This research involves the application of methods to actively control the vibrations of an experiment rack shelf. The rack shelf is constructed from a solid rectangular plate restrained along segments of the short sides and is designed to be similar to the experiment rack shelves used in the International Space Station (ISS). Those shelves are subject to vibrations that may adversely affect experiments. Piezoelectric actuators have been proposed as a solution for controlling the rack shelf vibrations. In this work, a two-dimensional asymmetric piezoelectric actuator model is developed first. Then, a Ritz expansion method is employed to derive the Equations of Motion for the active structure with discontinuous boundary conditions. Modal parameters from this analytical solution as well as from experiment modal analysis are used to determine the modal input factors for the piezoelectric actuators. Two control strategies, modal control and collocated output feedback control, are studied with Linear Quadratic Gaussian (LQG) control law. Experimental results show the effectiveness of the proposed control concepts in controlling the first two flexural vibration modes at frequencies below 400 Hz.

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