Semilinear Duhem model for rate-independent and rate-dependent hysteresis
The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If...
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| Veröffentlicht in: | IEEE transactions on automatic control 2005-05, Vol.50 (5), p.631-645 |
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| creator | JinHyoung Oh Bernstein, D.S. |
| description | The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed. |
| doi_str_mv | 10.1109/TAC.2005.847035 |
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In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.</description><identifier>ISSN: 0018-9286</identifier><identifier>EISSN: 1558-2523</identifier><identifier>DOI: 10.1109/TAC.2005.847035</identifier><identifier>CODEN: IETAA9</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Aerodynamics ; Applied sciences ; Computer science; control theory; systems ; Control theory. Systems ; Duhem ; Exact sciences and technology ; Frequency ; hysteresis ; Linear systems ; Magnetic fields ; Magnetic flux density ; Magnetic hysteresis ; Magnetic materials ; Nonlinear dynamical systems ; rate dependence ; Springs ; Terminology</subject><ispartof>IEEE transactions on automatic control, 2005-05, Vol.50 (5), p.631-645</ispartof><rights>2005 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2005</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c421t-a4b51338cd0ccddd5f74224831e265931d681634ab2bc9179a707947a27409d23</citedby><cites>FETCH-LOGICAL-c421t-a4b51338cd0ccddd5f74224831e265931d681634ab2bc9179a707947a27409d23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1431042$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27903,27904,54736</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1431042$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16769786$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>JinHyoung Oh</creatorcontrib><creatorcontrib>Bernstein, D.S.</creatorcontrib><title>Semilinear Duhem model for rate-independent and rate-dependent hysteresis</title><title>IEEE transactions on automatic control</title><addtitle>TAC</addtitle><description>The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.</description><subject>Aerodynamics</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control theory. Systems</subject><subject>Duhem</subject><subject>Exact sciences and technology</subject><subject>Frequency</subject><subject>hysteresis</subject><subject>Linear systems</subject><subject>Magnetic fields</subject><subject>Magnetic flux density</subject><subject>Magnetic hysteresis</subject><subject>Magnetic materials</subject><subject>Nonlinear dynamical systems</subject><subject>rate dependence</subject><subject>Springs</subject><subject>Terminology</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqFkbtLA0EQxhdRMEZrC5tD0O6SfT_KEF-BgIWxXja7c-TCPeLupch_74ULBGxsZphvfvPB8CF0T_CEEGymq9l8QjEWE80VZuICjYgQOqeCsks0wpjo3FAtr9FNStt-lJyTEVp8QV1WZQMuZi_7DdRZ3QaosqKNWXQd5GUTYAd9abrMNWEQz9LmkDqIkMp0i64KVyW4O_Ux-n57Xc0_8uXn-2I-W-aeU9Lljq8FYUz7gL0PIYhCcUq5ZgSoFIaRIDWRjLs1XXtDlHEKK8OVo4pjEygbo-fBdxfbnz2kztZl8lBVroF2nyw1mBGt1P-gxlIIYnrw8Q-4bfex6Z-wWjOmtGJHt-kA-dimFKGwu1jWLh4swfYYgO0DsMcA7BBAf_F0snXJu6qIrvFlOp9JJY3SsuceBq4EgPOaM4I5Zb9fX4xb</recordid><startdate>20050501</startdate><enddate>20050501</enddate><creator>JinHyoung Oh</creator><creator>Bernstein, D.S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Systems</topic><topic>Duhem</topic><topic>Exact sciences and technology</topic><topic>Frequency</topic><topic>hysteresis</topic><topic>Linear systems</topic><topic>Magnetic fields</topic><topic>Magnetic flux density</topic><topic>Magnetic hysteresis</topic><topic>Magnetic materials</topic><topic>Nonlinear dynamical systems</topic><topic>rate dependence</topic><topic>Springs</topic><topic>Terminology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>JinHyoung Oh</creatorcontrib><creatorcontrib>Bernstein, D.S.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>Aerospace Database</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>JinHyoung Oh</au><au>Bernstein, D.S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semilinear Duhem model for rate-independent and rate-dependent hysteresis</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>2005-05-01</date><risdate>2005</risdate><volume>50</volume><issue>5</issue><spage>631</spage><epage>645</epage><pages>631-645</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><abstract>The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TAC.2005.847035</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
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| source | IEEE Electronic Library (IEL) |
| subjects | Aerodynamics Applied sciences Computer science control theory systems Control theory. Systems Duhem Exact sciences and technology Frequency hysteresis Linear systems Magnetic fields Magnetic flux density Magnetic hysteresis Magnetic materials Nonlinear dynamical systems rate dependence Springs Terminology |
| title | Semilinear Duhem model for rate-independent and rate-dependent hysteresis |
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