Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2006/842318 |
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| _version_ | 1850221909954789376 |
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| author | A.F. EL-Bassiouny |
| author_facet | A.F. EL-Bassiouny |
| author_sort | A.F. EL-Bassiouny |
| collection | DOAJ |
| description | Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations. |
| format | Article |
| id | doaj-art-719d954ea3df4e30b2a1a66eb7aaea42 |
| institution | OA Journals |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-719d954ea3df4e30b2a1a66eb7aaea422025-08-20T02:06:32ZengWileyShock and Vibration1070-96221875-92032006-01-01132658310.1155/2006/842318Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State FeedbackA.F. EL-Bassiouny0Department of Mathematics, Faculty of Science, Benha University, Benha 13518, EgyptTime delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.http://dx.doi.org/10.1155/2006/842318 |
| spellingShingle | A.F. EL-Bassiouny Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback Shock and Vibration |
| title | Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback |
| title_full | Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback |
| title_fullStr | Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback |
| title_full_unstemmed | Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback |
| title_short | Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback |
| title_sort | fundamental and subharmonic resonances of harmonically oscillation with time delay state feedback |
| url | http://dx.doi.org/10.1155/2006/842318 |
| work_keys_str_mv | AT afelbassiouny fundamentalandsubharmonicresonancesofharmonicallyoscillationwithtimedelaystatefeedback |