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Piezoelectric optimal delayed feedback control for nonlinear vibration of beams

An optimal delayed feedback control methodology is developed to mitigate the primary and super harmonic resonances of a flexible simply-simply supported beam with piezoelectric sensor and actuator. Stable vibratory regions of the feedback gains are obtained by using the stability conditions of eigenvalue equation. Attenuation ratio is used to evaluate the performance of vibration control by taking the proportion of peak amplitude of primary or super harmonic resonances for the suspension system with and without controllers. Optimal control parameters are obtained using an optimal method, which takes attenuation ratio as the objective function and the stable vibratory regions of the time delay and feedback gains as constraint conditions. The piezoelectric optimal controllers are designed to control the dynamic behaviour of the nonlinear dynamic system. It is found that the optimal feedback gains obtained by the optimal method result in a good control performance.