{"id":"https://openalex.org/W4411102894","doi":"https://doi.org/10.3390/axioms14060444","title":"Improving Stability and Reducing Vibrations of the Smooth and Discontinuous Oscillator Using a Proportional\u2013Derivative Controller","display_name":"Improving Stability and Reducing Vibrations of the Smooth and Discontinuous Oscillator Using a Proportional\u2013Derivative Controller","publication_year":2025,"publication_date":"2025-06-05","ids":{"openalex":"https://openalex.org/W4411102894","doi":"https://doi.org/10.3390/axioms14060444"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14060444","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060444","pdf_url":"https://www.mdpi.com/2075-1680/14/6/444/pdf?version=1749136294","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/6/444/pdf?version=1749136294","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081691626","display_name":"M. N. Abd El-Salam","orcid":"https://orcid.org/0000-0001-8333-4222"},"institutions":[{"id":"https://openalex.org/I160419504","display_name":"Higher Technological Institute","ror":"https://ror.org/051q8jk17","country_code":"EG","type":"education","lineage":["https://openalex.org/I160419504"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"M. N. Abd El-Salam","raw_affiliation_strings":["Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City 44634, Egypt"],"affiliations":[{"raw_affiliation_string":"Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City 44634, Egypt","institution_ids":["https://openalex.org/I160419504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072247080","display_name":"Rageh K. Hussein","orcid":"https://orcid.org/0000-0003-4497-9778"},"institutions":[{"id":"https://openalex.org/I240666556","display_name":"Imam Mohammad ibn Saud Islamic University","ror":"https://ror.org/05gxjyb39","country_code":"SA","type":"education","lineage":["https://openalex.org/I240666556"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Rageh K. Hussein","raw_affiliation_strings":["Physics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Physics Department, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia","institution_ids":["https://openalex.org/I240666556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082605584","display_name":"Sabry M. El-Shourbagy","orcid":null},"institutions":[{"id":"https://openalex.org/I160419504","display_name":"Higher Technological Institute","ror":"https://ror.org/051q8jk17","country_code":"EG","type":"education","lineage":["https://openalex.org/I160419504"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Sabry M. El-Shourbagy","raw_affiliation_strings":["Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City 44634, Egypt"],"affiliations":[{"raw_affiliation_string":"Basic Sciences Department, Higher Technological Institute, 10th of Ramadan City 44634, Egypt","institution_ids":["https://openalex.org/I160419504"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5081691626"],"corresponding_institution_ids":["https://openalex.org/I160419504"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.1589,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78553983,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"14","issue":"6","first_page":"444","last_page":"444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.7681000232696533,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.7681000232696533,"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/T13644","display_name":"Control Systems in Engineering","score":0.7174999713897705,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11372","display_name":"Hydraulic and Pneumatic Systems","score":0.7135000228881836,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/control-theory","display_name":"Control theory (sociology)","score":0.7728537321090698},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.6128273010253906},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5924872159957886},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.564785897731781},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5506443977355957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3495821952819824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3330535292625427},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32909834384918213},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.21440118551254272},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.0838187038898468},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.06670454144477844},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.060771793127059937}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7728537321090698},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.6128273010253906},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5924872159957886},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.564785897731781},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5506443977355957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3495821952819824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3330535292625427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32909834384918213},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.21440118551254272},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0838187038898468},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.06670454144477844},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.060771793127059937},{"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/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14060444","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060444","pdf_url":"https://www.mdpi.com/2075-1680/14/6/444/pdf?version=1749136294","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:fa42639added4117ad7a9b12bdbfa586","is_oa":true,"landing_page_url":"https://doaj.org/article/fa42639added4117ad7a9b12bdbfa586","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 6, p 444 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14060444","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14060444","pdf_url":"https://www.mdpi.com/2075-1680/14/6/444/pdf?version=1749136294","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1053352659","display_name":null,"funder_award_id":"IMSIU-DDRSP2503","funder_id":"https://openalex.org/F4320325415","funder_display_name":"Al-Imam Muhammad Ibn Saud Islamic University"}],"funders":[{"id":"https://openalex.org/F4320325415","display_name":"Al-Imam Muhammad Ibn Saud Islamic University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411102894.pdf","grobid_xml":"https://content.openalex.org/works/W4411102894.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1969392248","https://openalex.org/W1989295440","https://openalex.org/W1995765489","https://openalex.org/W2019213050","https://openalex.org/W2046317816","https://openalex.org/W2080864525","https://openalex.org/W2320563909","https://openalex.org/W2325335742","https://openalex.org/W2546842683","https://openalex.org/W2955090473","https://openalex.org/W3097665321","https://openalex.org/W3128847601","https://openalex.org/W3209854568","https://openalex.org/W3212608377","https://openalex.org/W4239794412","https://openalex.org/W4323928801","https://openalex.org/W4360979447","https://openalex.org/W4362496388","https://openalex.org/W4401991336","https://openalex.org/W6637129262"],"related_works":["https://openalex.org/W1982160337","https://openalex.org/W1971380437","https://openalex.org/W1983548084","https://openalex.org/W2141691317","https://openalex.org/W2110846987","https://openalex.org/W2160609742","https://openalex.org/W1997414638","https://openalex.org/W2031091109","https://openalex.org/W2049254832","https://openalex.org/W2383436541"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"the":[3,19,24,30,33,53,60,71,73,76,79,87,97,101,110,117],"Proportional":[4,20],"and":[5,23,35,75,92,116],"Derivative":[6,25],"Controller":[7,21,26],"(PD)":[8],"is":[9,106],"presented":[10],"as":[11,45],"a":[12,46,65],"modified":[13],"control":[14],"that":[15,96],"combines":[16],"features":[17],"of":[18,32,52,70],"(P-Controller)":[22],"(D-Controller)":[27],"to":[28,64],"suppress":[29],"vibrations":[31],"Smooth":[34],"Discontinuous":[36],"Oscillator":[37],"(SD).":[38],"The":[39,48,68,90],"investigated":[40],"model":[41],"has":[42,56,82],"been":[43,57,83],"derived":[44],"one-degree-of-freedom.":[47],"frequency":[49],"response":[50],"equation":[51],"controlled":[54],"system":[55,102],"obtained":[58],"using":[59],"perturbation":[61,121],"technique":[62],"up":[63],"second":[66],"approximation.":[67],"influence":[69],"P-Controller,":[72],"D-Controller,":[74],"PD-Controller":[77,98],"on":[78],"SD-Oscillator":[80],"amplitude":[81],"studied":[84],"by":[85],"plotting":[86],"time":[88,114],"histories.":[89],"numerical":[91,111],"approximate":[93,118],"simulation":[94],"established":[95],"can":[99],"inhibit":[100],"vibration.":[103],"Finally,":[104],"there":[105],"high":[107],"closeness":[108],"between":[109],"solutions":[112,119],"(from":[113,120],"histories)":[115],"analysis).":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
