Efficient compensation of nonlinear transfer characteristics for piezoceramic actuators

In order to compensate for hysteresis errors in tracking and manipulation tasks, models describing the piezoceramic actuator nonlinearities are required. These models have to meet the following two criteria: (i) Efficiency and (ii) a bidirectional description of hysteresis phenomena. Due to its flexibility and efficiency, the Preisach operator is a promising tool to model transfer behavior of ferroelectric actuators in forward direction. However, the model cannot be inverted analytically. The scope of this contribution is therefore to introduce a novel, efficient algorithm for the numerical inversion of the Preisach operator. The algorithm is characterized as well as applied to linearize the voltage-deflection hysteresis of trimorph bending actuators. It is shown that independent of the model discretization, a maximum sampling frequency of 6.5 kHz is allowed for the proposed numerical inversion scheme. As result of this fast inversion technique, the Preisach model becomes interesting for real-time hysteresis compensation tasks. It shows to be competitive to other hysteresis models which are directly invertible, such as the Prandtl-Ishlinskii hysteresis operator.