{"id":"https://openalex.org/W7225322175","doi":"https://doi.org/10.1007/s42417-026-02859-0","title":"A Sub-Optimal Control of a Non-linear Vibrating System Excited by a Non-ideal Energy Source","display_name":"A Sub-Optimal Control of a Non-linear Vibrating System Excited by a Non-ideal Energy Source","publication_year":2026,"publication_date":"2026-11-05","ids":{"openalex":"https://openalex.org/W7225322175","doi":"https://doi.org/10.1007/s42417-026-02859-0"},"language":"en","primary_location":{"id":"doi:10.1007/s42417-026-02859-0","doi":"https://doi.org/10.1007/s42417-026-02859-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42417-026-02859-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42417-026-02859-0.pdf","source":{"id":"https://openalex.org/S4210184340","display_name":"Journal of Vibration Engineering & Technologies","issn_l":"2321-3558","issn":["2321-3558","2523-3920","2523-3939"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Vibration Engineering & Technologies","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s42417-026-02859-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073153356","display_name":"Jos\u00e9 Manoel Balthazar","orcid":"https://orcid.org/0000-0002-9796-3609","observed_orcids":["https://orcid.org/0000-0002-9796-3609","https://orcid.org/0000-0002-6082-4832"]},"institutions":[{"id":"https://openalex.org/I879563668","display_name":"Universidade Estadual Paulista (Unesp)","ror":"https://ror.org/00987cb86","country_code":"BR","type":"education","lineage":["https://openalex.org/I879563668"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jose M. Balthazar","raw_affiliation_strings":["Faculty of Mechanical Engineering, S\u00e3o Paulo State University (UNESP), Bauru, S\u00e3o Paulo, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-6082-4832","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, S\u00e3o Paulo State University (UNESP), Bauru, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I879563668"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070047434","display_name":"\u00c2ngelo Marcelo Tusset","orcid":"https://orcid.org/0000-0003-3144-0407","observed_orcids":["https://orcid.org/0000-0003-3144-0407"]},"institutions":[{"id":"https://openalex.org/I1283613182","display_name":"Universidade Tecnol\u00f3gica Federal do Paran\u00e1","ror":"https://ror.org/002v2kq79","country_code":"BR","type":"education","lineage":["https://openalex.org/I1283613182"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Angelo M. Tusset","raw_affiliation_strings":["Department of Mathematics, Federal University of Technology \u2013 Paran\u00e1, Ponta Grossa, Paran\u00e1, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-3144-0407","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Federal University of Technology \u2013 Paran\u00e1, Ponta Grossa, Paran\u00e1, Brazil","institution_ids":["https://openalex.org/I1283613182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073251360","display_name":"Julijana D. Simonovi\u0107","orcid":"https://orcid.org/0000-0002-2330-6948","observed_orcids":["https://orcid.org/0000-0002-2330-6948"]},"institutions":[{"id":"https://openalex.org/I152518017","display_name":"University of Nis","ror":"https://ror.org/00965bg92","country_code":"RS","type":"education","lineage":["https://openalex.org/I152518017"]}],"countries":["RS"],"is_corresponding":false,"raw_author_name":"Julijana Simonovic","raw_affiliation_strings":["Faculty of Mechanical Engineering, University of Ni\u0161, Ni\u0161, Serbia"],"raw_orcid":"https://orcid.org/0000-0002-2330-6948","affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, University of Ni\u0161, Ni\u0161, Serbia","institution_ids":["https://openalex.org/I152518017"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101441016","display_name":"Jorge Luis Palacios F\u00e9lix","orcid":"https://orcid.org/0000-0002-2975-6317","observed_orcids":["https://orcid.org/0000-0002-2975-6317"]},"institutions":[{"id":"https://openalex.org/I3130004620","display_name":"Universidade Federal da Fronteira Sul","ror":"https://ror.org/03z9wm572","country_code":"BR","type":"education","lineage":["https://openalex.org/I3130004620"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jorge L. P Felix","raw_affiliation_strings":["Technology Center of Alegrete, Federal University of Fronteira Sul, Alegrete, Rio Grande do Sul, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-2975-6317","affiliations":[{"raw_affiliation_string":"Technology Center of Alegrete, Federal University of Fronteira Sul, Alegrete, Rio Grande do Sul, Brazil","institution_ids":["https://openalex.org/I3130004620"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061755665","display_name":"Jeferson Jos\u00e9 de