Abstract
This paper proposes a method for controlling the bending and torsional vibration of a flexible structure using Ha based optimal control. For this propose, we make a reduced order lumped mass model expressed by 3-DOF systems, considering the first three vibration modes and neglecting all the other high frequency modes. These neglected modes are regarded as unstructured uncertainties in the design stage. To prevent spillover instability caused by neglected mode, a modeling method based on the occurrence of uncontrollability and unobservability realized structurally at the nodes of the vibration modes is applied. Then, a static state feedback controller is designed based on the reduced order model and the approximate knowledge of the unmodeled uncertainties. The first three vibration modes of the flexible structure are controlled using a hybrid dynamic absorber. The discrete model and the controller design are verified through numerical simulations and experimental studies.
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