Towards Integrated Design of a Robust Feedback Controller and Topography Estimator for Atomic Force Microscopy

In Atomic Force Microscopy (AFM), the force between the measurement tip and the sample is controlled in a feedback loop to prevent damage to the tip and sample during imaging, and to convert the measurement of the tip-sample force into an estimation of the sample topography. Dynamical uncertainties of the system pose a strong limitation on the achievable control bandwidth, and on the accuracy of the estimated topography. This contribution discusses an integrated approach to design a robust feedback controller and topography estimator, taking into account the dynamical uncertainties of the imaging system. It is shown that for a given AFM system there exist a direct trade-off between the closed-loop bandwidth and the guaranteed bounds on the topography estimation error due to the dynamic uncertainties in the system.