A novel control design for high-speed Atomic Force Microscopy*

In this paper, we propose a novel transform-based imaging mode for Atomic Force Microscopy (AFM), where the cantilever oscillations are made to track the output of a mockmodel system. The states of the resulting tracking error dynamics is appended by another set of suitably designed states, which enable a specific time-varying coordinate transformation, which in turn results in dynamic models that are very conducive to linear control synthesis design methods. The proposed imaging mode enables higher throughput in AFM imaging without the need for significantly high resonant frequency AFM cantilever probes. This method overcomes the fundamental limitation of nonlinear input-output relationship in Amplitude Modulation AFM (AM-AFM) imaging mode by applying an appropriately chosen real-time transform on the output signal. In combination with model-based reference generation, the proposed real-time transform yields linear dynamical input-output characteristics. Simulations on detailed AFM models with ${\mathcal{H}_\infty }$ optimal control designs show the efficacy of the proposed imaging mode for feature bandwidths higher than 5% of the cantilever resonant frequency.