Abstract
Proportional–derivative (PD) controller is applied in this work to study the effects of time delay on its performance for reducing the oscillations of a rotating beam at varying speed. The dual-system vibrational modes are linearly coupled so we have applied the controller to only one mode and the other coupled mode tracks it. The worst resonance cases—verified numerically—in this paper are the primary and the principal parametric resonance cases that should be controlled. The overall nonlinear behavior of the system with and without control is investigated through the remarkable multiple time scales method. Different response curves are involved to investigate controller effect.
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