A Preisach model for quantifying hysteresis in an atomic force microscope

Atomic force microscopes employ stacked or cylindrical piezoceramic actuators to achieve sub-angstrom resolution. While these devices produce excellent set-point accuracy, they exhibit hysteresis and constitutive nonlinearities even at low drive levels. Feedback mechanisms can mitigate the deleterious effects of these nonlinearities for low frequency operation but such techniques fail at higher frequencies due to increased noise to signal ratios. In this paper, we quantify the hysteresis and constitutive nonlinearities through a Preisach model. As illustrated through a comparison with experimental data, this provides a characterization which is sufficiently accurate for inclusion as an inverse compensator in various control designs.