Lima","orcid":"https://orcid.org/0000-0001-6342-6162","observed_orcids":["https://orcid.org/0000-0001-6342-6162"]},"institutions":[{"id":"https://openalex.org/I1283613182","display_name":"Universidade Tecnol\u00f3gica Federal do Paran\u00e1","ror":"https://ror.org/002v2kq79","country_code":"BR","type":"education","lineage":["https://openalex.org/I1283613182"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Jeferson J. Lima","raw_affiliation_strings":["Department of Electronics, Federal University of Technology \u2013 Paran\u00e1, Ponta Grossa, Paran\u00e1, Brazil"],"raw_orcid":"https://orcid.org/0000-0001-6342-6162","affiliations":[{"raw_affiliation_string":"Department of Electronics, Federal University of Technology \u2013 Paran\u00e1, Ponta Grossa, Paran\u00e1, Brazil","institution_ids":["https://openalex.org/I1283613182"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5061755665"],"corresponding_institution_ids":["https://openalex.org/I1283613182"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"8","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.8960000276565552,"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"}},"topics":[{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.8960000276565552,"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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.047600001096725464,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.0210999995470047,"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/nonlinear-vibration-control","display_name":"nonlinear vibration control","score":0.7009999752044678},{"id":"https://openalex.org/keywords/nonlinear-damping","display_name":"nonlinear damping","score":0.6589999794960022},{"id":"https://openalex.org/keywords/nonlinear-stiffness","display_name":"nonlinear stiffness","score":0.9470000267028809},{"id":"https://openalex.org/keywords/time-varying-excitation","display_name":"time-varying excitation","score":0.9779999852180481},{"id":"https://openalex.org/keywords/vibration-reduction","display_name":"vibration suppression","score":0.8209999799728394},{"id":"https://openalex.org/keywords/multi-degree-of-freedom-systems","display_name":"multi-degree-of-freedom systems","score":0.7099999785423279}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.79830002784729},{"id":"https://openalex.org/C83581075","wikidata":"https://www.wikidata.org/wiki/Q1361503","display_name":"Excitation","level":2,"score":0.6650999784469604},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6524999737739563},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6010000109672546},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5432999730110168},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5126000046730042},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4361000061035156},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.4350000023841858},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C50942859","wikidata":"https://www.wikidata.org/wiki/Q4967193","display_name":"Rectification","level":3,"score":0.41519999504089355},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.41040000319480896},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.4097999930381775},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.40939998626708984},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3882000148296356},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.3709000051021576},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3626999855041504},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3312999904155731},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3181999921798706},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.30720001459121704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3059999942779541},{"id":"https://openalex.org/C89227174","wikidata":"https://www.wikidata.org/wiki/Q2388981","display_name":"Electric power system","level":3,"score":0.30320000648498535},{"id":"https://openalex.org/C40678858","wikidata":"https://www.wikidata.org/wiki/Q6934874","display_name":"Multiple-scale analysis","level":3,"score":0.2572000026702881}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s42417-026-02859-0","doi":"https://doi.org/10.1007/s42417-026-02859-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42417-026-02859-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42417-026-02859-0.pdf","source":{"id":"https://openalex.org/S4210184340","display_name":"Journal of Vibration Engineering & Technologies","issn_l":"2321-3558","issn":["2321-3558","2523-3920","2523-3939"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Vibration Engineering & Technologies","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s42417-026-02859-0","doi":"https://doi.org/10.1007/s42417-026-02859-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s42417-026-02859-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s42417-026-02859-0.pdf","source":{"id":"https://openalex.org/S4210184340","display_name":"Journal of Vibration Engineering & Technologies","issn_l":"2321-3558","issn":["2321-3558","2523-3920","2523-3939"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Vibration Engineering & Technologies","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331167","display_name":"Universidade Tecnol\u00f3gica Federal do Paran\u00e1","ror":"https://ror.org/002v2kq79"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225322175.pdf","grobid_xml":"https://content.openalex.org/works/W7225322175.