Murti V. Salapaka

High bandwidth nano-positioner: A robust control approach

This article presents the design, identification, and control of a nano-positioning device suited to image biological samples as part of an atomic force microscope. The device is actuated by a piezoelectric stack and its motion is sensed by a linear variable differential transformer. It is demonstrated that the conventional proportional-integral control architecture does not meet the bandwidth requirements for positioning. The design and implementation of an H∞ controller demonstrates substantial improvements in the positioning speed and precision, while eliminating the undesirable nonlinear effects of the actuator. The characterization of the resulting device in terms of bandwidth, resolution, and repeatability provided illustrates the effectiveness of the modern robust control paradigm.

Scanning Probe Microscopy

This article describes new perspectives on SPM-related science and technology, based on systems and control theory. These perspectives have led to a better understanding of SPM technology, overcome hurdles that limited the efficacy of SPM, and resulted in new modes of SPM-based interrogation. ThNcAFM, based on systems principles, has made it possible to image with resolution as high as 0.25 Aring in ambient conditions. The orders-of-magnitude improvements achieved in areas such as precision positioning, sample imaging, and sample detection rates emphasize the potential of systems tools in nanotechnology. The concept of using models in online operation has significant potential for SPM. For instance, TF-AFM, which uses models for online operation, resolves competing objectives of high resolution and detection rate by using a design from a systems perspective that makes detection bandwidth independent of the quality factor of the probe and, therefore, independent of resolution. The systems perspective also facilitates the interpretation of data since it provides a precise means for delineating the effects of the inherent dynamics of the interrogation system from the properties of the sample being probed. Devices such as SPMs are sensitive to operating conditions, ambient conditions, and modeling inaccuracies. Modern control theory provides a framework where such challenges can be effectively addressed. This aspect translates to reliable experiments in terms of repeatability, which is crucial in many nanoscience studies.

Structured optimal and robust control with multiple criteria: a convex solution

In this paper, the design of controllers that incorporate structural and multiobjective performance requirements is considered. The control structures under study cover nested, chained, hierarchical, delayed interaction and communications, and symmetric systems. Such structures are strongly related to several modern-day and future applications including integrated flight propulsion systems, platoons of vehicles, micro-electro-mechanical systems, networked control, control of networks, production lines and chemical processes. It is shown that the system classes presented have the common feature that all stabilizing controllers can be characterized by convex constraints on the Youla-Kucera parameter. Using this feature, a solution to a general optimal performance problem that incorporates time domain and frequency domain constraints is obtained. A synthesis procedure is provided which at every step yields a feasible controller together with a measure of its performance with respect to the optimal. Convergence to the optimal performance is established. An example of a multinode network congestion control problem is provided that illustrates the effectiveness of the developed methodology.

Brief Paper: Dynamical analysis and control of microcantilevers

In this paper, we study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation and the interaction between the sample and cantilever by a van der Waals (vdW) potential. The cantilever is vibrated by a sinusoidal input, and its deflection is detected optically. We analyze the forced dynamics using Melnikov method, which reveals the region in the space of physical parameters where chaotic motion is possible. In addition, using a proportional and derivative controller we compute the Melnikov function in terms of the parameters of the controller. Using this relation it is possible to design controllers that will remove the possibility of chaos.

A practical approach to operating survivable WDM networks

Several methods have been developed for joint working and spare capacity planning in survivable wavelength-division-multiplexing (WDM) networks. These methods have considered a static traffic demand and optimized the network cost assuming various cost models and survivability paradigms. Our interest primarily lies in network operation under dynamic traffic. We formulate various operational phases in survivable WDM networks as a single integer linear programming (ILP) optimization problem. This common framework avoids service disruption to the existing connections. However, the complexity of the optimization problem makes the formulation applicable only for network provisioning and offline reconfiguration. The direct use of this method for online reconfiguration remains limited to small networks with few tens of wavelengths. Our goal in this paper is to develop an algorithm for fast online reconfiguration. We propose a heuristic algorithm based on LP relaxation technique to solve this problem. Since the ILP variables are relaxed, we provide a way to derive a feasible solution from the relaxed problem. The algorithm consists of two steps. In the first step, the network topology is processed based on the demand set to be provisioned. This preprocessing step is done to ensure that the LP yields a feasible solution. The preprocessing step in our algorithm is based on: (a) the assumption that in a network, two routes between any given node pair are sufficient to provide effective fault tolerance and (b) an observation on the working of the ILP for such networks. In the second step, using the processed topology as input, we formulate and solve the LP problem. Interestingly, the LP relaxation heuristic yielded a feasible solution to the ILP in all our experiments. We provide insights into why the LP formulation yields a feasible solution to the ILP We demonstrate the use of our algorithm on practical size backbone networks with hundreds of wavelengths per link. The results indicate that the run time of our heuristic algorithm is fast enough (in order of seconds) to be used for online reconfiguration.

Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy

We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction.

Piezoelectric scanners for atomic force microscopes: design of lateral sensors, identification and control

This paper presents the identification and control of piezoelectric positioners used in atomic force microscopes (AFM) with the goal of improving probe positioning on the sample surface. A novel sensor was developed for this task and employed to infer a sixth order linear two input two output model of the piezos lateral dynamics. The piezo model was used to design a controller for tracking reference signals common in AFM operation. The controller and sensor were shown to significantly improve the microscopes ability to position the probe on the samples surface, enabling the AFM user to precisely scan areas on a surface based on images from previous scans.

Transient-signal-based sample-detection in atomic force microscopy

In typical dynamic mode operation of atomic force microscopes, steady state signals like amplitude and phase are used for detection and imaging of material. In these methods, the resolution and bandwidth are dictated by the quality factor (Q) of the cantilever. In this letter, we present a methodology that exploits the deflection signal during the transient of the cantilever motion. The principle overcomes the fundamental limitations on the trade off between resolution and bandwidth present in existing methods and makes it independent of the quality factor. Experimental results provided corroborate the theoretical development.

On the Problem of Reconstructing an Unknown Topology via Locality Properties of the Wiener Filter

Determining interrelatedness structure of various entities from multiple time series data is of significant interest to many areas. Knowledge of such a structure can aid in identifying cause and effect relationships, clustering of similar entities, identification of representative elements and model reduction. The majority of existing results are based on correlation based indices which effectively assume a static relationship between the time series data and are not suitable for detecting interrelatedness when the time series are dynamically related or when the time series involve loops. In this paper, a methodology for identifying the interrelatedness structure of dynamically related time series data is presented that also allows for the presence of loops in the connectivity structure. A linear dynamic graph model is presented where it is assumed that each time series data is the sum of an independent stochastic noise source and a dynamically weighted sum of other time series data. A link is assumed to be present between two time series if the weight of a time series, which is a linear time-invariant filter, is nonzero in the formation of the other. Reconstruction of the link connectivity structure under various scenarios is considered. It is shown that when the linear dynamic graph is allowed to admit non-causal weights, then the links structure can be recovered with the possibility of identifying spurious connections. However, it is shown that the spurious links remain local, where, a spurious link is restricted to be within one hop of a true link. Furthermore, strategies for exact reconstruction of the link structure when the weights are restricted to be causal are developed. The main tools for determining the network topology are based on variations of Wiener filtering. A significant insight provided by the article is that, in the class of network models considered in the paper, the Wiener filter estimating a stochastic process based on other processes remains local in the sense that the Wiener filter utilizes only measurements local to the node being estimated.

A Review of the Systems Approach to the Analysis of Dynamic-Mode Atomic Force Microscopy

The atomic force microscope (AFM) is one of the foremost tools for imaging, measuring and manipulating matter at the nanoscale. This brief presents a review of the systems and control approach to analyzing the challenging dynamic-mode operation of the AFM. A Lure system perspective of the AFM dynamics facilitates the application of powerful tools from systems theory for the analysis. The harmonic balance method provides significant insights into the steady-state behavior as well as a framework for identifying the tip-sample interaction force. A simple piecewise-linear tip-sample interaction model and its identification using the harmonic balance method is presented. The dominant first harmonic is analyzed using multivalued frequency responses and the corresponding stability conditions. The ability of the simple tip-sample interaction model to capture the intricate nonlinear behavior of the first harmonic is demonstrated. This also points to the importance of studying the higher harmonics to obtain finer details of the tip-sample interaction. The suitability of the Lure system perspective for the analysis of the higher harmonics is demonstrated.