H∞ optimization of positive position feedback control for mitigation of nonlinear vibrations

This paper investigates the potential of using positive position feedback control for the mitigation of nonlinear vibrations. Closed form expressions for the H 8 optimal control parameters that minimize the maximal response of the structure are firstly derived for the linear case and then extended to the nonlinear case. The resonant vibration of a Duffing oscillator is considered to illustrate the proposed tuning of the optimal control parameters and the harmonic balance method is employed to approximate the analytical solutions. Numerical simulations are performed to demonstrate and validate the proposed method