Optimal control design of a bimorph optical beam deflector

The optical beam deflector is composed of two piezoelectric layers, one sandwiched brass layer in the middle with both ends clamped and a mirror attached to the upper surface of the top piezoelectric layer in the central position. This structure is designed to deflect the mirror to a certain angular position by applying external voltage supply to piezo-layers. This study proposes an optimal angular position control scheme of the attached mirror. The governing partial differential equations are first derived for the ensuing analysis and control design, which is followed by the establishment of finite element model in ten nodes specified at some longitudinal points of the optical beam deflector. In order to achieve a faster convergent rate for the deflector to reach the desired angular position, the optimal control of LQ regulator with final states fixed is employed to explore the possibility of shorter transient response and less cost of control effort and states. The optimal feedback control is obtained based on solving a dynamic Riccati equation backward in time. The numerical simulation results are finally provided to validate the theoretical control design.