC)":[96],"rules.":[97],"SIMC":[99],"rules":[100],"require":[101],"transfer":[102],"functions":[103],"process,":[106],"we":[108],"obtain":[109],"these":[110],"compare":[116],"performances":[119],"based":[120],"on":[121],"systematic":[122],"tests":[123],"both":[125],"simulated":[131],"QTS.":[132],"measure":[134],"in":[137,146],"terms":[138],"tracking":[140,164,219],"errors":[141,220],"rate":[143,234],"movement":[145],"manipulated":[148],"variables.":[149],"perform":[155,173],"better":[156,176],"than":[157,177],"for":[163],"pre-announced":[165],"time-varying":[166],"setpoints.":[167,197],"For":[168],"disturbance":[169],"rejection,":[170],"MPCs":[172,187,207],"only":[174],"slightly":[175,217],"controller.":[181],"primary":[183],"advantage":[184],"their":[189],"ability":[190],"use":[192],"information":[194],"future":[196],"demonstrate":[199],"this":[200],"by":[201],"providing":[202],"results":[204],"without":[210],"such":[211],"information.":[212],"Finally,":[213],"achieves":[216],"improved":[218],"compared":[221],"but":[225],"at":[226],"expense":[228],"having":[230],"higher":[232],"input":[233],"movement.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-12T00:00:00"}
