E.G.O. Nóbrega).performance and robustness for controlled systems. However, SHM and AVC methods are independently designed in general, despite the fact that damage may significantly affect the AVC performance. Aiming to overcome the controller performance decline due to damage, this paper presents a framework to design damage-tolerant active controllers for noncollocated flexible structures, based on a novel double-loop modal controller, which may be adaptively reconfigured in real time. The proposed methodology is inserted into a wide multidisciplinary, involving concepts of AVC, modal control, fault-tolerant control, adaptive control, and SHM, in order to mitigate structural damage effects.The integration between SHM and vibration control techniques has been receiving considerable attention in recent decades [10][11][12][13]. Initially, SHM and control techniques were integrated only in the design phase, with the respective strategy consisting in the simultaneous design of the SHM and control modules [14][15][16]. These two subsystems were independently operated in the beginning and then, responding to challenges in the civil engineering area, progress has been made in improving the integration approach. New semi-active controllers have been proposed based on magneto-rheological dampers, using the output of the SHM module to update the respective controller parameters [17][18][19][20]. However, the increasing demands of larger and lightweight structures with high structural performance lead to the evolution of AVC methods and applications. Despite semi-active controllers intrinsic stability, which represents an advantage for several cases, AVC strategies provide better performance than the passive and the semi-active approaches in structural vibration control [21,22]. After almost two decades of research, the integration of the SHM and the AVC approaches is still a challenge, and regular AVC methods rarely consider, as a design requirement, damage effect mitigation in structural vibrations.Damage-tolerant active control (DTAC) is a recent research area that has intersections with both fault-tolerant control (FTC) and AVC areas. Specific fault detection and isolation techniques are used by fault-tolerant controllers to provide online parameter adaptation aiming to maintain an adequate performance for controlled systems [23][24][25]. In the same way, DTAC methods use SHM to design controllers presenting damage-tolerant performance. DTAC methods may be considered an extension of FTC, focusing fundamentally on structural vibration control and aiming to expand the applicability of modern smart structures. However, adapting FTC methods to face damage-induced vibration in flexible structures leads to new challenges. The infinite number of structural vibration modes, which constitutes the beginning of the DTAC research area, demands a controller robustness that is complicated by the dynamic changes due to damage perturbation [3]. The literature regarding vibration control of structures subject to damage is limited. Cha...