Vibrations control of a suspended cable via PPF controller.

Document Type : Original Article

Authors

1 Mathematics department, Faculty of Science, Zagazig University

2 Basic sciences department, Modern Academy

3 Basic sciences department, Higher Technological Institute, Tenth of Ramadan City

Abstract

One of the important types of control to vibrating systems is the PPF, which, described by a single degree of freedom system that, its frequency tuned to one of the structural frequencies.
In our consideration, we derived the equations of motion of the suspended cable. To obtain the approximate solution up to the first approximation, we applied the multiple scale method. The positive position feedback controllers (PPF) used for minimizing vibrations of the suspended cable under external and parametric forces. The worst resonance case is simultaneous resonance case (one-to-one internal and primary) is studied to get the response of the non-linear system. The equations of frequency response are in use to investigate the stability of the obtained solution. Numerically, we used Matlab (R2014a) take out the solution of the system. We investigated all different parameters effectiveness of the suspended cable. The influence of some chosen coefficient is illustrated numerically and analytically. The rapprochement between numeric and analytic solution is offered.

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