{"id":"https://openalex.org/W4411787593","doi":"https://doi.org/10.3390/a18070391","title":"PI-D\u00c6: An Adaptive PID Controller Utilizing a New Adaptive Exponent (\u00c6) Algorithm to Solve Derivative Term Issues","display_name":"PI-D\u00c6: An Adaptive PID Controller Utilizing a New Adaptive Exponent (\u00c6) Algorithm to Solve Derivative Term Issues","publication_year":2025,"publication_date":"2025-06-27","ids":{"openalex":"https://openalex.org/W4411787593","doi":"https://doi.org/10.3390/a18070391"},"language":"en","primary_location":{"id":"doi:10.3390/a18070391","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18070391","pdf_url":"https://www.mdpi.com/1999-4893/18/7/391/pdf?version=1751026580","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/18/7/391/pdf?version=1751026580","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5118701488","display_name":"Juan M. Barrera-Fern\u00e1ndez","orcid":null},"institutions":[{"id":"https://openalex.org/I4210117848","display_name":"Center for Engineering and Industrial Development","ror":"https://ror.org/03cf87p34","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210117848","https://openalex.org/I4210163111"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Juan M. Barrera-Fern\u00e1ndez","raw_affiliation_strings":["Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico","institution_ids":["https://openalex.org/I4210117848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022619877","display_name":"Juan Pablo Manzo Hern\u00e1ndez","orcid":"https://orcid.org/0009-0005-7464-0670"},"institutions":[{"id":"https://openalex.org/I4210117848","display_name":"Center for Engineering and Industrial Development","ror":"https://ror.org/03cf87p34","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210117848","https://openalex.org/I4210163111"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Juan Pablo Manzo Hern\u00e1ndez","raw_affiliation_strings":["Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"],"raw_orcid":"https://orcid.org/0009-0005-7464-0670","affiliations":[{"raw_affiliation_string":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico","institution_ids":["https://openalex.org/I4210117848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5118701489","display_name":"Kevin Miramontes Escobedo","orcid":"https://orcid.org/0000-0001-6638-448X"},"institutions":[{"id":"https://openalex.org/I4210117848","display_name":"Center for Engineering and Industrial Development","ror":"https://ror.org/03cf87p34","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210117848","https://openalex.org/I4210163111"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Kevin Miramontes Escobedo","raw_affiliation_strings":["Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"],"raw_orcid":"https://orcid.org/0000-0001-6638-448X","affiliations":[{"raw_affiliation_string":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico","institution_ids":["https://openalex.org/I4210117848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002647425","display_name":"Alberto V\u00e1zquez\u2010Cervantes","orcid":"https://orcid.org/0000-0002-9911-4328"},"institutions":[{"id":"https://openalex.org/I4210117848","display_name":"Center for Engineering and Industrial Development","ror":"https://ror.org/03cf87p34","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210117848","https://openalex.org/I4210163111"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Alberto V\u00e1zquez-Cervantes","raw_affiliation_strings":["Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-9911-4328","affiliations":[{"raw_affiliation_string":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico","institution_ids":["https://openalex.org/I4210117848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029611415","display_name":"Julio C\u00e9sar Solano Vargas","orcid":"https://orcid.org/0000-0003-4745-0175"},"institutions":[{"id":"https://openalex.org/I4210117848","display_name":"Center for Engineering and Industrial Development","ror":"https://ror.org/03cf87p34","country_code":"MX","type":"facility","lineage":["https://openalex.org/I4210117848","https://openalex.org/I4210163111"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Julio-C\u00e9sar Solano-Vargas","raw_affiliation_strings":["Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico"],"raw_orcid":"https://orcid.org/0000-0003-4745-0175","affiliations":[{"raw_affiliation_string":"Centro de Ingenier\u00eda y Desarrollo Industrial (CIDESI), Av. Pie de la Cuesta 702, Quer\u00e9taro 76125, Mexico","institution_ids":["https://openalex.org/I4210117848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029611415"],"corresponding_institution_ids":["https://openalex.org/I4210117848"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":1.031,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.75135555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"18","issue":"7","first_page":"391","last_page":"391"},"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9987999796867371,"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":0.9965999722480774,"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/pid-controller","display_name":"PID controller","score":0.8171291351318359},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6956052780151367},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6580930948257446},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.6010251641273499},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5553186535835266},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5359002351760864},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46166354417800903},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.4262961745262146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40434277057647705},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1435495913028717},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12423035502433777},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.12296310067176819},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.09190207719802856},{"id":"https://openalex.org/keywords/temperature-control","display_name":"Temperature