Identification, control and hysteresis compensation of a 3 DOF metrological AFM

Atomic Force Microscopes (AFMs) are widely used for the investigation of samples at the nanometer scale. The metrological AFM used in this work uses a 3 degrees-of-freedom (DOFs) stage, driven by piezo-stack actuators, for sample manipulation in combination with a fixed cantilever. The piezo-stack actuators suffer from hysteresis, which acts as a nonlinear disturbance on the system and/or can change the system dynamics. The contributions of this paper are the application of feedback control to all 3 DOFs of the metrological AFM and the design and application of a hysteresis feedforward for the asymmetric hysteresis present in the system. The amount of coupling between the DOFs is assessed by a non-parametric multiple-input-multiple-output (MIMO) identification. Since the dynamics appear to be decoupled in the frequency range of interest, feedback controllers are designed for each DOF separately. For the modeling of the asymmetric hysteresis an extended Coleman-Hodgdon model is proposed. This model is used for feedforward compensation of the hysteresis. The combination of feedback control for all DOFs and the asymmetric hysteresis feedforward enables the AFM to track scanning profiles within the sensor bound of 5 nm. Real-time imaging of the sample is possible with an accuracy of 2 nm.