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

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt.

2 Department of Basic Sciences, Modern Academy for Engineering and Technology, Maadi, Egypt

3 Department of Mathematics, Faculty of Science(Girls), Al-Azhar University, Nasr City, Egypt

4 Department 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
 

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