Nonlinear positive position feedback control for mitigation of nonlinear vibrations. (1st October 2019) - Zhao, G.; Paknejad, A.; Raze, G.; Deraemaeker, A.; Kerschen, G.; Collette, C.
Highlights: Linear and nonlinear positive position feedback controllers are investigated. Closed-form expressions of the optimal parameters of the controllers are obtained. The nonlinear controller outperforms its linear counterpart for a Duffing oscillator. The analytical study is validated experimentally. 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.