control","score":0.07308188080787659},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.05367553234100342}],"concepts":[{"id":"https://openalex.org/C47116090","wikidata":"https://www.wikidata.org/wiki/Q716829","display_name":"PID controller","level":3,"score":0.8171291351318359},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6956052780151367},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6580930948257446},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.6010251641273499},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5553186535835266},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5359002351760864},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46166354417800903},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.4262961745262146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40434277057647705},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1435495913028717},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12423035502433777},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.12296310067176819},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09190207719802856},{"id":"https://openalex.org/C536315585","wikidata":"https://www.wikidata.org/wiki/Q7698332","display_name":"Temperature control","level":2,"score":0.07308188080787659},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.05367553234100342},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a18070391","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18070391","pdf_url":"https://www.mdpi.com/1999-4893/18/7/391/pdf?version=1751026580","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d648a315e08844739c4f72698bf55ddc","is_oa":true,"landing_page_url":"https://doaj.org/article/d648a315e08844739c4f72698bf55ddc","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 18, Iss 7, p 391 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18070391","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18070391","pdf_url":"https://www.mdpi.com/1999-4893/18/7/391/pdf?version=1751026580","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F7795900982","display_name":"Centro de Ingenier\u00eda y Desarrollo Industrial","ror":"https://ror.org/03cf87p34"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411787593.pdf","grobid_xml":"https://content.openalex.org/works/W4411787593.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1969313263","https://openalex.org/W2084424121","https://openalex.org/W2096222424","https://openalex.org/W2140246545","https://openalex.org/W2478823755","https://openalex.org/W2550491676","https://openalex.org/W2931147900","https://openalex.org/W2946678433","https://openalex.org/W2972395049","https://openalex.org/W3008862071","https://openalex.org/W3018050809","https://openalex.org/W3028570313","https://openalex.org/W3092550000","https://openalex.org/W3153764790","https://openalex.org/W3162840570","https://openalex.org/W4234535513","https://openalex.org/W4312212936","https://openalex.org/W4313889467","https://openalex.org/W4322503304","https://openalex.org/W4385067594","https://openalex.org/W4385688776","https://openalex.org/W4387461165","https://openalex.org/W4402055027","https://openalex.org/W6767498585","https://openalex.org/W6794591966"],"related_works":["https://openalex.org/W2002388147","https://openalex.org/W3098928304","https://openalex.org/W2394883510","https://openalex.org/W2150958483","https://openalex.org/W2165013373","https://openalex.org/W2121097709","https://openalex.org/W2922503265","https://openalex.org/W2023324176","https://openalex.org/W2576987672","https://openalex.org/W3212795132"],"abstract_inverted_index":{"This":[0,72,162],"study":[1],"proposes":[2],"an":[3],"enhanced":[4],"derivative":[5,17,24],"control":[6,187],"strategy,":[7],"named":[8],"PI-D\u00c6,":[9],"designed":[10],"to":[11,82,172],"overcome":[12],"key":[13],"limitations":[14],"of":[15,153],"the":[16,59,64,74,149],"(D)":[18],"term,":[19],"such":[20,137],"as":[21,138],"noise":[22],"amplification,":[23],"kick":[25],"(D-k),":[26],"and":[27,70,111,151,169,177,182,196],"tuning":[28],"difficulties.":[29],"These":[30],"issues":[31],"often":[32],"arise":[33],"in":[34,40,79,108,115,192],"high-frequency":[35],"or":[36,143,159],"rapidly":[37],"changing":[38,83],"systems,":[39],"which":[41,77,193],"traditional":[42],"PID":[43,121],"controllers":[44],"struggle.":[45],"The":[46,85],"proposed":[47],"solution":[48,188],"introduces":[49],"a":[50,100,105,112,126,167,185],"novel":[51],"adaptive":[52,163],"exponent":[53,164],"algorithm":[54],"(\u00c6)":[55],"that":[56,97],"dynamically":[57],"modulates":[58],"D":[60],"term":[61],"based":[62],"on":[63,93],"evolving":[65],"relationship":[66],"between":[67],"system":[68],"output":[69],"setpoint.":[71],"yields":[73],"PI-D\u00c6":[75,98,147],"controller,":[76],"adapts":[78],"real":[80],"time":[81,117],"conditions.":[84],"results":[86,92],"show":[87],"significant":[88],"performance":[89,176],"improvements.":[90],"Simulation":[91],"two":[94],"systems":[95],"demonstrate":[96],"achieves":[99],"90%":[101],"faster":[102],"response":[103],"time,":[104,110],"35%":[106],"reduction":[107],"peak":[109],"100%":[113],"improvement":[114],"settling":[116],"compared":[118],"with":[119],"conventional":[120],"controllers,":[122],"all":[123],"while":[124],"maintaining":[125],"near-zero":[127],"steady-state":[128],"error":[129],"even":[130],"under":[131],"external":[132],"disturbances.":[133],"Unlike":[134],"more-complex":[135],"alternatives":[136],"fuzzy":[139],"logic,":[140],"neural":[141],"networks,":[142],"sliding":[144],"mode":[145],"control,":[146],"retains":[148],"simplicity":[150],"robustness":[152,178],"PID,":[154,174],"avoiding":[155],"high":[156],"computational":[157],"costs":[158],"intricate":[160],"setups.":[161],"strategy":[165],"offers":[166],"practical":[168],"scalable":[170],"enhancement":[171],"classical":[173],"improving":[175],"without":[179],"added":[180],"complexity,":[181],"thus":[183],"provides":[184],"promising":[186],"for":[189],"real-world":[190],"applications":[191],"simplicity,":[194],"adaptability,":[195],"reliability":[197],"are":[198],"essential.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-06-30T00:00:00"}