ℋ∞ optimization of an enhanced force feedback controller for mitigation of nonlinear vibrations

In this paper, a nonlinear active damping strategy based on force feedback is proposed, where only the modal stiffness ratio of the system when the actuator is installed and removed is required to design an effective controller. Closed-form expressions are derived using the ℋ∞ optimization criterion wherein the optimal feedback gains are achieved to minimize the maximal response of the structure. The resonant vibration of a Duffing oscillator is considered to illustrate the proposed tuning of the optimal control gain and the harmonic balance method is employed to approximate the analytical solutions. It is shown that the amplitude of the resonance peaks does not change substantially when the weight of the nonlinearity increases, which means that the response of the coupled system is almost proportional to the forcing amplitude, as it would be the case for a linear system.