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Optimization of actuator placement and hybrid controller design in flexible plates using PZT actuators

The objective of this investigation is to present a computational scheme for the optimal placement of actuating devices in flexible plates that utilize piezoceramic patches as actuators. In addition to controllability criteria, the candidate locations are required to also exhibit robustness with respect to the spatial distribution of disturbances. These PZT actuators are bonded at optimal locations that are determined by statically minimizing the optimal value of a disturbance-to-output transfer function with respect to the worst distribution of disturbances. Once the optimal actuator locations are determined, that in addition to performance specifications also satisfy a spatial robustness criterion, a suitable LQR-based controller is designed. At a given interval of time, only one PZT is activated and the remaining ones are kept dormant. The rationale of actuator/controller switching is to demonstrate the better vibration alleviation characteristics of switching between actuators over the use of a single actuator that is always in continuous use. The optimality of switching is made with respect to a cost-to-go performance index that corresponds to each actuating device. Extensive computer simulations with repeatable spatiotemporally varying disturbance profiles, reveal that this algorithm offers better performance over the non-switched case.