Abstract
This paper investigates the potential of using a nonlinear positive position feedback controller for vibration mitigation of a Duffing oscillator. The proposed controller is designed based on the principle of similarity which states that anti-vibration devices should be governed by the same equations as those of the host structure. Closed-form expressions for the H∞ optimal control parameters that minimise the maximal response of the structure are firstly derived for the linear positive position feedback controller and then extended to the nonlinear counterpart. The harmonic balance method is employed to approximate the analytical solutions. Both numerical simulations and experimental validations are performed to demonstrate the proposed control strategy.
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