Design of discrete PID controllers for maximizing stability margins
The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficie...
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| Veröffentlicht in: | Asian journal of control 2023-03, Vol.25 (2), p.824-839 |
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| container_title | Asian journal of control |
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| creator | Guo, Tong‐Yi Hwang, Chyi Lu, Li‐Shin |
| description | The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed‐loop poles being inside the circle of radius
ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number
ε, a minimum value
ρε* and the corresponding
ρε*−stabilizing discrete PID controller set for achieving at least
1−ρε* of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability‐margin discrete PID controller design, two numerical examples are provided. |
| doi_str_mv | 10.1002/asjc.2940 |
| format | Article |
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ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number
ε, a minimum value
ρε* and the corresponding
ρε*−stabilizing discrete PID controller set for achieving at least
1−ρε* of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability‐margin discrete PID controller design, two numerical examples are provided.</description><identifier>ISSN: 1561-8625</identifier><identifier>EISSN: 1934-6093</identifier><identifier>DOI: 10.1002/asjc.2940</identifier><language>eng</language><publisher>Hoboken: Wiley Subscription Services, Inc</publisher><subject>Algorithms ; Control systems design ; Controllers ; digital PID ; discrete‐time systems ; D‐partition theory ; Maximization ; maximum stability margin ; Optimization ; Proportional integral derivative ; stabilizing controller set</subject><ispartof>Asian journal of control, 2023-03, Vol.25 (2), p.824-839</ispartof><rights>2022 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.</rights><rights>2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2970-c7e0a2a214fd4cff5dc1e42735efdd4bfaa6b0d9f7f1584e0546d893e7eae2b33</citedby><cites>FETCH-LOGICAL-c2970-c7e0a2a214fd4cff5dc1e42735efdd4bfaa6b0d9f7f1584e0546d893e7eae2b33</cites><orcidid>0000-0003-0674-2075</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fasjc.2940$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fasjc.2940$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Guo, Tong‐Yi</creatorcontrib><creatorcontrib>Hwang, Chyi</creatorcontrib><creatorcontrib>Lu, Li‐Shin</creatorcontrib><title>Design of discrete PID controllers for maximizing stability margins</title><title>Asian journal of control</title><description>The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed‐loop poles being inside the circle of radius
ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number
ε, a minimum value
ρε* and the corresponding
ρε*−stabilizing discrete PID controller set for achieving at least
1−ρε* of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability‐margin discrete PID controller design, two numerical examples are provided.</description><subject>Algorithms</subject><subject>Control systems design</subject><subject>Controllers</subject><subject>digital PID</subject><subject>discrete‐time systems</subject><subject>D‐partition theory</subject><subject>Maximization</subject><subject>maximum stability margin</subject><subject>Optimization</subject><subject>Proportional integral derivative</subject><subject>stabilizing controller set</subject><issn>1561-8625</issn><issn>1934-6093</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKsH_0HAk4dtk2yS3T2WrR-VgoJ6DtlkUlK2m5ps0frr3VqvnmYYnpl5eRC6pmRCCWFTndZmwipOTtCIVjnPJKny06EXkmalZOIcXaS0JkTSvBQjVM8h-VWHg8PWJxOhB_yymGMTuj6GtoWYsAsRb_SX3_hv361w6nXjW9_vh2Fc-S5dojOn2wRXf3WM3u_v3urHbPn8sKhny8ywqiCZKYBophnlznLjnLCGAmdFLsBZyxuntWyIrVzhqCg5EMGlLascCtDAmjwfo5vj3W0MHztIvVqHXeyGl4oVpaCylFUxULdHysSQUgSnttEPSfeKEnVwpA6O1MHRwE6P7KdvYf8_qGavT_Xvxg8xRmmn</recordid><startdate>202303</startdate><enddate>202303</enddate><creator>Guo, Tong‐Yi</creator><creator>Hwang, Chyi</creator><creator>Lu, Li‐Shin</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0003-0674-2075</orcidid></search><sort><creationdate>202303</creationdate><title>Design of discrete PID controllers for maximizing stability margins</title><author>Guo, Tong‐Yi ; Hwang, Chyi ; Lu, Li‐Shin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2970-c7e0a2a214fd4cff5dc1e42735efdd4bfaa6b0d9f7f1584e0546d893e7eae2b33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Control systems design</topic><topic>Controllers</topic><topic>digital PID</topic><topic>discrete‐time systems</topic><topic>D‐partition theory</topic><topic>Maximization</topic><topic>maximum stability margin</topic><topic>Optimization</topic><topic>Proportional integral derivative</topic><topic>stabilizing controller set</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Guo, Tong‐Yi</creatorcontrib><creatorcontrib>Hwang, Chyi</creatorcontrib><creatorcontrib>Lu, Li‐Shin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Asian journal of control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guo, Tong‐Yi</au><au>Hwang, Chyi</au><au>Lu, Li‐Shin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Design of discrete PID controllers for maximizing stability margins</atitle><jtitle>Asian journal of control</jtitle><date>2023-03</date><risdate>2023</risdate><volume>25</volume><issue>2</issue><spage>824</spage><epage>839</epage><pages>824-839</pages><issn>1561-8625</issn><eissn>1934-6093</eissn><abstract>The objective of this paper is to provide a discrete PID controller design procedure for maximizing stability margins. First, a new and complete characterization of the entire set of stabilizing discrete PID controllers for a given plant is presented. Then, based on this characterization, an efficient algorithm is developed for testing if, for a given plant, there exists a digital PID controller gain parameter space corresponding to closed‐loop poles being inside the circle of radius
ρ centered at the origin. The developed algorithm is finally applied along with a bisection strategy to determine, for a specified small positive number
ε, a minimum value
ρε* and the corresponding
ρε*−stabilizing discrete PID controller set for achieving at least
1−ρε* of stability margin. To illustrate the features of our new characterization of stabilizing digital PID controller sets and the effectiveness of the presented algorithms to the maximum stability‐margin discrete PID controller design, two numerical examples are provided.</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/asjc.2940</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0003-0674-2075</orcidid></addata></record> |
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| language | eng |
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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | Algorithms Control systems design Controllers digital PID discrete‐time systems D‐partition theory Maximization maximum stability margin Optimization Proportional integral derivative stabilizing controller set |
| title | Design of discrete PID controllers for maximizing stability margins |
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