Fault Detection and Isolation (FDI) techniques have captured extensive interest and attention in modern autonomous systems; in particular, they are of foremost importance in space applications, due to their scientific relevance, cost and current inability of doing on-orbit maintenance of space systems. In this scenario, FDI strategies are required to counteract possible failure events that, if not properly handled, can reduce system performance or compromise the realization of the mission objectives. In this paper, a model-based FDI strategy is implemented onboard a satellite equipped with a very large mesh reflector on which a distributed network of smart actuators/sensors is mounted to actively counteract undesired elastic vibrations. In particular, the detection and isolation of a possible piezo-actuator failure occurring in the Active Vibration Control (AVC) system of the antenna is addressed by a bank of Unknown Input Observers (UIOs). The design of the proposed UIOs is derived by solving a Linear Matrix Inequality (LMI) problem, which provides the conditions for their existence, and it is based on the linearized 3D state-space model of the controlled spacecraft, under the assumption that all the uncertainties, exogenous disturbances and measurement noises are neglected. Furthermore, pole assignment in the sense of D-stability is integrated in the standard formulation of the UIO to guarantee an adequate transient behaviour of the observers. Finally, an extensive Monte Carlo simulation campaign is conducted to assess the effectiveness of the proposed FDI architecture and its robustness against modelling uncertainties and measurement noise.