Hysteresis Modeling and Compensation of Fast Steering Mirrors with Hysteresis Operator Based Back Propagation Neural Networks

Fast steering mirrors (FSMs), driven by piezoelectric ceramics, are usually used as actuators for high-precision beam control. A FSM generally contains four ceramics that are distributed in a crisscross pattern. The cooperative movement of the two ceramics along one radial direction generates the deflection of the FSM in the same orientation. Unlike the hysteresis nonlinearity of a single piezoelectric ceramic, which is symmetric or asymmetric, the FSM exhibits complex hysteresis characteristics. In this paper, a systematic way of modeling the hysteresis nonlinearity of FSMs is proposed using a Madelung's rules based symmetric hysteresis operator with a cascaded neural network. The hysteresis operator provides a basic hysteresis motion for the FSM. The neural network modifies the basic hysteresis motion to accurately describe the hysteresis nonlinearity of FSMs. The wiping-out and congruency properties of the proposed method are also analyzed. Moreover, the inverse hysteresis model is constructed to reduce the hysteresis nonlinearity of FSMs. The effectiveness of the presented model is validated by experimental results.