Granular fuzzy PID controller
In this paper an uncertain dynamical system is investigated in which the coefficients are as a class of fuzzy sets and the fuzzy derivative is considered as the granular derivative. Furthermore, the notions of granular second order derivative of a fuzzy function, fuzzy overshoot, fuzzy rise-time, an...
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| Veröffentlicht in: | Expert systems with applications 2021-04, Vol.167, p.114182, Article 114182 |
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| description | In this paper an uncertain dynamical system is investigated in which the coefficients are as a class of fuzzy sets and the fuzzy derivative is considered as the granular derivative. Furthermore, the notions of granular second order derivative of a fuzzy function, fuzzy overshoot, fuzzy rise-time, and fuzzy peak-time are introduced. As a result, designing a class of PID controllers called granular Fuzzy PID (gr-FPID) controller is presented based on fuzzy mathematics. The gr-FPID consists of granular integral, granular derivative with fuzzy coefficients. Moreover, the Particle Swarm Optimization (PSO) algorithm is used to tune gr-FPID fuzzy coefficients. It is demonstrated that the gr-FPID controller can effectively control the temperature in a continuous stirred tank reactor in which the parameters are uncertain.
•Presenting granular second order derivative of a fuzzy function.•Defining fuzzy overshoot, fuzzy rise time, and fuzzy peak time.•Presenting an approach for the linearization of a nonlinear model around a fuzzy operating point.•A new kind of fuzzy PID controller is designed (gr-FPID).•Explaining the process of PSO algorithm for tuning the fuzzy parameters of gr-FPID. |
| doi_str_mv | 10.1016/j.eswa.2020.114182 |
| format | Article |
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•Presenting granular second order derivative of a fuzzy function.•Defining fuzzy overshoot, fuzzy rise time, and fuzzy peak time.•Presenting an approach for the linearization of a nonlinear model around a fuzzy operating point.•A new kind of fuzzy PID controller is designed (gr-FPID).•Explaining the process of PSO algorithm for tuning the fuzzy parameters of gr-FPID.</description><identifier>ISSN: 0957-4174</identifier><identifier>EISSN: 1873-6793</identifier><identifier>DOI: 10.1016/j.eswa.2020.114182</identifier><language>eng</language><publisher>New York: Elsevier Ltd</publisher><subject>Algorithms ; Coefficients ; Continuously stirred tank reactors ; Controllers ; Fuzzy control ; Fuzzy sets ; Granular second order derivative ; Horizontal membership functions ; Mathematical analysis ; Overshoot ; Parameter uncertainty ; Particle swarm optimization ; PID controller ; Proportional integral derivative ; PSO algorithm ; Rise-time</subject><ispartof>Expert systems with applications, 2021-04, Vol.167, p.114182, Article 114182</ispartof><rights>2020 Elsevier Ltd</rights><rights>Copyright Elsevier BV Apr 1, 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c328t-7b0128692ee1f110b4b95082addd18d1d697a52c201ad3834b24d4b1531def023</citedby><cites>FETCH-LOGICAL-c328t-7b0128692ee1f110b4b95082addd18d1d697a52c201ad3834b24d4b1531def023</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0957417420309155$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids></links><search><creatorcontrib>Najariyan, Marzieh</creatorcontrib><creatorcontrib>Zhao, Yi</creatorcontrib><title>Granular fuzzy PID controller</title><title>Expert systems with applications</title><description>In this paper an uncertain dynamical system is investigated in which the coefficients are as a class of fuzzy sets and the fuzzy derivative is considered as the granular derivative. Furthermore, the notions of granular second order derivative of a fuzzy function, fuzzy overshoot, fuzzy rise-time, and fuzzy peak-time are introduced. As a result, designing a class of PID controllers called granular Fuzzy PID (gr-FPID) controller is presented based on fuzzy mathematics. The gr-FPID consists of granular integral, granular derivative with fuzzy coefficients. Moreover, the Particle Swarm Optimization (PSO) algorithm is used to tune gr-FPID fuzzy coefficients. It is demonstrated that the gr-FPID controller can effectively control the temperature in a continuous stirred tank reactor in which the parameters are uncertain.
