Controllability assessment of plate-like structures with uncertainties under piezoelectric actuation

A controllability assessment of plate-like structures with uncertainties under piezoelectric actuation is performed in this paper. Different from the previous studies, a novel index is proposed to quantify the degree of controllability using the sensor/actuator transfer function. Influences of unmodelled high-frequency dynamics and structural parameter variations on controllability are discussed, and the relationship between the indices for the nominal and uncertain cases is derived. In order to validate the controllability assessment numerically, the modelling of a plate with piezoelectric actuation is developed with the consideration of the full coupling between the PZT actuators and the host plate, and verified by experiments. It is demonstrated that a proper design of the polyvinylidene flouride sensor would help eliminate effects of higher order modes on the basis of strain mode shapes. Since the latter is very sensitive to the mass and stiffness added by PZT actuators, the dynamics of PZT actuators must be taken into account during the design, as opposed to the case where a point transducer is used.