{"id":"https://openalex.org/W3032811699","doi":"https://doi.org/10.1109/tase.2020.2993277","title":"An Improved Bouc\u2013Wen Model Based on Equitorque Discretization for a Load-Dependent Nonlinear Stiffness Actuator","display_name":"An Improved Bouc\u2013Wen Model Based on Equitorque Discretization for a Load-Dependent Nonlinear Stiffness Actuator","publication_year":2020,"publication_date":"2020-05-27","ids":{"openalex":"https://openalex.org/W3032811699","doi":"https://doi.org/10.1109/tase.2020.2993277","mag":"3032811699"},"language":"en","primary_location":{"id":"doi:10.1109/tase.2020.2993277","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2020.2993277","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automation Science and Engineering","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/A5060387989","display_name":"Zhibin Song","orcid":"https://orcid.org/0000-0002-3715-2003"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhibin Song","raw_affiliation_strings":["Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, China","School of Mechanical Engineering, Tianjin University, Tianjin, China"],"raw_orcid":"https://orcid.org/0000-0002-3715-2003","affiliations":[{"raw_affiliation_string":"Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101605608","display_name":"Dong Gao","orcid":"https://orcid.org/0000-0002-9485-5223"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong Gao","raw_affiliation_strings":["Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, China","School of Mechanical Engineering, Tianjin University, Tianjin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101788941","display_name":"Yaru Zhao","orcid":"https://orcid.org/0000-0002-3675-7318"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yaru Zhao","raw_affiliation_strings":["Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, China","School of Mechanical Engineering, Tianjin University, Tianjin, China"],"raw_orcid":"https://orcid.org/0000-0002-3675-7318","affiliations":[{"raw_affiliation_string":"Key Laboratory of Mechanism Theory and Equipment Design of the Ministry of Education, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Tianjin University, Tianjin, China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040440410","display_name":"Jian S. Dai","orcid":"https://orcid.org/0000-0002-9729-1662"},"institutions":[{"id":"https://openalex.org/I183935753","display_name":"King's College London","ror":"https://ror.org/0220mzb33","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I183935753"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jian S. Dai","raw_affiliation_strings":["Centre for Robotics Research, School of Physical Sciences and Engineering, King\u2019s College London, London, U.K"],"raw_orcid":"https://orcid.org/0000-0002-9729-1662","affiliations":[{"raw_affiliation_string":"Centre for Robotics Research, School of Physical Sciences and Engineering, King\u2019s College London, London, U.K","institution_ids":["https://openalex.org/I183935753"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7289,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.70035434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"18","issue":"2","first_page":"840","last_page":"849"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11525","display_name":"Piezoelectric Actuators and Control","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"}},"topics":[{"id":"https://openalex.org/T11525","display_name":"Piezoelectric Actuators and Control","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/T11023","display_name":"Prosthetics and Rehabilitation Robotics","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10868","display_name":"Soft Robotics and Applications","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/stiffness","display_name":"Stiffness","score":0.7896792888641357},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.7351294159889221},{"id":"https://openalex.org/keywords/actuator","display_name":"Actuator","score":0.7083518505096436},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6483789682388306},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5764064788818359},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.5458614230155945},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.5321986079216003},{"id":"https://openalex.org/keywords/hysteresis","display_name":"Hysteresis","score":0.5267635583877563},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4546549320220947},{"id":"https://openalex.org/keywords/compensation","display_name":"Compensation (psychology)","score":0.4419023096561432},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.36329716444015503},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.3560692071914673},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.2508721351623535},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1511172354221344},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.10955578088760376},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08550167083740234}],"concepts":[{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.7896792888641357},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7351294159889221},{"id":"https://openalex.org/C172707124","wikidata":"https://www.wikidata.org/wiki/Q423488","display_name":"Actuator","level":2,"score":0.7083518505096436},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6483789682388306},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5764064788818359},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.5458614230155945},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.5321986079216003},{"id":"https://openalex.org/C123299182","wikidata":"https://www.wikidata.org/wiki/Q190837","display_name":"Hysteresis","level":2,"score":0.5267635583877563},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4546549320220947},{"id":"https://openalex.org/C2780023022","wikidata":"https://www.wikidata.org/wiki/Q1338171","display_name":"Compensation (psychology)","level":2,"score":0.4419023096561432},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.36329716444015503},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3560692071914673},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.2508721351623535},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1511172354221344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.10955578088760376},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08550167083740234},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tase.2020.2993277","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tase.2020.2993277","pdf_url":null,"source":{"id":"https://openalex.org/S34881539","display_name":"IEEE Transactions on Automation Science and Engineering","issn_l":"1545-5955","issn":["1545-5955","1558-3783"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automation Science and Engineering","raw_type":"journal-article"},{"id":"pmh:oai:kclpure.kcl.ac.uk:publications/24875eca-aca5-4fc1-8895-419704d5530e","is_oa":false,"landing_page_url":"https://kclpure.kcl.ac.uk/portal/en/publications/24875eca-aca5-4fc1-8895-419704d5530e","pdf_url":null,"source":{"id":"https://openalex.org/S4306400216","display_name":"Research Portal (King's College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I183935753","host_organization_name":"King's College London","host_organization_lineage":["https://openalex.org/I183935753"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Song, Z, Gao, D, Zhao, Y & Dai, J S 2021, 'An Improved Bouc-Wen Model Based on Equitorque Discretization for a Load-Dependent Nonlinear Stiffness Actuator', IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, vol. 18, no. 2, 9102432, pp. 840-849. https://doi.org/10.1109/TASE.2020.2993277","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3602877896","display_name":null,"funder_award_id":"51535008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4105187712","display_name":null,"funder_award_id":"EP/S019790/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4214010829","display_name":null,"funder_award_id":"51975401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4733962744","display_name":"REST: Reconfigurable lower limb Exoskeleton for effective Stroke Treatment in residential settings","funder_award_id":"EP/S019790/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5342750064","display_name":null,"funder_award_id":"51721003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5629947592","display_name":"Investigation and Development of a New Class of Mechanisms: Metamorphic Mechanisms with