A modal H∞-norm-based performance requirement for damage-tolerant active controller design

Damage-tolerant active control (DTAC) is a recent research area that encompasses control design methodologies resulting from the application of fault-tolerant control methods to vibration control of structures subject to damage. The possibility of damage occurrence is not usually considered in the active vibration control design requirements. Damage changes the structure dynamics, which may produce unexpected modal behavior of the closed-loop system, usually not anticipated by the controller design approaches. A modal H∞ norm and a respective robust controller design framework were recently introduced, and this method is here extended to face a new DTAC strategy implementation. Considering that damage affects each vibration mode differently, this paper adopts the modal H∞ norm to include damage as a design requirement. The basic idea is to create an appropriate energy distribution over the frequency range of interest and respective vibration modes, guaranteeing robustness, damage tolerance, and adequate overall performance, taking into account that it is common to have previous knowledge of the structure regions where damage may occur during its operational life. For this purpose, a structural health monitoring technique is applied to evaluate modal modifications caused by damage. This information is used to create modal weighing matrices, conducting to the modal H∞ controller design. Finite element models are adopted for a case study structure, including different damage severities, in order to validate the proposed control strategy. Results show the effectiveness of the proposed methodology with respect to damage tolerance.