Active Vibration Control of a Rectangular Flexible Wall of an Empty and Fluid-Filled Tank

A rectangular plate bolted to a thick Plexiglas rectangular container is investigated in the case of empty and water-filled tank. A modal analysis is firstly realized in order to verify the effects of different water levels and of the free surface waves on the modal parameters and on the modal shapes. A filtered-x LMS (least mean square) adaptive feedforward algorithm is then applied to the perturbed system realizing structural vibration control in linear field with a SISO approach. Five piezoelectric PZT actuators apply the secondary control input in a nearly-collocated configuration. Their positioning is based on the knowledge on the deformation energy of the plate. The present study investigates primarily the control of the first vibration mode, but second and third modes are also experimentally studied. Satisfactory reductions (up to about 45 dB on the second mode measured on Channel 4) are reached for vibration amplitude of the three modes investigated in absence of water. For each modal shape, a particular effectiveness of the optimally placed actuators clearly appears. The introduction of water in the tank reduces the effectiveness of control of the first mode (maximum 5.5 dB of reduction of the vibration amplitude), but the five control channels show a more global uniform effectiveness.