A dynamic modal $$H_{2}$$ output-feedback approach applied to damage-tolerant active control of smart flexible structures

Abstract This paper presents a novel modal control technique for active vibration control of smart flexible structures subjected to damage. Damage causes different dynamic effects in each vibration mode, which can be exacerbated in a structure under regular active control. However, if the attenuation of the most affected modes is appropriately incorporated into the control system design, performance loss and instability can be avoided. For this purpose, a new $$H_2$$ modal norm is introduced, enabling an effective control design that ensures unique modal selectivity, focusing on the energy weighting of the specific vibration modes affected by the response to structural damage. This modal norm is applied to design modal $$H_2$$ controllers based on a linear matrix inequality approach. A finite element software models a case study structure with multiple and noncollocated piezoelectric transducers, including different damage severities that simulate three progressive crack sizes. Tests compare the performance of modal and regular $$H_2$$ strategies concerning vibration attenuation for healthy and damaged structure conditions. Results show the effectiveness of the proposed modal $$H_2$$ approach over the regular $$H_2$$ approach for active vibration control due to an efficient modal control energy distribution, even when the structure is under damage occurrence.