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1640674606","https://openalex.org/W1998481540","https://openalex.org/W2042994047","https://openalex.org/W2087566540","https://openalex.org/W2098403928","https://openalex.org/W2163273462","https://openalex.org/W2531162562","https://openalex.org/W2794253021","https://openalex.org/W2972877438","https://openalex.org/W2977907610","https://openalex.org/W3003653730","https://openalex.org/W3010675562","https://openalex.org/W3022126370","https://openalex.org/W3081891467","https://openalex.org/W3182418035","https://openalex.org/W4226029387","https://openalex.org/W4287835787","https://openalex.org/W4292117636","https://openalex.org/W4367693263","https://openalex.org/W4385767137","https://openalex.org/W4388134575","https://openalex.org/W4388227272","https://openalex.org/W4389391653","https://openalex.org/W4400129413","https://openalex.org/W4403518729","https://openalex.org/W4403714558","https://openalex.org/W4405071974","https://openalex.org/W4408055630","https://openalex.org/W4415000393","https://openalex.org/W4415357249","https://openalex.org/W4416807746","https://openalex.org/W4417066370","https://openalex.org/W4417170925","https://openalex.org/W7125916111","https://openalex.org/W7135222267"],"related_works":["https://openalex.org/W7125916111","https://openalex.org/W1991854169","https://openalex.org/W2794253021","https://openalex.org/W2207885067","https://openalex.org/W4226319012","https://openalex.org/W2080465842","https://openalex.org/W6999911729","https://openalex.org/W2058256075","https://openalex.org/W2473895569","https://openalex.org/W1997575653"],"abstract_inverted_index":{"Abstract":[0],"Purpose":[1],"Non-Ideal":[2,53],"Systems":[3,54],"(NIS)":[4,55],"are":[5,61,178],"distinguished":[6],"by":[7,121,180],"their":[8,181],"unique":[9],"dynamic":[10,91],"properties,":[11],"which":[12],"present":[13,24,161],"considerable":[14],"challenges":[15],"to":[16,86],"the":[17,95,104,110,117,127,137,141,192],"application":[18],"of":[19,40,52,59,73,175,184],"conventional":[20],"control":[21,79,106,194],"techniques.":[22],"The":[23,49,71,160,172,188],"study":[25,162],"examines":[26],"non-ideal":[27,128,204],"excitation":[28,139,165,205],"sources":[29,166,177],"with":[30,56],"limited":[31],"power.":[32],"Nonlinear":[33],"phenomena":[34],"were":[35],"observed":[36],"in":[37,153],"a":[38,74,84],"range":[39],"applications,":[41],"providing":[42],"insights":[43],"for":[44,64,199],"future":[45],"NIS":[46],"engineering.":[47],"Methods":[48],"governing":[50],"equations":[51],"multiple":[57],"degrees":[58],"freedom":[60],"derived,":[62],"accounting":[63],"nonlinear":[65,148],"damping,":[66],"stiffness,":[67],"and":[68,90,115,123,146,156,186,203],"time-varying":[69],"excitations.":[70],"implementation":[72],"state-dependent":[75],"Riccati":[76],"equation":[77],"(SDRE)":[78],"strategy":[80,107,195],"is":[81],"proposed":[82,105],"as":[83,119],"means":[85],"optimise":[87],"system":[88,97,129],"stability":[89],"performance.":[92],"Results":[93],"For":[94,126],"ideal":[96,170,202],"(case":[98,130],"1,":[99],"$$a_0":[100,132],"=":[101],"0$$":[102,134],"),":[103,135],"effectively":[108],"regulates":[109],"system\u2019s":[111],"response,":[112],"reducing":[113],"amplitude":[114],"stabilizing":[116],"orbits,":[118],"confirmed":[120],"time-domain":[122],"frequency-domain":[124,157],"analyses.":[125],"2,":[131],">":[133],"despite":[136],"increased":[138],"complexity,":[140],"controller":[142],"successfully":[143],"suppresses":[144],"vibrations":[145],"mitigates":[147],"effects,":[149],"demonstrating":[150],"robust":[151],"performance":[152],"both":[154,201],"time-":[155],"measures.":[158],"Conclusions":[159],"focuses":[163],"on":[164],"that":[167,191],"deviate":[168],"from":[169],"conditions.":[171],"inherent":[173],"limitations":[174],"these":[176],"characterised":[179],"constant":[182],"parameters":[183],"power":[185],"inertia.":[187],"article":[189],"demonstrates":[190],"chosen":[193],"yields":[196],"satisfactory":[197],"results":[198],"controlling":[200],"systems.":[206]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-11-06T00:00:00"}