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Abstract This manuscript presents connect a Proportional-Derivative (PD) controller with a macro-fiber composite (MFC) laminated shell system. Nonlinear equations of the MFC laminated shell have been established. The simultaneous resonance case Ω 1 ≅ ω 1 ≅ ω 2 considered as worst resonance. The main motivation of this research is applying a suitable vibration control to reduce or diminish the high vibration caused by the model. So, we used here PD controller in controlling the behavior MFC laminated shell structure. The goal of using the PD controller is to increase the system stability by improving control since it has an ability to predict the future error of the framework response. This control method makes stability increased, maximum peak overshoot decreased, settling time decreases. This controller is applied to recover the framework transient response. A second-order approximate solution has gained via applying multiple time scale perturbation (MTSP) technique. Every expected resonance case at this approximation order is extracted. After adding the PD-controller of the current framework, it eliminates the vibration amplitudes of the considered structure. Frequency (angular speed) response curves examined at special uncontrolled and controlled coefficients of the system. Finally, the conclusion shows a high efficiency of the measured control algorithm for eliminating vibrations of the modified system. A comparison between other approaches control algorithms had been prepared. The results are compared with the numerical simulations, and this shows a good verification for the approximate solution and for the control algorithm used in this manuscript. A comparison with earlier available papers is involved at the end.
Bauomy et al. (2020) studied this question.