VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER
Amer, Y., EL-Sayed, A., Saleh, A., Abdel-Wahab, A., Salman, H. (2019). VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER. EKB Journal Management System, 30(Issue 1-B), 9-26. doi: 10.21608/absb.2019.42891
Y. A. Amer; A. T. EL-Sayed; A. A. Saleh; A. M. Abdel-Wahab; Hala F. Salman. "VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER". EKB Journal Management System, 30, Issue 1-B, 2019, 9-26. doi: 10.21608/absb.2019.42891
Amer, Y., EL-Sayed, A., Saleh, A., Abdel-Wahab, A., Salman, H. (2019). 'VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER', EKB Journal Management System, 30(Issue 1-B), pp. 9-26. doi: 10.21608/absb.2019.42891
Amer, Y., EL-Sayed, A., Saleh, A., Abdel-Wahab, A., Salman, H. VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER. EKB Journal Management System, 2019; 30(Issue 1-B): 9-26. doi: 10.21608/absb.2019.42891

VIBRATIONS CONTROL OF THE HARMONICALLY EXCITED NONLINEAR SYSTEM VIA POSITIVE POSITION FEEDBACK CONTROLLER

Al-Azhar Bulletin of Science
Article 2, Volume 30, Issue 1-B, June 2019, Page 9-26  XML PDF (1002.43 K)
Document Type: Original Article
DOI: 10.21608/absb.2019.42891
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Authors
Y. A. Amer1; A. T. EL-Sayed2; A. A. Saleh3; A. M. Abdel-Wahab3; Hala F. Salman email 4
1Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.
2Department of Basic Sciences, Modern Academy for Engineering and Technology, Maadi, Egypt
3Department of Mathematics, Faculty of Science(Girls), Al-Azhar University, Nasr City, Egypt
4Department of Basic Sciences, Faculty of Computers and Information, Cairo University, Giza, Egypt
Abstract
In this paper, the vibration reducing of the harmonically excited nonlinear system is presented via applying positive position feedback controller (PPF). The analytical results are obtained by applying the multiple-scale perturbation techniques (MSPT) up to second-order approximations. The frequency response equation (FRE) is studied to test the be havior of the steady state solutions near the simultaneous resonances. The effects of the several parameters and the behavior of the system at resonance case are investigated to illustrate the optimum
working conditions for the PPF controller. The stabilit y analysis for the uncontrolled system is investigated by applying the phase portrait technique. Moreover, numerical simulation is used to compare between time-history and the analytical solution. The analytical and numerical solutions are compared to show the validity of the results. Finally, a comparison with the available results in the literature is presented
 
Keywords
Nonlinear system; Multiple scales method; Resonance; PPF controller; Stability, phase plane
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