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

Robust Repetitive Controller for Fast AFM Imaging

Currently, Atomic Force Microscopy (AFM) is the most preferred Scanning Probe Microscopy (SPM) method due to its numerous advantages. However, increasing the scanning speed and reducing the interaction forces between the probe's tip and the sample surface are still the two main challenges in AFM. To meet these challenges, we take advantage of the fact that the lateral movements performed during an AFM scan is a repetitive motion and propose a Repetitive Controller (RC) for the z-axis movements of the piezo-scanner. The RC utilizes the profile of the previous scan line while scanning the current line to achieve a better scan performance. The results of the scanning experiments performed with our AFM set-up show that the proposed RC significantly outperforms a conventional PI controller that is typically used for the same task. The scan error and the average tapping forces are reduced by 66% and 58%, respectively when the scan speed is increased by 7-fold

Single-Molecule Force Spectroscopy: Experiments, Analysis, and Simulations

International audienceThe mechanical properties of cells and of subcellular components are important to obtain a mechanistic molecular understanding of biological processes. The quantification of mechanical resistance of cells and biomolecules using biophysical methods matured thanks to the development of nanotechnologies such as optical and magnetic tweezers, the biomembrane force probe and atomic force microscopy (AFM). The quantitative nature of force spectroscopy measurements has converted AFM into a valuable tool in biophysics. Force spectroscopy allows the determination of the forces required to unfold protein domains and to disrupt individual receptor/ligand bonds. Molecular simulation as a computational microscope allows investigation of similar biological processes with an atomistic detail. In this chapter, we first provide a step-by-step protocol of force spectroscopy including sample preparation, measurement and analysis of force spectroscopy using AFM and its interpretation in terms of available theories. Next, we present the background for molecular dynamics (MD) simulations focusing on steered molecular dynamics (SMD) and the importance of bridging of computational tools with experimental technique

Zellen als lebende Materialien: Kraftspektroskopische Untersuchung der Mechanotransduktion

Mechanotransduction describes a cellular mechanism of sensing and converting mechanical cues into biochemical signals to regulate cell processes, such as adhesion, migration, proliferation and/or apoptosis. Thus, becoming an ever-growing field of research with high potential for medical applications. I present a new strategy towards reliable microindentation measurements, which is essential for investigating mechanotransduction using soft substrates. I show a precise, reproducible determination of Young’s moduli through an automatic analysis of indentation data. The algorithm presented detects Young’s moduli in a region without dependence on indentation depth while minimizing the fitting error. This strategy is a step towards a comprehensive study of soft materials on a spatial scale similar to cell interactions. It has broad applicability ranging from fundamental research to developing innovative implants that match the in vivo situation. Also, I present novel approaches for multifaceted cellular manipulation. I show that layer thickness of a soft material fixed to a stiff underlying substrate can be crucial for cell adhesion. These findings are pioneer for new implant designs and advanced application fields. I present two atomic force microscopy-based manipulation systems that allow applying specific mechanical stimuli to single cells and a subsequent correlation to whole cell detachment and single bond strengths. The unique AFM-based shear system presented combines application of shear stimuli and cell detachment measurements, whereas the AFM-based modulation system combines oscillatory pushing and pulling with cell detachment measurements. Both shear and oscillatory forces are essential in our body. Thus, the strategies presented in this thesis are of significant medical interest allowing an overarching study of mechanotransduction and may pave the way towards smart stimulation devices that allow cell adhesion on demand

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

Automated DNA Fragments Recognition and Sizing through AFM Image Processing

This paper presents an automated algorithm to determine DNA fragment size from atomic force microscope images and to extract the molecular profiles. The sizing of DNA fragments is a widely used procedure for investigating the physical properties of individual or protein-bound DNA molecules. Several atomic force microscope (AFM) real and computer-generated images were tested for different pixel and fragment sizes and for different background noises. The automated approach minimizes processing time with respect to manual and semi-automated DNA sizing. Moreover, the DNA molecule profile recognition can be used to perform further structural analysis. For computer-generated images, the root mean square error incurred by the automated algorithm in the length estimation is 0.6% for a 7.8 nm image pixel size and 0.34% for a 3.9 nm image pixel size. For AFM real images we obtain a distribution of lengths with a standard deviation of 2.3% of mean and a measured average length very close to the real one, with an error around 0.33%