Decentralized resonant controller for vibroacoustic active control

The problem addressed in this paper concerns the stability of decentralized resonant controller (DRC) for the disturbance rejection of a harmonic vibration disturbance. A resonant controller is presented within the formalism of the complex envelope. It is shown that the problem of stability only concerns the frequency responses at the disturbance frequency: a necessary condition of stability is to have the matrix of transfer functions Hurwitz stable at the disturbance frequency. To illustrate this condition, simulations and experimental results are presented in the case of a simply-supported panel with collocated actuator-sensor pairs.