Koopman operator models for self-reconfiguring vibration control and structural health monitoring

Active vibration control is widely implemented in flexible structural systems to maintain safe operating conditions under healthy states. Mechanical structures, however, are vulnerable to damage that alters mass, stiffness, or damping due to mechanisms such as cracks, delaminations, or loose connections. Such variations can significantly reduce the effectiveness of vibration control and may lead to system failure. Therefore, it is essential not only to monitor the system’s condition but also to update the control strategy to restore performance and re-establish the response characteristics of the undamaged state. This task is particularly challenging when relying solely on existing control instrumentation, which typically consists of a single actuator and sensor, and when the system’s physical properties change markedly before and after damage in both open- and closed-loop scenarios. This article introduces a novel approach that utilizes the Koopman operator to implement a real-time vibration control procedure with integrated structural health monitoring. The proposed method does not require prior knowledge of the structure’s physical model and can update the system representation online. Experimental validation is performed using a flexible cantilever beam equipped with three piezoelectric patches functioning as an actuator, a sensor, and a disturbance input. As a proof of concept, concentrated mass variations are introduced to simulate structural changes that affect the performance and reduce the effectiveness of vibration control. Different disturbance profiles are investigated, along with increasing mass removal. The results demonstrate that the proposed procedure can detect this structural variation, recompute the state-space model using the Koopman operator, update the controller, and ultimately enable self-reconfiguring behavior in the system.