Coupled dynamic reaction force study of a large-aperture piezoelectric fast steering mirror

The reaction force of a large-aperture piezoelectric fast steering mirror (PFSM) has adverse coupling interference for the stability and pointing accuracy of laser beams, and the dynamic characteristics of the reaction force are coupled with the inner components of the PFSM. In order to compensate for and eliminate the reaction force, it is essential to accurately analyze the dynamic characteristics. In this paper, a simplified piezoelectric-coupling model of PFSM is established. The coupling mathematical equations for investigating the characteristics of the reaction force are deducted based on the piezoelectric constitutive equation and Hamiltonian's principle. Then the coupling characteristics of the reaction force are probed by a finite element (FE) piezoelectric-coupling method. The simulations for three large apertures' (250, 320, and 400 mm) FE models show that the reaction force has a linear positive correlation with the actuating voltage, and coupled with the materials of the central flexure hinge, the relationship between the reaction force and driving frequency is not completely quadratic. Experiments with the 320 mm aperture are completed, and the testing results are consistent with the mathematical model and the FE piezoelectric-coupling simulation. The dynamic characteristics of the reaction force demonstrated in this paper are significance for the accurate estimation of the reaction force, the design of compensation structure, and the optimization of algorithm for beam jitter controlling.