Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator

The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measur...

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Autores principales:	Noussaiba Gasmi, Mohamed Boutayeb, Assem Thabet, Ghazi Bel Haj Frej, Mohamed Aoun
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Lipschitz discrete-time systems observer-based stabilization design parametric uncertainties sliding window approach ARDUINO UNO R3 device Materials of engineering and construction. Mechanics of materials TA401-492 Production of electric energy or power. Powerplants. Central stations TK1001-1841
Acceso en línea:	https://doaj.org/article/f5d9450f21be40d092f767907e329b3d
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id	oai:doaj.org-article:f5d9450f21be40d092f767907e329b3d
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spelling	oai:doaj.org-article:f5d9450f21be40d092f767907e329b3d2021-11-25T15:56:59ZRobust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator10.3390/act101103032076-0825https://doaj.org/article/f5d9450f21be40d092f767907e329b3d2021-11-01T00:00:00Zhttps://www.mdpi.com/2076-0825/10/11/303https://doaj.org/toc/2076-0825The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements in the observer and the control law structures which increase the number of decision variables in the constraint to be solved and offers less restrictive Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI) which is solved in two steps. First, by using a slack variable technique and an appropriate reformulation of the Young’s inequality. Second, by introducing a useful approach to transform the obtained constraint to a more suitable one easily tractable by standard software algorithms. A comparison with the standard case is provided to show the superiority of the proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> observer-based controller which offers greater degree of freedom. The accuracy and the potential of the proposed process are shown through real time implementation of the one-link flexible joint robot to ARDUINO UNO R3 device and numerical comparison with some existing results.Noussaiba GasmiMohamed BoutayebAssem ThabetGhazi Bel Haj FrejMohamed AounMDPI AGarticleLipschitz discrete-time systemsobserver-based stabilization designparametric uncertaintiessliding window approachARDUINO UNO R3 deviceMaterials of engineering and construction. Mechanics of materialsTA401-492Production of electric energy or power. Powerplants. Central stationsTK1001-1841ENActuators, Vol 10, Iss 303, p 303 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Lipschitz discrete-time systems observer-based stabilization design parametric uncertainties sliding window approach ARDUINO UNO R3 device Materials of engineering and construction. Mechanics of materials TA401-492 Production of electric energy or power. Powerplants. Central stations TK1001-1841
spellingShingle	Lipschitz discrete-time systems observer-based stabilization design parametric uncertainties sliding window approach ARDUINO UNO R3 device Materials of engineering and construction. Mechanics of materials TA401-492 Production of electric energy or power. Powerplants. Central stations TK1001-1841 Noussaiba Gasmi Mohamed Boutayeb Assem Thabet Ghazi Bel Haj Frej Mohamed Aoun Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
description	The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements in the observer and the control law structures which increase the number of decision variables in the constraint to be solved and offers less restrictive Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI) which is solved in two steps. First, by using a slack variable technique and an appropriate reformulation of the Young’s inequality. Second, by introducing a useful approach to transform the obtained constraint to a more suitable one easily tractable by standard software algorithms. A comparison with the standard case is provided to show the superiority of the proposed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">H</mi><mo>∞</mo></msub></semantics></math></inline-formula> observer-based controller which offers greater degree of freedom. The accuracy and the potential of the proposed process are shown through real time implementation of the one-link flexible joint robot to ARDUINO UNO R3 device and numerical comparison with some existing results.
format	article
author	Noussaiba Gasmi Mohamed Boutayeb Assem Thabet Ghazi Bel Haj Frej Mohamed Aoun
author_facet	Noussaiba Gasmi Mohamed Boutayeb Assem Thabet Ghazi Bel Haj Frej Mohamed Aoun
author_sort	Noussaiba Gasmi
title	Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
title_short	Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
title_full	Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
title_fullStr	Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
title_full_unstemmed	Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator
title_sort	robust control of a class of nonlinear discrete-time systems: design and experimental results on a real-time emulator
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/f5d9450f21be40d092f767907e329b3d
work_keys_str_mv	AT noussaibagasmi robustcontrolofaclassofnonlineardiscretetimesystemsdesignandexperimentalresultsonarealtimeemulator AT mohamedboutayeb robustcontrolofaclassofnonlineardiscretetimesystemsdesignandexperimentalresultsonarealtimeemulator AT assemthabet robustcontrolofaclassofnonlineardiscretetimesystemsdesignandexperimentalresultsonarealtimeemulator AT ghazibelhajfrej robustcontrolofaclassofnonlineardiscretetimesystemsdesignandexperimentalresultsonarealtimeemulator AT mohamedaoun robustcontrolofaclassofnonlineardiscretetimesystemsdesignandexperimentalresultsonarealtimeemulator
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Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator

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