Internal Model Control of Cycloid Trajectory for Video-Rate AFM Imaging with a SOI-MEMS Nanopositioner

We demonstrate high-performance tracking of a cycloid trajectory for video-rate atomic force microscopy imaging by employing internal model control. To acquire sequential images using cycloid scanning, the stage needs to follow a slow periodic triangular wave superimposed on a sinusoidal signal along one axis with the remaining axis tracking a purely sinusoidal signal. The sharp turnarounds in the triangular signal result in a large tracking error. We utilize a trapezoidal signal to address this issue. To obtain high-precision positioning, the controller comprises the internal model of harmonic waveforms and the ramp signal plus additional integrator to compensate for stage nonlinearities. The controller is implemented on a two degree of freedom microelectromechanical system nanopositioner and operated at scan frequencies ranging from 500 Hz to 2580 Hz in a window size of 5 µm by 10 µm. While the pitch size of the trajectory is set to be 46 nm, the RMS value of tracking error remains below 7 nm. The highest scan rate of 20 frames per second is achieved at f =2580 Hz with the maximum transient tracking error of 15 nm.