Optimal control using derivative feedback for linear systems
Abstract This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived whi...
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| Veröffentlicht in: | Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering Journal of systems and control engineering, 2010-03, Vol.224 (2), p.185-202 |
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| container_title | Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering |
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| creator | Abdelaziz, T H S |
| description | Abstract
This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived which minimize the non-standard quadratic performance index. An explicit expression of the optimal state-derivative feedback gain is derived. Additionally, a convergent algorithm to solve the output-derivative feedback gains is demonstrated. The problems are studied for non-singular and singular open-loop state matrices. The necessary conditions for the existence of optimal gains are established. Finally, simulation results are included to show the effectiveness of the proposed approach. |
| doi_str_mv | 10.1243/09596518JSCE886 |
| format | Article |
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This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived which minimize the non-standard quadratic performance index. An explicit expression of the optimal state-derivative feedback gain is derived. Additionally, a convergent algorithm to solve the output-derivative feedback gains is demonstrated. The problems are studied for non-singular and singular open-loop state matrices. The necessary conditions for the existence of optimal gains are established. Finally, simulation results are included to show the effectiveness of the proposed approach.</description><identifier>ISSN: 0959-6518</identifier><identifier>EISSN: 2041-3041</identifier><identifier>DOI: 10.1243/09596518JSCE886</identifier><language>eng</language><publisher>London, England: SAGE Publications</publisher><subject>Algorithms ; Computer simulation ; Control systems ; Control theory ; Controllers ; Derivatives ; Design optimization ; Economic models ; Feedback ; Feedback control ; Feedback control systems ; Gain ; Linear systems ; Mathematical analysis ; Matrices (mathematics) ; Mechanical engineering ; Optimal control ; Optimization ; Performance indices ; Programmable logic controllers</subject><ispartof>Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering, 2010-03, Vol.224 (2), p.185-202</ispartof><rights>2010 Institution of Mechanical Engineers</rights><rights>Copyright Professional Engineering Publishing Ltd 2010</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c365t-34039b27dd767604e8faedb7ac4e339ec7bdbe5c6975a5e121625c7ccbb4c153</citedby><cites>FETCH-LOGICAL-c365t-34039b27dd767604e8faedb7ac4e339ec7bdbe5c6975a5e121625c7ccbb4c153</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://journals.sagepub.com/doi/pdf/10.1243/09596518JSCE886$$EPDF$$P50$$Gsage$$H</linktopdf><linktohtml>$$Uhttps://journals.sagepub.com/doi/10.1243/09596518JSCE886$$EHTML$$P50$$Gsage$$H</linktohtml><link.rule.ids>314,780,784,21819,27924,27925,43621,43622</link.rule.ids></links><search><creatorcontrib>Abdelaziz, T H S</creatorcontrib><title>Optimal control using derivative feedback for linear systems</title><title>Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering</title><description>Abstract
This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived which minimize the non-standard quadratic performance index. An explicit expression of the optimal state-derivative feedback gain is derived. Additionally, a convergent algorithm to solve the output-derivative feedback gains is demonstrated. The problems are studied for non-singular and singular open-loop state matrices. The necessary conditions for the existence of optimal gains are established. Finally, simulation results are included to show the effectiveness of the proposed approach.</description><subject>Algorithms</subject><subject>Computer simulation</subject><subject>Control systems</subject><subject>Control theory</subject><subject>Controllers</subject><subject>Derivatives</subject><subject>Design optimization</subject><subject>Economic models</subject><subject>Feedback</subject><subject>Feedback control</subject><subject>Feedback control systems</subject><subject>Gain</subject><subject>Linear systems</subject><subject>Mathematical analysis</subject><subject>Matrices (mathematics)</subject><subject>Mechanical engineering</subject><subject>Optimal control</subject><subject>Optimization</subject><subject>Performance indices</subject><subject>Programmable logic 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This paper presents the solution of the linear optimal control problem using derivative feedback for continuous, time-invariant, linear systems. The state-derivative and output-derivative feedback controllers are investigated. In this work, the optimal feedback gain matrices are derived which minimize the non-standard quadratic performance index. An explicit expression of the optimal state-derivative feedback gain is derived. Additionally, a convergent algorithm to solve the output-derivative feedback gains is demonstrated. The problems are studied for non-singular and singular open-loop state matrices. The necessary conditions for the existence of optimal gains are established. Finally, simulation results are included to show the effectiveness of the proposed approach.</abstract><cop>London, England</cop><pub>SAGE Publications</pub><doi>10.1243/09596518JSCE886</doi><tpages>18</tpages></addata></record> |
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| ispartof | Proceedings of the Institution of Mechanical Engineers. Part I, Journal of systems and control engineering, 2010-03, Vol.224 (2), p.185-202 |
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| source | Access via SAGE |
| subjects | Algorithms Computer simulation Control systems Control theory Controllers Derivatives Design optimization Economic models Feedback Feedback control Feedback control systems Gain Linear systems Mathematical analysis Matrices (mathematics) Mechanical engineering Optimal control Optimization Performance indices Programmable logic controllers |
| title | Optimal control using derivative feedback for linear systems |
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