Bending and torsional vibration control of a flexible plate structure using H-infinity-based robust control law

This paper presents a method of controlling the bending and torsional vibra tion modes of a flexible plate structure (theoretically which has infinite number of vibration modes) using H-infinity-based robust control. For this purpose, a three degree of freedom (DOF) reduced order lumped mass model of a plate 'structure is derived by considering first three vibration modes a nd neglecting the all other high-frequency modes. These neglected modes con stitute the unstructured uncertainties of the system and taken care of in t he time of design process. An idea is proposed to reduce the unmodeled syst em uncertainties by placing actuators in the node points of a neglected mod e. As a result, it is possible to avoid the spillover instability (avoid th e influence of a neglected mode) without affecting the control of lower ord er modes. Then a static state feedback controller is designed based on the reduced order model and the approximate knowledge of unmodeled uncertaintie s. The efficacy of feedback controller is shown through simulation and expe rimental studies.