Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller
This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent ex...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/9174284 |
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| _version_ | 1832564601801146368 |
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| author | Firas Turki Hassène Gritli Safya Belghith |
| author_facet | Firas Turki Hassène Gritli Safya Belghith |
| author_sort | Firas Turki |
| collection | DOAJ |
| description | This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance. |
| format | Article |
| id | doaj-art-3e3028991ff14b429669bad281c7aa0f |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-3e3028991ff14b429669bad281c7aa0f2025-02-03T01:10:41ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/91742849174284Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback ControllerFiras Turki0Hassène Gritli1Safya Belghith2Laboratory of Robotics, Informatics and Complex Systems (RISC-Lab, LR16ES07), National Engineering School of Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, TunisiaLaboratory of Robotics, Informatics and Complex Systems (RISC-Lab, LR16ES07), National Engineering School of Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, TunisiaLaboratory of Robotics, Informatics and Complex Systems (RISC-Lab, LR16ES07), National Engineering School of Tunis, Université de Tunis El Manar, BP. 37, Le Belvédère, 1002 Tunis, TunisiaThis paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.http://dx.doi.org/10.1155/2019/9174284 |
| spellingShingle | Firas Turki Hassène Gritli Safya Belghith Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller Complexity |
| title | Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller |
| title_full | Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller |
| title_fullStr | Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller |
| title_full_unstemmed | Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller |
| title_short | Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller |
| title_sort | robust position control of a two sided 1 dof impacting mechanical oscillator subject to an external persistent disturbance by means of a state feedback controller |
| url | http://dx.doi.org/10.1155/2019/9174284 |
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