Fractional Repetitive Control of Nanopositioning Stages for High-Speed Scanning Using Low-Pass FIR Variable Fractional Delay Filter

This work was supported by the National Natural Science Foundation of China under Grant 51975375, the Binks Trust Visiting Research Fellowship (2018) (University of Aberdeen, UK) awarded to Dr. Sumeet S. Aphale and the SJTU overseas study grant awarded to Linlin Li. The authors would like to thank Mr. Wulin Yan for his assistance with the experiments.Peer reviewedPostprin

High-bandwidth nanopositioning via active control of system resonance

Acknowledgements This work was supported in part by the National Natural Science Foundation of China (Grant Nos. U2013211 and 51975375), the Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems, China (Grant No. GZKF-202003), and the Binks Trust Visiting Research Fellowship (2018), University of Aberdeen, UK, awarded to Dr. Sumeet S. Aphale.Peer reviewedPublisher PD

Design and implementation of high-bandwidth, high-resolution imaging in atomic force microscopy

Video-rate imaging with subnanometer resolution without compromising on the scan range has been a long-awaited goal in Atomic Force Microscopy (AFM). The past decade saw significant advances in hardware used in atomic force microscopes, which further enable the feasibility of high-speed Atomic Force Microscopy. Control design in AFMs plays a vital role in realizing the achievable limits of the device hardware. Almost all AFMs in use today use Proportional-Integral-Derivative(PID) control designs, which can be majorly improved upon for performance and robustness. We address the problem of AFM control design through a systems approach to design model-based control laws that can give major improvements in the performance and robustness of AFM imaging. First, we propose a cascaded control design approach to tapping mode imaging, which is the most common mode of AFM imaging. The proposed approach utilizes the vertical positioning sensor in addition to the cantilever deflection sensor in the feedback loop. The control design problem is broken down into that of an inner control loop and an outer control loop. We show that by appropriate control design, unwanted effects arising out of model uncertainties and nonlinearities of the vertical positioning system are eliminated. Experimental implementation of the proposed control design shows improved imaging quality at up to 30% higher speeds. Secondly, we address a fundamental limitation in tapping mode imaging by proposing a novel transform-based imaging mode to achieve an order of magnitude improvement in AFM imaging bandwidth. We introduce a real-time transform that effects a frequency shift of a given signal. We combine model-based reference generation along with the real-time transform. The proposed method is shown to have linear dynamical characteristics, making it conducive for model-based control designs, thus paving the way for achieving superior performance and robustness in imaging

Improvement in the Imaging Performance of Atomic Force Microscopy: A Survey

Nanotechnology is the branch of science which deals with the manipulation of matters at an extremely high resolution down to the atomic level. In recent years, atomic force microscopy (AFM) has proven to be extremely versatile as an investigative tool in this field. The imaging performance of AFMs is hindered by: 1) the complex behavior of piezo materials, such as vibrations due to the lightly damped low-frequency resonant modes, inherent hysteresis, and creep nonlinearities; 2) the cross-coupling effect caused by the piezoelectric tube scanner (PTS); 3) the limited bandwidth of the probe; 4) the limitations of the conventional raster scanning method using a triangular reference signal; 5) the limited bandwidth of the proportional-integral controllers used in AFMs; 6) the offset, noise, and limited sensitivity of position sensors and photodetectors; and 7) the limited sampling rate of the AFM's measurement unit. Due to these limitations, an AFM has a high spatial but low temporal resolution, i.e., its imaging is slow, e.g., an image frame of a living cell takes up to 120 s, which means that rapid biological processes that occur in seconds cannot be studied using commercially available AFMs. There is a need to perform fast scans using an AFM with nanoscale accuracy. This paper presents a survey of the literature, presents an overview of a few emerging innovative solutions in AFM imaging, and proposes future research directions.This work was supported in part by the Australian Research Council (ARC) under Grant FL11010002 and Grant DP160101121 and the UNSW Canberra under a Rector's Visiting Fellowshi

Dynamics and Control of Flexure-based Large Range Nanopositioning Systems.

