Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems
► An IFT algorithm which sets the step size to guarantee the convergence is suggested. ► An inequality-type convergence condition is derived from Popov’s hyperstability theory. ► Discrete-time input affine SISO systems are considered. ► Lyapunov’s direct method is applied to tune Takagi–Sugeno–Kang...
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| Veröffentlicht in: | Expert systems with applications 2013-01, Vol.40 (1), p.188-199 |
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| creator | Precup, Radu-Emil Rădac, Mircea-Bogdan Tomescu, Marius L. Petriu, Emil M. Preitl, Stefan |
| description | ► An IFT algorithm which sets the step size to guarantee the convergence is suggested. ► An inequality-type convergence condition is derived from Popov’s hyperstability theory. ► Discrete-time input affine SISO systems are considered. ► Lyapunov’s direct method is applied to tune Takagi–Sugeno–Kang PI-fuzzy controllers. ► An IFT-based tuned PI-fuzzy controller for a servo system shows performance improvement.
This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included. |
| doi_str_mv | 10.1016/j.eswa.2012.07.023 |
| format | Article |
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This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.</description><identifier>ISSN: 0957-4174</identifier><identifier>EISSN: 1873-6793</identifier><identifier>DOI: 10.1016/j.eswa.2012.07.023</identifier><language>eng</language><publisher>Amsterdam: Elsevier Ltd</publisher><subject>Algorithms ; Applied sciences ; Computer science; control theory; systems ; Control system analysis ; Control systems ; Control theory ; Control theory. Systems ; Convergence ; Discrete-time input affine SISO systems ; Dynamical systems ; Exact sciences and technology ; Feedback ; Iterative feedback tuning ; Nonlinear dynamics ; Optimal control ; PI-fuzzy controllers ; Real-time experimental results ; Stability ; Stability analysis</subject><ispartof>Expert systems with applications, 2013-01, Vol.40 (1), p.188-199</ispartof><rights>2012 Elsevier Ltd</rights><rights>2014 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c396t-72fe3654e2daa97673e777315d87b2fe9f4fa277210e6a246dbf3cf69c25dc943</citedby><cites>FETCH-LOGICAL-c396t-72fe3654e2daa97673e777315d87b2fe9f4fa277210e6a246dbf3cf69c25dc943</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.eswa.2012.07.023$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,4024,27923,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=27095897$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Precup, Radu-Emil</creatorcontrib><creatorcontrib>Rădac, Mircea-Bogdan</creatorcontrib><creatorcontrib>Tomescu, Marius L.</creatorcontrib><creatorcontrib>Petriu, Emil M.</creatorcontrib><creatorcontrib>Preitl, Stefan</creatorcontrib><title>Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems</title><title>Expert systems with applications</title><description>► An IFT algorithm which sets the step size to guarantee the convergence is suggested. ► An inequality-type convergence condition is derived from Popov’s hyperstability theory. ► Discrete-time input affine SISO systems are considered. ► Lyapunov’s direct method is applied to tune Takagi–Sugeno–Kang PI-fuzzy controllers. ► An IFT-based tuned PI-fuzzy controller for a servo system shows performance improvement.
