MONITORING AND CONTROL OF STRUCTURES SUBJECT TO VIBRATION AND DAMAGE USING THE KOOPMAN OPERATOR

Abstract

Due to the effects of fatigue and excessive vibration, structures may present a different health condition than initially observed. The change in system behavior due to damage also causes the system to demand more energy, which can saturate the actuators and make the system unstable. In this context, this work proposes to estimate in real-time the dynamics of a structure and control the undesired effects of vibration and damage. A data-driven model will be developed based on the Koopman operator, analyzing only data from sensors and actuators already installed by the control system. The information obtained by this updated model can be used to monitor changes in structural health and adapt a controller to meet performance specifications, even if the system dynamics vary over time. Changes in the spectral characteristics of the Koopman operator can help identify damage in the structure. In addition, an adaptive model predictive controller can incorporate the possible changes in dynamics in real time, adjusting the optimization problem according to the current estimated model. Therefore, our results have demonstrated the benefits and limitations of this online monitoring and control strategy based on data already measured by the controller. REFERENCES [1] N. Mechbal and E. G. O. Nóbrega, Damage tolerant active control: Concept and state of art. IFAC Proceedings Volumes, vol. 45, no. 20, pp. 63–71, 2012. [2] M. Korda and I. Mezić, Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control. Automatica, vol. 93, pp. 149–160, 2018.