The objective of this thesis is to demonstrate desktop-size and cost-effective flexure-based multi-axis nanopositioning capability over a motion range of several millimeters per axis. Increasing the motion range will overcome one of the main drawbacks of existing nanopositioning systems, thereby significantly improving the coverage area in nanometrology and nanomanufacturing applications. A single-axis nanopositioning system, comprising a symmetric double parallelogram flexure bearing and a traditional-architecture moving magnet actuator, is designed, fabricated, and tested. A figure of merit for the actuator is derived and shown to directly impact the system-level trade-offs in terms of range, resolution, bandwidth, and temperature rise. While linear feedback controllers provide good positioning performance for point-to-point commands, the tracking error for dynamic commands prove to be inadequate due to the nonlinearities in the actuator and its driver. To overcome this, an iterative learning controller is implemented in conjunction with linear feedback to reduce the periodic component of the tracking error by more than two orders of magnitude. Experimental results demonstrate 10 nm RMS tracking error over 8 mm motion range in response to a 2 Hz bandlimited triangular command. For the XY nanopositioning system, a lumped-parameter model of an existing XY flexure bearing is developed in order to understand the unexplained variation observed in the transfer function zeros over the operating range of motion. It is shown that the kinematic coupling, due to geometric nonlinearities in the beam mechanics, and small dimensional asymmetry, due to manufacturing tolerances, may conspire to produce complex-conjugate nonminimum phase zeros at certain operating points in the system's workspace. This phenomenon significantly restricts the overall performance of the feedback control system. After intentional use of large asymmetry is employed to overcome this problem, independent feedback and iterative learning controllers are implemented along each axis. Experimental results demonstrate 20 nm RMS radial tracking error while traversing a 2 mm diameter circle at 2 Hz.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/107086/1/parmar_1.pd

Algorithmic approaches to high speed atomic force microscopy

Thesis (Ph.D.)--Boston UniversityThe atomic force microscope (AFM) has a unique set of capabilities for investigating biological systems, including sub-nanometer spatial resolution and the ability to image in liquid and to measure mechanical properties. Acquiring a high quality image, however, can take from minutes to hours. Despite this limited frame rate, researchers use the instrument to investigate dynamics via time-lapse imaging, driven by the need to understand biomolecular activities at the molecular level. Studies of processes such as DNA digestion with DNase, DNA-RNA polymerase binding and RNA transcription from DNA by RNA polymerase redefined the potential of AFM in biology. As a result of the need for better temporal resolution, advanced AFMs have been developed. The current state of the art in high-speed AFM (HS-AFM) for biological studies is an instrument developed by Toshio Ando at Kanazawa University in Japan. This instrument can achieve 12 frames/sec and has successfully visualized the motion of protein motors at the molecular level. This impressive instrument as well as other advanced AFMs, however, comes with tradeoffs that include a small scan size, limited imaging modes and very high cost. As a result, most AFM users still rely on standard commercial AFMs. The work in this thesis develops algorithmic approaches that can be implemented on existing instruments, from standard commercial systems to cutting edge HS-AFM units, to enhance their capabilities. There are four primary contributions in this thesis. The first is an analysis of the signals available in an AFM with respect to the information they carry and their suitability for imaging at different scan speeds. The next two are algorithmic approaches to HS-AFM that take advantage of these signals in different ways. The first algorithm involves a new sample profile estimator that yields accurate topology at speeds beyond the bandwidth of the limiting actuator. The second involves more efficient sampling, using the data in real time to steer the tip. Both algorithms yield at least an order of magnitude improvement in imaging rate but with different tradeoffs. The first operates beyond the bandwidth of the controller managing the tip-sample interaction and therefore the applied force is not well-regulated. The second keeps this control intact but is effective only on a limited set of samples, namely biopolymers or other string-like samples. Experiments on calibration samples and λ-DNA show that both of the algorithms improve the imaging rate by an order of magnitude. In the fourth contribution, extended applications of AFMs equipped with the algorithmic approaches are the tracking of a macromolecule moving along a string-like sample and a time optimal path for repetitive non-raster scans along string-like samples

Data acquisition and imaging using wavelet transform: a new path for high speed transient force microscopy

The unique ability of Atomic Force Microscopy (AFM) to image, manipulate and characterize materials at the nanoscale has made it a remarkable tool in nanotechnology. In dynamic AFM, acquisition and processing of the photodetector signal originating from probe–sample interaction is a critical step in data analysis and measurements. However, details of such interaction including its nonlinearity and dynamics of the sample surface are limited due to the ultimately bounded bandwidth and limited time scales of data processing electronics of standard AFM. Similarly, transient details of the AFM probe's cantilever signal are lost due to averaging of data by techniques which correlate the frequency spectrum of the captured data with a temporally invariant physical system. Here, we introduce a fundamentally new approach for dynamic AFM data acquisition and imaging based on applying the wavelet transform on the data stream from the photodetector. This approach provides the opportunity for exploration of the transient response of the cantilever, analysis and imaging of the dynamics of amplitude and phase of the signals captured from the photodetector. Furthermore, it can be used for the control of AFM which would yield increased imaging speed. Hence the proposed method opens a pathway for high-speed transient force microscopy