Optimal placement of piezoelectric sensor/actuator pairs for vibration control of composite plates

Abstract

The optimal placement of piezoelectric sensor/actuator (S/A) pairs to maximize the damping effect of a composite plate under a classical control framework using the finite element approach is investigated. Due to the discretization of the spatial domain, the problem falls under the class of discrete optimization. Two optimization performance indices based on modal and system controllability are adopted. The classical direct pattern search method is employed to obtain local optima. It is proposed that the starting point for the pattern search be selected based on the maxima of integrated principal strains consistent with the size of piezoelectric patches used, which would maximize the virtual work done by the equivalent actuation forces along the corresponding mechanical displacements. In this way, the global optimal placement can be efficiently deduced. Numerical simulation using a cantilever composite plate under free vibration shows that the proposed strategy to locate the optimal placement is practical and efficient, with results very close to the global optimal layout from exhaustive search. The speed of convergence is rapid compared to an initial blind discrete pattern search approach. For the specific example used, the S/A pairs positioned close to the support are most effective whereas those near the free end are the least effective, for the first two modes. S/A pairs placed furthest from the centre line of the cantilever plate are most effective for torsional vibration control. These findings are in good agreement with the published results.