In this paper, the problem of the active vibration control of a thin and flexible disc is addressed. The mechanical structure tackled here is equipped with two piezoelectric circular patches: one of them works as a sensor and the other is used as an actuator. Both are fixed on the disc, one on each side, and centered according to its axis of symmetry. The model of this system is obtained from a finite element analysis, leading to a linear state space model. The design of the proposed control scheme is based on delayed proportional actions. As a matter of fact, recent works emphasized the stabilizing effect of delayed feedback if a real multiple spectral occurs in the closed-loop called multiplicity-induced-dominancy (MID) property allowing to an assignment approach. The purpose of this work is to investigate the properties of the proposed MID-based output feedback controller in terms of vibration damping.