Feedforward control approach to precision trajectory design and tracking : Theory and application to nano-mechanical property mapping using Scanning Probe Microscope

The output tracking problem has been extensively studied. The linear system case has been addressed by B. A. Francis. (1976) by converting the tracking problem to a regulator problem. Such an approach was later extended to nonlinear systems by A. Isidori. et al. (1990). On the feedforward control side, the stable inversion theory solved the challenging output tracking problem and achieved exact tracking of a given desired output trajectory for nonminimum phase systems (linear and nonlinear). The obtained solution is noncausal and requires the entire desired trajectory to be known a priori. This noncausality constraint has been alleviated through the development of the preview-based inversion approach, which showed the precision tracking can be achieved with a finite preview of the future desired trajectory, and the effect of the limited future trajectory information on output tracking can be quantified. Moreover, optimal scan trajectory design and control method provided a systematic approach to the optimal output-trajectory-design problem, where the output trajectory is repetitive and composed of pre-specified trajectory and unspecified trajectory for transition that returns from ending point to starting point in a given time duration. This dissertation focuses on the development of novel inversion-based feedforward control technique, with applications to output tracking problem with tracking and transition switchings, possibly non-repetitive. The motivate application examples come from atomic force microscope (AFM) imaging and material property measurements. The raster scanning process of AFM and optimal scan trajectory design and control method inspired the repetitive output trajectory tracking problem and attempt to solve in frequency domain. For the output tracking problem, especially for the AFM, there are several issues that have to be addressed. At first, the shape of the desired trajectory must be designed and optimized. Optimal output-trajectory-design problem provided a systematic approach to design the desired trajectory by minimizing the total input energy. However, the drawback is that the desired trajectory becomes very oscillatory when the system dynamics such as the dynamics of the piezoelectric actuator in AFM is lightly damped. Output oscillations need to be small in scanning operations of the AFM. In this dissertation, this problem is addressed through the pre-filter design in the optimal scan trajectory design and tracking framework, so that the trade off between the input energy and the output energy in the optimization is achieved. Secondly, the dissertation addressed the adverse effect of modeling error on the performance of feedforward control. For example, modeling errors can be caused in process of curve fitting. The contribution of this dissertation is the development of novel inversion based feedforward control techniques. Based on the inversion-based iterative learning control (S. Tien. et al. (2005)) technique, the dissertation developed enhanced inversion-based iterative control and the model-less inversion-based iterative control. The convergence of the iterative control law is discussed, and the frequency range of the convergence as well as the effect of the disturbance/noise to signal ratio is quantified. The proposed approach is illustrated by implementing them to high-speed force-distance curve measurements by using atomic force microscope (AFM). Then the control approach is extended to high-speed force-volume mapping. In high-speed force-volume mapping, the proposed approach utilizes the concept of signal decoupling-superimposition and the recently-developed model-less inversion-based iterative control (MIIC) technique. Experiment of force volume mapping on a Polydimethylsiloxane (PDMS) sample is presented to illustrate the proposed approach. The experimental results show that the mapping speed can be increased by over 20 times

