Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors
This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we desi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/11/3/374 |
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| author | Rabiaa Houili Mohamed Yacine Hammoudi Mohamed Benbouzid Abdennacer Titaouine |
| author_facet | Rabiaa Houili Mohamed Yacine Hammoudi Mohamed Benbouzid Abdennacer Titaouine |
| author_sort | Rabiaa Houili |
| collection | DOAJ |
| description | This paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system. |
| first_indexed | 2024-03-11T06:16:39Z |
| format | Article |
| id | doaj.art-cd60f8b2d2f847678ac1e20f43cfbeb7 |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-11T06:16:39Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-cd60f8b2d2f847678ac1e20f43cfbeb72023-11-17T12:15:37ZengMDPI AGMachines2075-17022023-03-0111337410.3390/machines11030374Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction MotorsRabiaa Houili0Mohamed Yacine Hammoudi1Mohamed Benbouzid2Abdennacer Titaouine3Laboratory of Energy Systems Modeling (LMSE), Department of Electrical Engineering, University of Biskra, BP 145, Biskra 07000, AlgeriaLaboratory of Energy Systems Modeling (LMSE), Department of Electrical Engineering, University of Biskra, BP 145, Biskra 07000, AlgeriaInstitut de Recherche Dupuy de Lôme (UMR CNRS 6027 IRDL), University of Brest, 29238 Brest, FranceLaboratory of Energy Systems Modeling (LMSE), Department of Electrical Engineering, University of Biskra, BP 145, Biskra 07000, AlgeriaThis paper deals with the stabilization problem of a nonlinear system described by a Takagi–Sugeno fuzzy (TSF) model with unmeasurable premise variables via a robust controller. Applying the sector nonlinearity techniques, the nonlinear system is represented by a decoupled fuzzy model. Then, we design a robust observer-based controller for the obtained fuzzy system by utilizing the differential mean value approach. The observer and controller gains are obtained by the separation principle, in which the problem is solved in the sum of linear matrix inequalities (LMIs). The paper presents two main contributions: A state feedback controller is designed using differential mean value (DMVT) which ensures robust stabilization of the nonlinear system. Additionally, the Luenberger observer is extended to the Takagi–Sugeno fuzzy models. The second contribution is to reduce conservatism in the obtained conditions, a non-quadratic Lyapunov function (known as the line integral Lyapunov fuzzy candidate (LILF)) is employed. Two examples are provided to further illustrate the efficiency and robustness of the proposed approach; specifically, the Takagi–Sugeno fuzzy descriptor of an induction motor is derived and a robust observer-based controller applied to the original nonlinear system.https://www.mdpi.com/2075-1702/11/3/374Takagi–Sugeno fuzzy systemslinear matrix inequalitiesstabilizationintegral Lyapunov fuzzy functionmean value theoremLuenberger observer |
| spellingShingle | Rabiaa Houili Mohamed Yacine Hammoudi Mohamed Benbouzid Abdennacer Titaouine Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors Machines Takagi–Sugeno fuzzy systems linear matrix inequalities stabilization integral Lyapunov fuzzy function mean value theorem Luenberger observer |
| title | Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors |
| title_full | Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors |
| title_fullStr | Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors |
| title_full_unstemmed | Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors |
| title_short | Observer-Based Controller Using Line Integral Lyapunov Fuzzy Function for TS Fuzzy Systems: Application to Induction Motors |
| title_sort | observer based controller using line integral lyapunov fuzzy function for ts fuzzy systems application to induction motors |
| topic | Takagi–Sugeno fuzzy systems linear matrix inequalities stabilization integral Lyapunov fuzzy function mean value theorem Luenberger observer |
| url | https://www.mdpi.com/2075-1702/11/3/374 |
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