Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller
In this paper, we suggest an improvement to our previously undertaken approach. Briefly, this approach consisted of applying the robust fractional predictive control (RFPC) for a class of constrained fractional systems implementing the min–max optimization technique. The RFPC controller requires res...
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| Format: | Article |
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MDPI AG
2022-01-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/11/2/268 |
| _version_ | 1797494442693754880 |
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| author | Aymen Rhouma Sami Hafsi Faouzi Bouani |
| author_facet | Aymen Rhouma Sami Hafsi Faouzi Bouani |
| author_sort | Aymen Rhouma |
| collection | DOAJ |
| description | In this paper, we suggest an improvement to our previously undertaken approach. Briefly, this approach consisted of applying the robust fractional predictive control (RFPC) for a class of constrained fractional systems implementing the min–max optimization technique. The RFPC controller requires resolution of a non-convex min–max optimization problem. The resolution of this problem, however, can only conduce to local solutions. The reason is simple: the objective function to be optimized is non-convex due to the presence of uncertainties. In the present work, we propose a global optimization-based RFPC controller for an uncertain fractional order system. A determinist global optimization method, namely, generalized geometric programming (GGP), is proposed to solve this problem for the uncertain fractional order system. The GGP method consists of converting a non-convex problem into a convex one via the application of variable changes. The technique of the convexification of this method is applied in line with the objective function to be optimized. Consequently, we obtained a new convex criterion and a convex problem. From an experimental point of view, we applied the proposed RFPC to a real thermal system using an STM32 microcontroller in order to control our thermal system. |
| first_indexed | 2024-03-10T01:34:21Z |
| format | Article |
| id | doaj.art-39d7f55618564620bfe0fd3aafc49b71 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T01:34:21Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-39d7f55618564620bfe0fd3aafc49b712023-11-23T13:34:59ZengMDPI AGElectronics2079-92922022-01-0111226810.3390/electronics11020268Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 MicrocontrollerAymen Rhouma0Sami Hafsi1Faouzi Bouani2Faculté des Sciences de Tunis, Université de Tunis El Manar, Tunis 2092, TunisieLR11ES20 Laboratoire Analyse, Conception et Commande des Systemes, Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar, Tunis 1002, TunisieLR11ES20 Laboratoire Analyse, Conception et Commande des Systemes, Ecole Nationale d’Ingénieurs de Tunis, Université de Tunis El Manar, Tunis 1002, TunisieIn this paper, we suggest an improvement to our previously undertaken approach. Briefly, this approach consisted of applying the robust fractional predictive control (RFPC) for a class of constrained fractional systems implementing the min–max optimization technique. The RFPC controller requires resolution of a non-convex min–max optimization problem. The resolution of this problem, however, can only conduce to local solutions. The reason is simple: the objective function to be optimized is non-convex due to the presence of uncertainties. In the present work, we propose a global optimization-based RFPC controller for an uncertain fractional order system. A determinist global optimization method, namely, generalized geometric programming (GGP), is proposed to solve this problem for the uncertain fractional order system. The GGP method consists of converting a non-convex problem into a convex one via the application of variable changes. The technique of the convexification of this method is applied in line with the objective function to be optimized. Consequently, we obtained a new convex criterion and a convex problem. From an experimental point of view, we applied the proposed RFPC to a real thermal system using an STM32 microcontroller in order to control our thermal system.https://www.mdpi.com/2079-9292/11/2/268uncertain fractional order systemsrobust fractional predictive controlglobal optimizationgeneralized geometric programming |
| spellingShingle | Aymen Rhouma Sami Hafsi Faouzi Bouani Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller Electronics uncertain fractional order systems robust fractional predictive control global optimization generalized geometric programming |
| title | Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller |
| title_full | Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller |
| title_fullStr | Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller |
| title_full_unstemmed | Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller |
| title_short | Global Optimization in Robust Fractional Control of Uncertain Fractional Order Systems: A Thermal Application Using the STM32 Microcontroller |
| title_sort | global optimization in robust fractional control of uncertain fractional order systems a thermal application using the stm32 microcontroller |
| topic | uncertain fractional order systems robust fractional predictive control global optimization generalized geometric programming |
| url | https://www.mdpi.com/2079-9292/11/2/268 |
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