Loading…

Analysis of Piecewise Linear Systems by the Method of Integral Equations

Analysis of piecewise linear systems may require the solution of high-order linear differential equations whose parameters are constants within a given region but change into different constants for adjacent regions. The multiple regions of such a system may be identified with discrete intervals and...

Full description

Saved in:
Bibliographic Details
Published in:Journal of basic engineering 1964-03, Vol.86 (1), p.139-144
Main Authors: Shen, C. N, Wang, Hubert
Format: Article
Language:English
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 144
container_issue 1
container_start_page 139
container_title Journal of basic engineering
container_volume 86
creator Shen, C. N
Wang, Hubert
description Analysis of piecewise linear systems may require the solution of high-order linear differential equations whose parameters are constants within a given region but change into different constants for adjacent regions. The multiple regions of such a system may be identified with discrete intervals and it is a simple matter to obtain the system response by the method of integral equations. These solutions are given in the form of convergent infinite series, the terms of which may be easily evaluated by a digital computer. The time interval of each region is found by substituting successive values of these truncated series until the required boundary conditions are satisfied. The method is applied to a third order-type two system whose sustained oscillation, when subjected to dry friction, is to be eliminated by dead-zone compensation. The system has four regions with different parameters for each region of the differential equations which are converted into Volterra integral equations of the second kind. The variables are iterated within the digital computer until a convergent solution is found for the condition of sustained oscillation. Procedures are given to determine critical values of dead zone for various ramp rates at which the system is stable.
doi_str_mv 10.1115/1.3653098
format article
fullrecord <record><control><sourceid>asme_cross</sourceid><recordid>TN_cdi_asme_journals_392197</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>392197</sourcerecordid><originalsourceid>FETCH-LOGICAL-a124t-fa2a94812c1720caf0900595cd6927ec465d85191daf1994c0d574c5c4bf4e473</originalsourceid><addsrcrecordid>eNotkE1LAzEURYMoWKsL126ydTH1vXzMTJal1LZQUVDBXUgziZ3SzmjeFJl_b0u7unA5XLiHsXuEESLqJxzJXEsw5QUboBZlZgC_LtkADlUmBIhrdkO0AUApVTlg83Hjtj3VxNvI3-rgw19NgS_rJrjE33vqwo74qufdOvCX0K3b6kgumi58J7fl09-96-q2oVt2Fd2Wwt05h-zzefoxmWfL19liMl5mDoXqsuiEM6pE4bEQ4F0EA6CN9lVuRBG8ynVVajRYuYjGKA-VLpTXXq2iCqqQQ_Z42vWpJUoh2p9U71zqLYI9KrBozwoO7MOJdbQLdtPu0-EsWWkEmkL-AxHHVjU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Analysis of Piecewise Linear Systems by the Method of Integral Equations</title><source>ASME Transactions Journals (Archives)</source><creator>Shen, C. N ; Wang, Hubert</creator><creatorcontrib>Shen, C. N ; Wang, Hubert</creatorcontrib><description>Analysis of piecewise linear systems may require the solution of high-order linear differential equations whose parameters are constants within a given region but change into different constants for adjacent regions. The multiple regions of such a system may be identified with discrete intervals and it is a simple matter to obtain the system response by the method of integral equations. These solutions are given in the form of convergent infinite series, the terms of which may be easily evaluated by a digital computer. The time interval of each region is found by substituting successive values of these truncated series until the required boundary conditions are satisfied. The method is applied to a third order-type two system whose sustained oscillation, when subjected to dry friction, is to be eliminated by dead-zone compensation. The system has four regions with different parameters for each region of the differential equations which are converted into Volterra integral equations of the second kind. The variables are iterated within the digital computer until a convergent solution is found for the condition of sustained oscillation. Procedures are given to determine critical values of dead zone for various ramp rates at which the system is stable.</description><identifier>ISSN: 0098-2202</identifier><identifier>ISSN: 0021-9223</identifier><identifier>EISSN: 1528-901X</identifier><identifier>DOI: 10.1115/1.3653098</identifier><language>eng</language><publisher>ASME</publisher><ispartof>Journal of basic engineering, 1964-03, Vol.86 (1), p.139-144</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925,38519</link.rule.ids></links><search><creatorcontrib>Shen, C. N</creatorcontrib><creatorcontrib>Wang, Hubert</creatorcontrib><title>Analysis of Piecewise Linear Systems by the Method of Integral Equations</title><title>Journal of basic engineering</title><addtitle>J. Fluids Eng</addtitle><description>Analysis of piecewise linear systems may require the solution of high-order linear differential equations whose parameters are constants within a given region but change into different constants for adjacent