MICROCANTILEVER-BASED FORCE SENSING, CONTROL AND IMAGING

This dissertation presents a distributed-parameters base modeling framework for microcantilever (MC)-based force sensing and control with applications to nanomanipulation and imaging. Due to the widespread applications of MCs in nanoscale force sensing or atomic force microscopy with nano-Newton to pico-Newton force measurement requirements, precise modeling of the involved MCs is essential. Along this line, a distributed-parameters modeling framework is proposed which is followed by a modified robust controller with perturbation estimation to target the problem of delay in nanoscale imaging and manipulation. It is shown that the proposed nonlinear model-based controller can stabilize such nanomanipulation process in a very short time compared to available conventional methods. Such modeling and control development could pave the pathway towards MC-based manipulation and positioning. The first application of the MC-based (a piezoresistive MC) force sensors in this dissertation includes MC-based mass sensing with applications to biological species detection. MC-based sensing has recently attracted extensive interest in many chemical and biological applications due to its sensitivity, extreme applicability and low cost. By measuring the stiffness of MCs experimentally, the effect of adsorption of target molecules can be quantified. To measure MC\u27s stiffness, an in-house nanoscale force sensing setup is designed and fabricated which utilizes a piezoresistive MC to measure the force acting on the MC\u27s tip with nano-Newton resolution. In the second application, the proposed MC-based force sensor is utilized to achieve a fast-scan laser-free Atomic Force Microscopy (AFM). Tracking control of piezoelectric actuators in various applications including scanning probe microscopes is limited by sudden step discontinuities within time-varying continuous trajectories. For this, a switching control strategy is proposed for effective tracking of such discontinuous trajectories. A new spiral path planning is also proposed here which improves scanning rate of the AFM. Implementation of the proposed modeling and controller in a laser-free AFM setup yields high quality image of surfaces with stepped topographies at frequencies up to 30 Hz. As the last application of the MC-based force sensors, a nanomanipulator named here MM3A® is utilized for nanomanipulation purposes. The area of control and manipulation at the nanoscale has recently received widespread attention in different technologies such as fabricating electronic chipsets, testing and assembly of MEMS and NEMS, micro-injection and manipulation of chromosomes and genes. To overcome the lack of position sensor on this particular manipulator, a fused vision force feedback robust controller is proposed. The effects of utilization of the image and force feedbacks are individually discussed and analyzed for use in the developed fused vision force feedback control framework in order to achieve ultra precise positioning and optimal performance

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

Spiral high-speed scanning tunneling microscopy: Tracking atomic diffusion on the millisecond timescale

Scanning tunneling microscopy (STM) is one of the most prominent techniques to resolve atomic structures of flat surfaces and thin films. With the scope to answer fundamental questions in physics and chemistry, it was used to elucidate numerous sample systems at the atomic scale. However, dynamic sample systems are difficult to resolve with STM due to the long acquisition times of typically more than 100 s per image. Slow electronic feedback loops, slow data acquisition, and the conventional raster scan limit the scan speed. Raster scans introduce mechanical noise to the image and acquire data discontinuously. Due to the backward and upward scan or the flyback movement of the tip, image acquisition times are doubled or even quadrupled. By applying the quasi-constant height mode and by using a combination of high-speed electronics for data acquisition and innovative spiral scan patterns, we could increase the frame rate in STM significantly. In the present study, we illustrate the implementation of spiral scan geometries and focus on the scanner input signal and the image visualization. Constant linear and constant angular velocity spirals were tested on the Ru(0001) surface to resolve chemisorbed atomic oxygen. The spatial resolution of the spiral scans is comparable to slow raster scans, while the imaging time was reduced from ~100 s to ~8 ms. Within 8 ms, oxygen diffusion processes were atomically resolved

Volumetric Lissajous confocal microscopy with tunable spatiotemporal resolution

Dynamic biological systems present challenges to existing three-dimensional (3D) optical microscopes because of their continuous temporal and spatial changes. Most techniques are rigid in adapting the acquisition parameters over time, as in confocal microscopy, where a laser beam is sequentially scanned at a predefined spatial sampling rate and pixel dwell time. Such lack of tunability forces a user to provide scan parameters, which may not be optimal, based on the best assumption before an acquisition starts. Here, we developed volumetric Lissajous confocal microscopy to achieve unsurpassed 3D scanning speed with a tunable sampling rate. The system combines an acoustic liquid lens for continuous axial focus translation with a resonant scanning mirror. Accordingly, the excitation beam follows a dynamic Lissajous trajectory enabling sub-millisecond acquisitions of image series containing 3D information at a sub-Nyquist sampling rate. By temporal accumulation and/or advanced interpolation algorithms, the volumetric imaging rate is selectable using a post-processing step at the desired spatiotemporal resolution for events of interest. We demonstrate multicolor and calcium imaging over volumes of tens of cubic microns with 3D acquisition speeds of 30 Hz and frame rates up to 5 kHz

Direct detection of electron backscatter diffraction patterns.

