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Modified bang-bang piezoelectric control of vibrating beams

The converse piezoelectric effect is used to suppress the vibrations of a beam stiffened with piezoceramic actuators. The control problem involves the minimization of the dynamic response of the beam by using the voltage applied to the piezoactuators as a control variable. The dynamic response is defined as the vibrational energy of the beam, which is used as the cost functional of the control problem. The piezoactuators are bonded on the opposite surfaces of the beam and placed symmetrically with respect to the middle plane. The control moments are activated by applying out-of-phase voltages. The control voltage is subject to a maximum value constraint and is defined as a modified bang-bang type which can take this voltage as a plus or minus value as well as the zero value. It is found that the optimal active control takes the form of a piecewise constant alternating voltage with varying switch-over intervals.