Robust vibration control of uncertain flexible structures with poles placement

This paper develops linear fractional representations for uncertain flexible structures with non-collocated piezoelectric actuators and sensors in the modal space, taking into account uncertainties due to modal parameters variation and un-modeled residual high-frequency modes. Using linear matrix inequality, a dynamic output feedback controller is designed to suppress the vibration due to external disturbances by setting an upper bound on H-infinity norm from the disturbances to given performance outputs. In order to achieve a specified decay rate and damping ratio in all controlled modes, and achieve the desired dynamic response, closed-loop poles of the uncertain system are placed in the desired region. Finally, robust H-infinity method with uncertain poles assignment is compared with robust H-infinity method by a simple example. The simulation results show that, without obviously scarifying state-steady characteristics of the system, excellent dynamic response can be obtained by considering uncertain poles assignment in robust H-infinity vibration control.