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# Vibration Performance, Stability and Energy Transfer of Wind Turbine Tower via Pd Controller

Y. S. Hamed1, 2, *, Ayman A. Al3, 4, B. Sale3, 4, Ageel F. Alogla3, Awad M. Aljuaid3, Mosleh M. Alharthi0F5

1 Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, PO Box 888, Saudi Arabia.
2 Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, PO Box 32952, Egypt.
3 Department of Mechanical Engineering, College of Engineering, Taif University, Taif, PO Box 888, Saudi Arabia.
4 Department of Mechanical Engineering, Faculty of Engineering, Assiut University, Assiut, PO Box 71516, Egypt.
5 Department of Electrical Engineering, College of Engineering, Taif University, Taif, PO Box 888, Saudi Arabia.

* Corresponding Author: Y. S. Hamed. Email: .

Computers, Materials & Continua 2020, 64(2), 871-886. https://doi.org/10.32604/cmc.2020.08120

## Abstract

In this paper, we studied the vibration performance, energy transfer and stability of the offshore wind turbine tower system under mixed excitations. The method of multiple scales is utilized to calculate the approximate solutions of wind turbine system. The proportional-derivative controller was applied for reducing the oscillations of the controlled system. Adding the controller to single degree of freedom system equation is responsible for energy transfers in offshore wind turbine tower system. The steady state solution of stability at worst resonance cases is studied and examined. The offshore wind turbine system behavior was studied numerically at its different parameters values. Furthermore, the response and numerical results were obtained and discussed. The stability is also analyzed using technique of phase plane and equations of frequency response. In addition, the numerical results and comparison between analytical and numerical solutions were obtained with MAPLE and MATLAB algorithms.

## Keywords

APA Style
Hamed, Y.S., Al, A.A., Sale, B., Alogla, A.F., Aljuaid, A.M. et al. (2020). Vibration performance, stability and energy transfer of wind turbine tower via pd controller. Computers, Materials & Continua, 64(2), 871-886. https://doi.org/10.32604/cmc.2020.08120
Vancouver Style
Hamed YS, Al AA, Sale B, Alogla AF, Aljuaid AM, Alharthi0F MM. Vibration performance, stability and energy transfer of wind turbine tower via pd controller. Comput Mater Contin. 2020;64(2):871-886 https://doi.org/10.32604/cmc.2020.08120
IEEE Style
Y.S. Hamed, A.A. Al, B. Sale, A.F. Alogla, A.M. Aljuaid, and M.M. Alharthi0F "Vibration Performance, Stability and Energy Transfer of Wind Turbine Tower via Pd Controller," Comput. Mater. Contin., vol. 64, no. 2, pp. 871-886. 2020. https://doi.org/10.32604/cmc.2020.08120

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