الفهرس 
Chapter 2: Mathematical AnalysisOnly 14 pages are availabe for public view
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Abstract
The main objective of this thesis is a mathematical study for the mechanical vibrations of a magnetic levitation dynamical system described by a nonlinear ordinary differential equation. Some forms of active conventional control techniques have been applied to suppress such vibrations. Then, we have applied the multiple scales perturbation technique (MSPT) to solve those nonlinear equations. The corresponding frequency response equations have been extracted and presented graphically at different system parameters. The obtained graphs have been confirmed numerically applying Rung-Kutta algorithm of fourth order using MATLAB 7.5. The deduced results have been summarized and a comparison of the different control methods is presented. Another comparison with the previously published related work is reported. Finally, a list of references is cited. The thesis consists of four chapters as follows: The first chapter is concerned with introducing the background necessary to understand the mechanical vibration problem, some of the important researches that dealt with the nonlinear vibrations of the magnetic levitation system, the thesis objectives, and the thesis organization. A mathematical study for the magnetic levitation system subjected to different control techniques is presented in chapter two. The autonomous amplitude phase modulating equations were extracted applying MSPT. Then, the corresponding frequency response equations have been deduced. The third Chapter is devoted to present the results by plotting the frequency response equations given at chapter two. Also the discussion of each control case is presented. In chapter four, the most important results have been concluded and a comparison of the different control methods is presented. Another comparison with the previously published related work is reported, and then the recommendations for the open research directions are given.