regions. The multiple regions of such a system may be identified with discrete intervals and it is a simple matter to obtain the system response by the method of integral equations. These solutions are given in the form of convergent infinite series, the terms of which may be easily evaluated by a digital computer. The time interval of each region is found by substituting successive values of these truncated series until the required boundary conditions are satisfied. The method is applied to a third order-type two system whose sustained oscillation, when subjected to dry friction, is to be eliminated by dead-zone compensation. The system has four regions with different parameters for each region of the differential equations which are converted into Volterra integral equations of the second kind. The variables are iterated within the digital computer until a convergent solution is found for the condition of sustained oscillation. Procedures are given to determine critical values of dead zone for various ramp rates at which the system is stable.</description><issn>0098-2202</issn><issn>0021-9223</issn><issn>1528-901X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1964</creationdate><recordtype>article</recordtype><recordid>eNotkE1LAzEURYMoWKsL126ydTH1vXzMTJal1LZQUVDBXUgziZ3SzmjeFJl_b0u7unA5XLiHsXuEESLqJxzJXEsw5QUboBZlZgC_LtkADlUmBIhrdkO0AUApVTlg83Hjtj3VxNvI3-rgw19NgS_rJrjE33vqwo74qufdOvCX0K3b6kgumi58J7fl09-96-q2oVt2Fd2Wwt05h-zzefoxmWfL19liMl5mDoXqsuiEM6pE4bEQ4F0EA6CN9lVuRBG8ynVVajRYuYjGKA-VLpTXXq2iCqqQQ_Z42vWpJUoh2p9U71zqLYI9KrBozwoO7MOJdbQLdtPu0-EsWWkEmkL-AxHHVjU</recordid><startdate>19640301</startdate><enddate>19640301</enddate><creator>Shen, C. N</creator><creator>Wang, Hubert</creator><general>ASME</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19640301</creationdate><title>Analysis of Piecewise Linear Systems by the Method of Integral Equations</title><author>Shen, C. N ; Wang, Hubert</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a124t-fa2a94812c1720caf0900595cd6927ec465d85191daf1994c0d574c5c4bf4e473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1964</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shen, C. N</creatorcontrib><creatorcontrib>Wang, Hubert</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of basic engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shen, C. N</au><au>Wang, Hubert</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Analysis of Piecewise Linear Systems by the Method of Integral Equations</atitle><jtitle>Journal of basic engineering</jtitle><stitle>J. Fluids Eng</stitle><date>1964-03-01</date><risdate>1964</risdate><volume>86</volume><issue>1</issue><spage>139</spage><epage>144</epage><pages>139-144</pages><issn>0098-2202</issn><issn>0021-9223</issn><eissn>1528-901X</eissn><abstract>Analysis of piecewise linear systems may require the solution of high-order linear differential equations whose parameters are constants within a given region but change into different constants for adjacent regions. The multiple regions of such a system may be identified with discrete intervals and it is a simple matter to obtain the system response by the method of integral equations. These solutions are given in the form of convergent infinite series, the terms of which may be easily evaluated by a digital computer. The time interval of each region is found by substituting successive values of these truncated series until the required boundary conditions are satisfied. The method is applied to a third order-type two system whose sustained oscillation, when subjected to dry friction, is to be eliminated by dead-zone compensation. The system has four regions with different parameters for each region of the differential equations which are converted into Volterra integral equations of the second kind. The variables are iterated within the digital computer until a convergent solution is found for the condition of sustained oscillation. Procedures are given to determine critical values of dead zone for various ramp rates at which the system is stable.</abstract><pub>ASME</pub><doi>10.1115/1.3653098</doi><tpages>6</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0098-2202
ispartof Journal of basic engineering, 1964-03, Vol.86 (1), p.139-144
issn 0098-2202
0021-9223
1528-901X
language eng
recordid cdi_asme_journals_392197
source ASME Transactions Journals (Archives)
title Analysis of Piecewise Linear Systems by the Method of Integral Equations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T16%3A09%3A15IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-asme_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Analysis%20of%20Piecewise%20Linear%20Systems%20by%20the%20Method%20of%20Integral%20Equations&rft.jtitle=Journal%20of%20basic%20engineering&rft.au=Shen,%20C.%20N&rft.date=1964-03-01&rft.volume=86&rft.issue=1&rft.spage=139&rft.epage=144&rft.pages=139-144&rft.issn=0098-2202&rft.eissn=1528-901X&rft_id=info:doi/10.1115/1.3653098&rft_dat=%3Casme_cross%3E392197%3C/asme_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a124t-fa2a94812c1720caf0900595cd6927ec465d85191daf1994c0d574c5c4bf4e473%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true