Tracking of triangular or sawtooth waveforms is a major difficulty for achieving high-speed operation in many scanning applications such as scanning probe microscopy. Such non-smooth waveforms contain high order harmonics of the scan frequency that can excite mechanical resonant modes of the positioning system, limiting the scan range and bandwidth. Hence, fast raster scanning often leads to image distortion. This paper proposes analysis and design methodologies for a nonlinear and smooth closed curve, known as Lissajous pattern, which allows much faster operations compared to the ordinary scan patterns. A simple closed-form measure is formulated for the image resolution of the Lissajous pattern. This enables us to systematically determine the scan parameters. Using internal model controllers (IMC), this non-raster scan method is implemented on a commercial atomic force microscope driven by a low resonance frequency positioning stage. To reduce the tracking errors due to actuator nonlinearities, higher order harmonic oscillators are included in the IMC controllers. This results in significant improvement compared to the traditional IMC method. It is shown that the proposed IMC controller achieves much better tracking performances compared to integral controllers when the noise rejection performances is a concern.

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Abstract-Raster scanning is common in atomic force microscopy (AFM). The nonsmooth raster waveform contains highfrequency content that can excite mechanical resonances of an AFM nanopositioner during a fast scan, causing severe distortions in the resulting image. The mainstream approach to avoid scan-induced vibrations in video-rate AFM is to employ a highbandwidth nanopositioner with the first lateral resonance frequency above 20 kHz. In this paper, video-rate scanning on a nanopositioner with 11.3-kHz resonance frequency is reported using a smooth Lissajous scan pattern. The Lissajous trajectory is constructed by tracking two sinusoidal waveforms on the lateral axes of the nanopositioner. By combining an analog integral resonant controller (IRC) with an internal model controller, 1-and 2-kHz single tone set-points were successfully tracked. Highquality time lapsed AFM images of a calibration grating recorded at 9 and 18 frames/s without noticeable image distortions are reported.Index Terms-Atomic force microscopy, flexure-based, integral resonant control, internal model control, Lissajous-scan, nonraster scanning, video-rate.

Abstract-In this paper, we design feedback controllers for lateral and transversal axes of an atomic force microscope (AFM) piezoelectric tube scanner. The controllers are constrained to keep the standard deviation of the measurement noise fed back to the displacement output around 0.13 nm. It is shown that the incorporation of appropriate inner loops provides disturbance rejection capabilities and robustness against dc gain uncertainties, two requirements for satisfactory operation of signal transformation method. Simulations and experiments show significant improvement of steady-state tracking error with signal transformation, while limiting the projected measurement noise.

Mohammad Maroufi received the B.Sc. degrees in mechanical engineering and applied physics and the M.Sc. degree in mechatronics from the Amirkabir University of Technology, Tehran, Iran, in 2008 and 2011, respectively. He is currently pursuing the Ph.D. degree in electrical engineering with the University of Newcastle, Callaghan, NSW, Australia.His current research interests include design and control of MEMS nanopositioning systems, MEMSbased sensing and actuation, on-chip atomic force microscopy, and mechanical modeling of smart materials and structures.Ali Bazaei (M'10) received the B.Sc. and M.Sc. . His current research interests include nonlinear systems, including control and modeling of structurally flexible systems, friction modeling and compensation, neural networks, and microposition sensors.