Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems
In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the lite...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2017-06-01
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| Series: | Nonlinear Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/nleng-2016-0059 |
| _version_ | 1818691515503869952 |
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| author | Rajagopal Karthikeyan Karthikeyan Anitha Duraisamy Prakash |
| author_facet | Rajagopal Karthikeyan Karthikeyan Anitha Duraisamy Prakash |
| author_sort | Rajagopal Karthikeyan |
| collection | DOAJ |
| description | In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable. |
| first_indexed | 2024-12-17T12:43:07Z |
| format | Article |
| id | doaj.art-7e23788fbe934faa9b5419eb7e575652 |
| institution | Directory Open Access Journal |
| issn | 2192-8010 2192-8029 |
| language | English |
| last_indexed | 2024-12-17T12:43:07Z |
| publishDate | 2017-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj.art-7e23788fbe934faa9b5419eb7e5756522022-12-21T21:47:52ZengDe GruyterNonlinear Engineering2192-80102192-80292017-06-0162798710.1515/nleng-2016-0059Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine SystemsRajagopal Karthikeyan0Karthikeyan Anitha1Duraisamy Prakash2Center for Non-Linear Dynamics, Defense University, Austin, EthiopiaElectronics Engineering, Chennai Institute of Technology, Kundrathur, IndiaProduction Engineering, College of Engineering, Defense University, Austin, EthiopiaIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.https://doi.org/10.1515/nleng-2016-0059chaos suppressionfractional order systemspermanent magnet synchronous generatorspeed and current controllyapunov stability |
| spellingShingle | Rajagopal Karthikeyan Karthikeyan Anitha Duraisamy Prakash Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems Nonlinear Engineering chaos suppression fractional order systems permanent magnet synchronous generator speed and current control lyapunov stability |
| title | Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems |
| title_full | Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems |
| title_fullStr | Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems |
| title_full_unstemmed | Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems |
| title_short | Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems |
| title_sort | chaos suppression in fractional order permanent magnet synchronous generator in wind turbine systems |
| topic | chaos suppression fractional order systems permanent magnet synchronous generator speed and current control lyapunov stability |
| url | https://doi.org/10.1515/nleng-2016-0059 |
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