Hybrid approach for deformable mirror online system identification using RLS algorithm and adaptive forgetting factor optimization.

In this study, an online system identification (SI) approach based on a recursive least squares algorithm with an adaptive forgetting factor (AFFRLS) is proposed to accurately identify the dynamic behavior of a deformable mirror (DM). Using AFFRLS, an adaptive expression that minimizes a weighted linear least squares cost function relating to the input and output signals is obtained. First, the selected identification signals in COMSOL multi-physics software were applied to the finite element (FE) model of the DM.

Calculation of the modified control matrix for a selected unimorph deformable mirror to compensate the piezoelectric hysteresis effect using the inverse Bouc-Wen model.

The hysteresis behavior of piezoelectric actuators degrades the positioning accuracy and bandwidth of nano-positioning systems. Therefore, considering the hysteresis of piezoelectric deformable mirrors is completely essential and also improves the modeling accuracy of adaptive optics layouts. Because of the unique adaptability and mathematical flexibility of the Bouc-Wen model it has gained popularity, and as a result, in many scientific applications, it is one of the most conventional models typically employed to describe nonlinear hysteretic systems.