Reconfigurability","funder_award_id":"EP/E012574/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G65223392","display_name":null,"funder_award_id":"EP/E012574/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W309562399","https://openalex.org/W595325313","https://openalex.org/W1521257674","https://openalex.org/W1535570778","https://openalex.org/W1581560749","https://openalex.org/W1603534388","https://openalex.org/W1976253484","https://openalex.org/W1978023077","https://openalex.org/W1992974134","https://openalex.org/W2006742133","https://openalex.org/W2039567866","https://openalex.org/W2041737075","https://openalex.org/W2058715873","https://openalex.org/W2070667485","https://openalex.org/W2075540265","https://openalex.org/W2087258540","https://openalex.org/W2088752982","https://openalex.org/W2103920070","https://openalex.org/W2110806298","https://openalex.org/W2111253117","https://openalex.org/W2113593135","https://openalex.org/W2140525274","https://openalex.org/W2159862980","https://openalex.org/W2169100281","https://openalex.org/W2175599199","https://openalex.org/W2267593487","https://openalex.org/W2315431736","https://openalex.org/W2344472183","https://openalex.org/W2527753112","https://openalex.org/W2545859404","https://openalex.org/W2579541812","https://openalex.org/W2725607297","https://openalex.org/W2902682211","https://openalex.org/W2920933901","https://openalex.org/W2941932431","https://openalex.org/W6631331923","https://openalex.org/W6644388615","https://openalex.org/W6683723944"],"related_works":["https://openalex.org/W1492103595","https://openalex.org/W2364741597","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W2555022781","https://openalex.org/W2765315036"],"abstract_inverted_index":{"A":[0],"novel":[1,240,277],"concept":[2,29],"of":[3,37,49,54,99,134,141,159,172,192,313,326],"designing":[4],"compliant":[5],"actuators":[6],"called":[7],"\u201csmall":[8],"load,":[9,13],"low":[10],"stiffness;":[11],"large":[12],"high":[14,207],"stiffness\u201d":[15],"was":[16,30,246],"applied":[17],"and":[18,42,91,170,209,217,302],"proven":[19,128],"effective":[20,129],"in":[21,24,51,83,130,229,248,256,267,290],"human-robot":[22],"interaction":[23,231],"our":[25,249],"previous":[26,250],"work.":[27,251],"This":[28],"proposed":[31,113,177,186,247,275,307,318],"based":[32],"on":[33,61],"a":[34,66,74,138,239,276,327,334],"common":[35,266],"scenario":[36],"interactive":[38],"action":[39],"where":[40],"humans":[41],"some":[43,222],"animals":[44],"can":[45,188,286,309,322],"adjust":[46],"the":[47,52,58,87,96,100,116,132,135,142,157,160,168,173,176,185,190,193,233,283,299,303,306,311,314,324],"stiffness":[48,70,216,243],"limbs":[50],"light":[53],"tasks":[55],"or":[56],"contacting":[57],"environment.":[59,234],"Based":[60],"this":[62,103,237,272],"concept,":[63],"we":[64,274],"developed":[65,202],"new":[67],"load-dependent":[68,241],"nonlinear":[69,242],"actuator":[71,244],"(LDNSA)":[72,245],"with":[73,86,146,175,232,282,298,333],"compact":[75],"elastic":[76,89,261],"mechanical":[77],"structure.":[78],"However,":[79,219,252],"hysteresis":[80,143,178,191,253,312,319],"is":[81,112,127,149,226,254,264],"brought":[82,255],"inevitably":[84],"along":[85],"nonideal":[88,260],"mechanism":[90],"assembly":[92],"errors,":[93],"which":[94,126,263,285],"limits":[95],"dynamic":[97],"performance":[98,133,169,325],"LDNSA.":[101,136,336],"In":[102,271],"article,":[104,273],"an":[105,259],"equitorque":[106],"discretization":[107],"to":[108,114,122,155,166,197,203,213,280],"implement":[109],"real-time":[110],"compensation":[111,144,179,278,320],"improve":[115,323],"classical":[117],"Bouc-Wen":[118,300],"model,":[119,305],"commonly":[120],"used":[121,228],"compensate":[123],"for":[124,330],"hysteresis,":[125,284],"controlling":[131],"Afterward,":[137],"stability":[139],"analysis":[140],"system":[145],"impedance":[147],"control":[148],"also":[150,265],"discussed":[151],"as":[152,154],"well":[153],"guarantee":[156],"safety":[158,211],"system.":[161],"Finally,":[162],"experiments":[163],"are":[164],"conducted":[165],"evaluate":[167],"advantages":[171],"LDNSA":[174,194,315],"method.":[180],"The":[181,317],"results":[182,294],"show":[183,295],"that":[184,225,296],"model":[187,301],"solve":[189,310],"well.":[195],"Note":[196],"Practitioners-Many":[198],"VSAs":[199],"have":[200],"been":[201],"realize":[204],"theoretically":[205],"both":[206],"bandwidth":[208],"good":[210],"due":[212],"completely":[214],"decoupling":[215],"load.":[218],"there":[220],"exists":[221],"redundancy":[223],"range":[224],"rarely":[227],"physical":[230],"To":[235],"avoid":[236],"redundancy,":[238],"via":[257],"adopting":[258],"element,":[262],"many":[268],"automated":[269],"devices.":[270],"algorithm":[279,308],"deal":[281],"be":[287],"carried":[288],"out":[289],"real":[291],"time.":[292],"Experimental":[293],"compared":[297],"PD":[304],"better.":[316],"methodology":[321],"rehabilitation":[328],"robot":[329],"shoulder":[331],"training":[332],"modularized":[335]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}