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Nonlinear Dynamics

, Volume 83, Issue 1–2, pp 919–939 | Cite as

Nonlinear analysis of vertical conveyor with positive position feedback (PPF) controllers

  • A. T. EL-Sayed
  • H. S. Bauomy
Original Paper

Abstract

In this paper, the two positive position feedback controllers (PPF) are used to reduce the vertical vibration in the vertical conveyors. An investigation is presented of the response of a four-degree-of-freedom system (4-DOF) with cubic nonlinearities and external excitations at primary resonance \((\Omega _1 \cong \omega _1 ,\Omega _2 \cong \omega _2)\) in the presence of 1:1 internal resonance \((\omega _3 \cong \omega _1 ,\omega _4 \cong \omega _2)\). Method of multiple scales is applied to the equations of the system to find approximate analytical solutions. Then, we derived the frequency response equation and the stability criteria for the system. Numerical solution show that the time histories of the main system and the PPF controllers to present the response with and without control. The frequency response curves for the system and the controllers are studied numerically. To discuss the validity of the results, we make comparison between the analytical and numerical solutions and also compared them with the available published work.

Keywords

Vertical conveyor Perturbation Simultaneous resonances PPF control Stability 

Notes

Acknowledgments

The authors greatly appreciate the comments of referees and suggestions for improving the quality of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Basic SciencesModern Academy for Engineering and TechnologyMaadiEgypt
  2. 2.Department of Mathematics, Faculty of ScienceZagazig UniversityZagazigEgypt
  3. 3.Department of Mathematics, College of Arts and Science in Wadi AddawasirPrince Sattam Bin Abdulaziz UniversityWadi AddawasirSaudi Arabia

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