101. Nonlinear analysis of vertical conveyor with positive position feedback (PPF) controllers
- Author
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A. T. EL-Sayed and H. S. Bauomy
- Subjects
Physics ,Frequency response ,Applied Mathematics ,Mechanical Engineering ,Mathematical analysis ,Positive position feedback ,Aerospace Engineering ,Perturbation (astronomy) ,Ocean Engineering ,02 engineering and technology ,01 natural sciences ,Omega ,Nonlinear system ,020303 mechanical engineering & transports ,0203 mechanical engineering ,Control and Systems Engineering ,Control theory ,0103 physical sciences ,Internal resonance ,Primary resonance ,Electrical and Electronic Engineering ,010301 acoustics ,Multiple-scale analysis - 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.
- Published
- 2015
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