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

This paper presents a method of controlling the bending and torsional vibration modes of a flexible plate structure (theoretically which has infinite number of vibration modes) using H_∞-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 and neglecting the all other high-frequency modes. These neglected modes constitute the unstructured uncertainties of the system and taken care of in the time of design process. An idea is proposed to reduce the unmodeled system uncertainties by placing actuators in the node points of a neglected mode. As a result, it is possible to avoid the spillover instability (avoid the influence of a neglected mode) without affecting the control of lower order modes. Then a static state feedback controller is designed based on the reduced order model and the approximate knowledge of unmodeled uncertainties. The efficacy of feedback controller is shown through simulation and experimental studies