Iterative image-based modeling and control for higher scanning probe microscope performance.

In this article, we develop an image-based approach to model and control the dynamics of scanning probe microscopes (SPMs) during high-speed operations. SPMs are key enabling tools in the experimental investigation and manipulation of nano- and subnanoscale phenomena; however, the speed at which the SPM probe can be positioned over the sample surface is limited due to adverse dynamic effects. It is noted that SPM speed can be increased using model-based control techniques. Modeling the SPM dynamics is, however, challenging because currently available sensing methods do not measure the SPM tip directly. Additionally, the resolution of currently available sensing methods is limited by noise at higher bandwidth. Our main contribution is an iterative image-based modeling method which overcomes these modeling difficulties (caused by sensing limitations). The method is applied to model an experimental scanning tunneling microscope (STM) system and to achieve high-speed imaging. Specifically, we model the STM up to a frequency of 2000 Hz (corresponds to approximately 23 of the resonance frequency of our system) and achieve approximately 1.2% error in 1 nm square images at that same frequency.

High-speed solution switching using piezo-based micropositioning stages.

Motion-induced vibration is a critical limitation in high-speed micropositioning stages used to achieve solution switching. Controlled rapid solution switching is used to study the fast activation and deactivation kinetics of ligand-gated ion-channel populations isolated in excised membrane patches--such studies are needed to understand fundamental mechanisms that mediate synaptic excitation and inhibition in the central nervous system. However, as the solution-switching speed is increased, vibration induced in the piezo-based positioning stages can result in undesired, repeated, ligand application to the excised patch. The article describes a method to use knowledge of the piezo-stage's vibrational dynamics to compensate for and reduce these unwanted vibrations. The method was experimentally verified using an open-electrode technique, and fast solution switching (100 micros range) was achieved.

Reduced-order modeling for hyperthermia: an extended balanced-realization-based approach.

Accurate thermal models are needed in hyperthermia cancer treatments for such tasks as actuator and sensor placement design, parameter estimation, and feedback temperature control. The complexity of the human body produces full-order models which are too large for effective execution of these tasks, making use of reduced-order models necessary. However, standard balanced-realization (SBR)-based model reduction techniques require a priori knowledge of the particular placement of actuators and sensors for model reduction. Since placement design is intractable (computationally) on the full-order models, SBR techniques must use ad hoc placements. To alleviate this problem, an extended balanced-realization (EBR)-based model-order reduction approach is presented. The new technique allows model order reduction to be performed over all possible placement designs and does not require ad hoc placement designs. It is shown that models obtained using the EBR method are more robust to intratreatment changes in the placement of the applied power field than those models obtained using the SBR method.

Control Issues in High-speed AFM for Biological Applications: Collagen Imaging Example.

This article considers the precision positioning problem associated with high-speed operation of the Atomic Force Microscope (AFM), and presents an inversion-based control approach to achieve precision positioning. Although AFMs have high (nanoscale) spatial resolution, a problem with current AFM systems is that they have low temporal resolution, i.e., AFM imaging is slow. In particular, current AFM imaging cannot be used to provide three-dimensional, time-lapse images of fast processes when imaging relatively-large, soft samples. For instance, current AFM imaging of living cells takes 1-2 minutes (per image frame) - such imaging speeds are too slow to study rapid biological processes that occur in seconds, e.g., to investigate the rapid movement of cells or the fast dehydration and denaturation of collagen. This inability, to rapidly image fast biological processes, motivates our current research to increase the operating speed of the AFM. We apply an inversion-based feedback/feedforward control approach to overcome positioning problems that limit the operating speed of current AFM systems. The efficacy of the method, to achieve high-speed AFM operation, is experimentally evaluated by applying it to image collagen samples.

Optimal actuator placement for large scale systems: a reduced-order modelling approach.

A recently developed, extended balanced realization, reduced order modelling technique for large-scale distributed systems is applied to the problem of optimal actuator placement for hyperthermia treatments. Extended balanced realization develops low-order models whose state reconstructions are robust to actuator and sensor placement changes, and hence can be effectively used to find optimal placements in a computationally efficient manner. This optimization approach has been tested on simulations of a scanned focused, ultrasound hyperthermia system and found to be robust and accurate over a wide range of models, and the savings in computational costs were found to be significant.

A comparison of reduced-order modelling techniques for application in hyperthermia control and estimation.

Reduced-order modelling techniques can make important contributions in the control and state estimation of large systems. In hyperthermia, reduced-order modelling can provide a useful tool by which a large thermal model can be reduced to the most significant subset of its full-order modes, making real-time control and estimation possible. Two such reduction methods, one based on modal decomposition and the other on balanced realization, are compared in the context of simulated hyperthermia heat transfer problems. The results show that the modal decomposition reduction method has three significant advantages over that of balanced realization. First, modal decomposition reduced models result in less error, when compared to the full-order model, than balanced realization reduced models of similar order in problems with low or moderate advective heat transfer. Second, because the balanced realization based methods require a priori knowledge of the sensor and actuator placements, the reduced-order model is not robust to changes in sensor or actuator locations, a limitation not present in modal decomposition. Third, the modal decomposition transformation is less demanding computationally. On the other hand, in thermal problems dominated by advective heat transfer, numerical instabilities make modal decomposition based reduction problematic. Modal decomposition methods are therefore recommended for reduction of models in which advection is not dominant and research continues into methods to render balanced realization based reduction more suitable for real-time clinical hyperthermia control and estimation.