•Presenting granular second order derivative of a fuzzy function.•Defining fuzzy overshoot, fuzzy rise time, and fuzzy peak time.•Presenting an approach for the linearization of a nonlinear model around a fuzzy operating point.•A new kind of fuzzy PID controller is designed (gr-FPID).•Explaining the process of PSO algorithm for tuning the fuzzy parameters of gr-FPID.</description><subject>Algorithms</subject><subject>Coefficients</subject><subject>Continuously stirred tank reactors</subject><subject>Controllers</subject><subject>Fuzzy control</subject><subject>Fuzzy sets</subject><subject>Granular second order derivative</subject><subject>Horizontal membership functions</subject><subject>Mathematical analysis</subject><subject>Overshoot</subject><subject>Parameter uncertainty</subject><subject>Particle swarm optimization</subject><subject>PID controller</subject><subject>Proportional integral derivative</subject><subject>PSO algorithm</subject><subject>Rise-time</subject><issn>0957-4174</issn><issn>1873-6793</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKxDAQhoMouK6-gCAseO46k6RNCl5k1XVhQQ96DmkyhZbarkmr7D69XerZ08Dwf_8MH2PXCEsEzO7qJcUfu-TAxwVK1PyEzVArkWQqF6dsBnmqEolKnrOLGGsAVABqxm7WwbZDY8OiHA6H_eJt87hwXduHrmkoXLKz0jaRrv7mnH08P72vXpLt63qzetgmTnDdJ6oA5DrLORGWiFDIIk9Bc-u9R-3RZ7myKXcc0HqhhSy49LLAVKCnEriYs9updxe6r4Fib-puCO140vAUBCoBIMcUn1IudDEGKs0uVJ827A2COWowtTlqMEcNZtIwQvcTROP_3xUFE11FrSNfBXK98V31H_4LZ9FjKA</recordid><startdate>20210401</startdate><enddate>20210401</enddate><creator>Najariyan, Marzieh</creator><creator>Zhao, Yi</creator><general>Elsevier Ltd</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20210401</creationdate><title>Granular fuzzy PID controller</title><author>Najariyan, Marzieh ; Zhao, Yi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c328t-7b0128692ee1f110b4b95082addd18d1d697a52c201ad3834b24d4b1531def023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>Coefficients</topic><topic>Continuously stirred tank reactors</topic><topic>Controllers</topic><topic>Fuzzy control</topic><topic>Fuzzy sets</topic><topic>Granular second order derivative</topic><topic>Horizontal membership functions</topic><topic>Mathematical analysis</topic><topic>Overshoot</topic><topic>Parameter uncertainty</topic><topic>Particle swarm optimization</topic><topic>PID controller</topic><topic>Proportional integral derivative</topic><topic>PSO algorithm</topic><topic>Rise-time</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Najariyan, Marzieh</creatorcontrib><creatorcontrib>Zhao, Yi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology 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><jtitle>Expert systems with applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Najariyan, Marzieh</au><au>Zhao, Yi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Granular fuzzy PID controller</atitle><jtitle>Expert systems with applications</jtitle><date>2021-04-01</date><risdate>2021</risdate><volume>167</volume><spage>114182</spage><pages>114182-</pages><artnum>114182</artnum><issn>0957-4174</issn><eissn>1873-6793</eissn><abstract>In this paper an uncertain dynamical system is investigated in which the coefficients are as a class of fuzzy sets and the fuzzy derivative is considered as the granular derivative. Furthermore, the notions of granular second order derivative of a fuzzy function, fuzzy overshoot, fuzzy rise-time, and fuzzy peak-time are introduced. As a result, designing a class of PID controllers called granular Fuzzy PID (gr-FPID) controller is presented based on fuzzy mathematics. The gr-FPID consists of granular integral, granular derivative with fuzzy coefficients. Moreover, the Particle Swarm Optimization (PSO) algorithm is used to tune gr-FPID fuzzy coefficients. It is demonstrated that the gr-FPID controller can effectively control the temperature in a continuous stirred tank reactor in which the parameters are uncertain.
•Presenting granular second order derivative of a fuzzy function.•Defining fuzzy overshoot, fuzzy rise time, and fuzzy peak time.•Presenting an approach for the linearization of a nonlinear model around a fuzzy operating point.•A new kind of fuzzy PID controller is designed (gr-FPID).•Explaining the process of PSO algorithm for tuning the fuzzy parameters of gr-FPID.</abstract><cop>New York</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.eswa.2020.114182</doi></addata></record> |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Algorithms Coefficients Continuously stirred tank reactors Controllers Fuzzy control Fuzzy sets Granular second order derivative Horizontal membership functions Mathematical analysis Overshoot Parameter uncertainty Particle swarm optimization PID controller Proportional integral derivative PSO algorithm Rise-time |
| title | Granular fuzzy PID controller |
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