Active control of a Vertical Conveyor System via Negative cubic velocity feedback through Simultaneous resonance

Document Type : Original Article

Authors

1 Department of Basic Sciences, Higher Technological Institute, 10th of Ramadan City, Egypt

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

3 Basic sciences department, Modern Academy

Abstract

In this paper, we concentrate on using active control to a nonlinear dynamical conveyor system to reduce its vibration. The mathematical solution of the nonlinear differential equations which describing the up system is studied by applying the multiple time scales method (MTSM). All resonance cases are obtained from second-order approximations. The stability analysis according to the Routh-Hurwitz criterion is investigated utilizing frequency response equations at the considered simultaneous sub-harmonic and combined resonance case . Then, the behavior of the system is studied with and without controller numerically by using the Runge-Kutta fourth-order (RK-4) method (package ode45 in Matlab R2014a). The effects of most system parameters are studied. The results showed that the suggested controller is efficient to reduce the vibrations. The outcomes confirm that the mathematical solution of the system is in good agreement with the numerical solution. Finally, we are making a comparison with the previously available published work.

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