Mixed sensitivity H∞ design for vibration control of piezoelectric smart beam

In this paper, the mixed sensitivity H-infinity designs methods for the smart beam structures bonded with piezoelectric materials are studied. First, the advances in the vibration control for the smart structures are summarized and the spillover mechanism on the system is analyzed. Then basing on these analyses, the mixed sensitivity H-infinity design methods are presented to overcome the spillover problems. From the point of engineering, the selection of the weighting functions is discussed. A LQR controller and a H-infinity controller are designed simultaneously for a smart beam structure, the simulation results display that H-infinity controller not only overcome the spillover problems occurred by LQR control but also obtain satisfied vibration suppression performance. So the mixed sensitivity H-infinity design method is a good robust design method for the vibration control of smart structures.