We report the first use of direct detection for recording electron backscatter diffraction patterns. We demonstrate the following advantages of direct detection: the resolution in the patterns is such that higher order features are visible; patterns can be recorded at beam energies below those at which conventional detectors usefully operate; high precision in cross-correlation based pattern shift measurements needed for high resolution electron backscatter diffraction strain mapping can be obtained. We also show that the physics underlying direct detection is sufficiently well understood at low primary electron energies such that simulated patterns can be generated to verify our experimental data

Image processing techniques for high-speed atomic force microscopy

Atomic force microscopy (AFM) is a powerful tool for imaging topography or other characteristics of sample surfaces at nanometer-scale spatial resolution by recording the interaction of a sharp probe with the surface. Dispute its excellent spatial resolution, one of the enduring challenges in AFM imaging is its poor temporal resolution relative to the rate of dynamics in many systems of interest. This has led to a large research effort on the development of high-speed AFM (HS-AFM). Most of these efforts focus on mechanical improvement and control algorithm design. This dissertation investigates a complementary HS-AFM approach based on the idea of undersampling which aims at increasing the imaging rate of the instrument by reducing the number of pixels in the sample surface that need to be acquired to create a high-quality image. The first part of this work focuses on the reconstruction of images sub-sampled according to a scheme known as μ path patterns. These patterns consist of randomly placed short and disjoint scans and are designed specifically for fast, efficient, and consistent data acquisition in AFM. We compare compressive sensing (CS) reconstruction methods with inpainting methods on recovering μ-path undersampled images. The results illustrate that the reconstruction quality depends on the choice of reconstruction methods and the sample under study, with CS generally producing a superior result for samples with sparse frequency content and inpainting performing better for samples with information limited to low frequencies. Motivated by the comparison, a basis pursuit vertical variation (BPVV) method, combing CS and inpainting, is proposed. Based on single image reconstruction results, we also extend our analysis to the problem of multiple AFM frames, in which higher overall video reconstruction quality is achieved by pixel sharing among different frames. The second part of the thesis considers patterns for sub-sampling in AFM. The allocation of measurements plays an important role in producing accurate reconstructions of the sample surface. We analyze the expected image reconstruction error using a greedy CS algorithm of our design, termed simplified matching pursuit (SMP), and propose a Monte Carlo-based strategy to create μ-path patterns that minimize the expected error. Because these μ path patterns involve a collection of disjoint scan paths, they require the tip of the instrument to be repeatedly lifted from and re-engaged to the surface. In many cases, the re-engagements make up a significant portion of the total data acquisition time. We therefore extend our Monte Carlo design strategy to find continuous scan patterns that minimize the reconstruction error without requiring the tip to be lifted from the surface. For the final part of the work, we provide a hardware demonstration on a commercial AFM. We describe hardware implementation details and image a calibration grating using the proposed μ-path and continuous scan patterns. The sample surface is reconstructed from acquired data using CS and inpainting methods. The recovered image quality and achievable imaging rate are compared to full raster-scans of the sample. The experimental results show that the proposed scanning combining with reconstruction methods can produce higher image quality with less imaging time

Frontiers in nanoscale electrochemical imaging : faster, multifunctional and ultrasensitive

A wide range of interfacial physicochemical processes, from electrochemistry to the functioning of living cells involve spatially localized chemical fluxes that are associated with specific features of the interface. Scanning electrochemical probe microscopes (SEPMs) represent a powerful means of visualizing interfacial fluxes, and this Feature Article highlights recent developments that have radically advanced the speed, spatial resolution, functionality and sensitivity of SEPMs. A major trend has been a coming together of SEPMs that developed independently, and the use of established SEPMs in completely new ways, greatly expanding their scope and impact. The focus is on nanopipette-based SEPMs, including scanning ion conductance microscopy (SICM), scanning electrochemical cell microscopy (SECCM), and hybrid techniques thereof, particularly with scanning electrochemical microscopy (SECM). Nanopipette-based probes are made easily, quickly and cheaply with tunable characteristics. They are reproducible and can be fully characterized, and their reponse can be modeled in considerable detail, so that quantitative maps of chemical fluxes and other properties (e.g. local charge) can be obtained and analyzed. This article provides an overview on the use of these probes for high speed imaging, to create movies of electrochemical processes in action, to carry out multifunctional mapping, such as simultaneous topography-charge and topography-activity, and to create nanoscale electrochemical cells for the detection, trapping and analysis of single entities, particularly individual molecules and nanoparticles (NPs). These studies provide a platform for the further application and diversification of SEPMs across a wide range of interfacial science