Piezoelectric patch control using an integral equation approach

Closed-loop displacement feedback control for a beam using bonded piezoelectric patch sensors and actuators is considered. It is shown that there is an equivalence between the eigensolutions of the differential equation formulation of the problem and the eigensolutions of a certain integral equation. It is also shown that a pair of aligned oriented sensors and actuators generate an orthogonal set of eigenfunctions. The natural frequencies are found numerically for a cantilevered beam using the integral equation.