Optimal location of piezoceramic actuators for vibration suppression of a flexible structure

In this work, the problem of optimal placement of piezoceramic actuators along a flexible structure is considered. The design goal is to optimize the actuators' performance in vibration suppression of a beam cantilevered on one end to a rotating hub. First, the control problem is presented as an infinite-dimensional linear quadratic regulator problem. Then, an approximation framework based on a Legendre polynomials based Galerkin method for approximating the control system is developed. Two different approximate performance measures that are based on the LQR cost function are considered and numerical examples are presented to illustrate effectiveness of each measure.