This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control system analysis</subject><subject>Control systems</subject><subject>Control theory</subject><subject>Control theory. Systems</subject><subject>Convergence</subject><subject>Discrete-time input affine SISO systems</subject><subject>Dynamical systems</subject><subject>Exact sciences and technology</subject><subject>Feedback</subject><subject>Iterative feedback tuning</subject><subject>Nonlinear dynamics</subject><subject>Optimal control</subject><subject>PI-fuzzy controllers</subject><subject>Real-time experimental results</subject><subject>Stability</subject><subject>Stability analysis</subject><issn>0957-4174</issn><issn>1873-6793</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqFkUtrGzEQgEVJoU6aP5CTLoVedqPH7o4FvZTQJIaAD27PQpZGRu5615VkF_vXR8Ymx-Q0h_nm9Q0hd5zVnPHufl1j-m9qwbioGdRMyE9kwqcgqw6UvCITplqoGg7NF3Kd0poxDozBhNhFNsseqRkcteOwx7jCIdOQMZoc9kg9olsa-5fm3RCGFR099bvj8XCicxz7HmOifozUhWQjZqxy2CBdzBZzmg4p4yZ9JZ-96RPeXuIN-fP46_fDc_Uyf5o9_HyprFRdrkB4lF3boHDGKOhAIgBI3ropLEtO-cYbASA4w86IpnNLL63vlBWts6qRN-T7ue82jv92mLLelJ2w782A4y7pcjJnkk9V-zEqG9VAgVlBxRm1cUwpotfbGDYmHjRn-iRfr_VJvj7J1wx0kV-Kvl36m2RN76MZbEhvlQLKP6YKCvfjzGHxsg8YdbIBB4suRLRZuzG8N-YVA0SbXQ</recordid><startdate>201301</startdate><enddate>201301</enddate><creator>Precup, Radu-Emil</creator><creator>Rădac, Mircea-Bogdan</creator><creator>Tomescu, Marius L.</creator><creator>Petriu, Emil M.</creator><creator>Preitl, Stefan</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><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>201301</creationdate><title>Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems</title><author>Precup, Radu-Emil ; Rădac, Mircea-Bogdan ; Tomescu, Marius L. ; Petriu, Emil M. ; Preitl, Stefan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c396t-72fe3654e2daa97673e777315d87b2fe9f4fa277210e6a246dbf3cf69c25dc943</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Control system analysis</topic><topic>Control systems</topic><topic>Control theory</topic><topic>Control theory. Systems</topic><topic>Convergence</topic><topic>Discrete-time input affine SISO systems</topic><topic>Dynamical systems</topic><topic>Exact sciences and technology</topic><topic>Feedback</topic><topic>Iterative feedback tuning</topic><topic>Nonlinear dynamics</topic><topic>Optimal control</topic><topic>PI-fuzzy controllers</topic><topic>Real-time experimental results</topic><topic>Stability</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Precup, Radu-Emil</creatorcontrib><creatorcontrib>Rădac, Mircea-Bogdan</creatorcontrib><creatorcontrib>Tomescu, Marius L.</creatorcontrib><creatorcontrib>Petriu, Emil M.</creatorcontrib><creatorcontrib>Preitl, Stefan</creatorcontrib><collection>Pascal-Francis</collection><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>Precup, Radu-Emil</au><au>Rădac, Mircea-Bogdan</au><au>Tomescu, Marius L.</au><au>Petriu, Emil M.</au><au>Preitl, Stefan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems</atitle><jtitle>Expert systems with applications</jtitle><date>2013-01</date><risdate>2013</risdate><volume>40</volume><issue>1</issue><spage>188</spage><epage>199</epage><pages>188-199</pages><issn>0957-4174</issn><eissn>1873-6793</eissn><abstract>► An IFT algorithm which sets the step size to guarantee the convergence is suggested. ► An inequality-type convergence condition is derived from Popov’s hyperstability theory. ► Discrete-time input affine SISO systems are considered. ► Lyapunov’s direct method is applied to tune Takagi–Sugeno–Kang PI-fuzzy controllers. ► An IFT-based tuned PI-fuzzy controller for a servo system shows performance improvement.
This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi–Sugeno–Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov’s direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov’s hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.eswa.2012.07.023</doi><tpages>12</tpages></addata></record> |
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| subjects | Algorithms Applied sciences Computer science control theory systems Control system analysis Control systems Control theory Control theory. Systems Convergence Discrete-time input affine SISO systems Dynamical systems Exact sciences and technology Feedback Iterative feedback tuning Nonlinear dynamics Optimal control PI-fuzzy controllers Real-time experimental results Stability Stability analysis |
| title | Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems |
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