Barry E. DeMartini

Bio: Barry E. DeMartini is an academic researcher from University of California, Santa Barbara. The author has contributed to research in topics: Nonlinear system & Mathieu function. The author has an hindex of 9, co-authored 16 publications receiving 887 citations.

Design and Modeling of a High-Speed AFM-Scanner

Abstract: A new mechanical scanner design for a high-speed atomic force microscope (AFM) is presented and discussed in terms of modeling and control. The positioning range of this scanner is 13 mum in the X- and Y-directions and 4.3 mum in the vertical direction. The lowest resonance frequency of this scanner is above 22 kHz. This paper is focused on the vertical direction of the scanner, being the crucial axis of motion with the highest precision and bandwidth requirements for gentle imaging with the AFM. A second- and a fourth-order mathematical model of the scanner are derived that allow new insights into important design parameters. Proportional-integral (Pl)-feedback control of the high-speed scanner is discussed and the performance of the new AFM is demonstrated by imaging a calibration grating and a biological sample at 8 frames/s.

Linear and Nonlinear Tuning of Parametrically Excited MEMS Oscillators

Abstract: Microelectromechanical oscillators utilizing noninterdigitated combdrive actuators have the ability to be parametrically excited, which leads to distinct advantages over harmonically driven oscillators. Theory predicts that this type of actuator, when dc voltage is applied, can also be used for tuning the effective linear and nonlinear stiffnesses of an oscillator. For instance, the parametric instability region can be rotated by using a previously developed linear tuning scheme. This can be accomplished by implementing two sets of noninterdigitated combdrives, choosing the correct geometry and alignment for each, and applying ac excitation voltages to one set and proportional dc tuning voltages to the other set. Such an oscillator can also be tuned to display a desired nonlinear behavior: softening, hardening, or mixed nonlinearity. Nonlinear tuning is attained by carefully designing combdrive geometry, flexure geometry, and applying the correct dc voltages to the second set of actuators. Here, two oscillators have been designed, fabricated, and tested to prove these tuning concepts experimentally

Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation

Abstract: A variety of microelectromechanical (MEM) oscillators is governed by a version of the Mathieu equation that harbors both linear and cubic nonlinear time-varying stiffness terms. In this paper, chaotic behavior is predicted and shown to occur in this class of MEM device. Specifically, by using Melnikov's method, an inequality that describes the region of parameter space where chaos lives is derived. Numerical simulations are performed to show that chaos indeed occurs in this region of parameter space and to study the system's behavior for a variety of parameters. A MEM oscillator utilizing non interdigitated comb drives for actuation and stiffness tuning was designed and fabricated, which satisfies the inequality. Experimental results for this device that are consistent with results from numerical simulations are presented and convincingly show chaotic behavior.

A single input-single output coupled microresonator array for the detection and identification of multiple analytes

Abstract: This work reports the experimental demonstration of single input-single output, multianalyte detection and identification using a coupled array of microresonators. A prototype sensor with four frequency-mistuned microbeam sensors, each coupled to a common shuttle mass resonator, is presented. Tailored localized modes of vibration in this coupled system are exploited to embed all requisite resonance shift information into the response of the common shuttle. Four standard polymers are applied to the microbeams to functionalize them for vapor detection. Toluene and methanol vapors, as well as toluene/methanol mixtures, are detected and identified using a single input signal and a single output signal.

Stochastic Differential Equations

Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Feedback Systems: An Introduction for Scientists and Engineers

Abstract: This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl strm and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. strm and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences.Covers the mathematics needed to model, analyze, and design feedback systems Serves as an introductory textbook for students and a self-contained resource for researchers Includes exercises at the end of every chapter Features an electronic solutions manual Offers techniques applicable across a range of disciplines

Invited review article: high-speed flexure-guided nanopositioning: mechanical design and control issues.

Abstract: Recent interest in high-speed scanning probe microscopy for high-throughput applications including video-rate atomic force microscopy and probe-based nanofabrication has sparked attention on the development of high-bandwidth flexure-guided nanopositioning systems (nanopositioners). Such nanopositioners are designed to move samples with sub-nanometer resolution with positioning bandwidth in the kilohertz range. State-of-the-art designs incorporate uniquely designed flexure mechanisms driven by compact and stiff piezoelectric actuators. This paper surveys key advances in mechanical design and control of dynamic effects and nonlinearities, in the context of high-speed nanopositioning. Future challenges and research topics are also discussed.

A review of feedforward control approaches in nanopositioning for high-speed spm

Abstract: Control can enable high-bandwidth nanopositioning needed to increase the operating speed of scanning probe microscopes (SPMs). High-speed SPMs can substantially impact the throughput of a wide range of emerging nanosciences and nanotechnologies. In particular, inversion-based control can find the feedforward input needed to account for the positioning dynamics and, thus, achieve the required precision and bandwidth. This article reviews inversion-based feedforward approaches used for high-speed SPMs such as optimal inversion that accounts for model uncertainty and inversion-based iterative control for repetitive applications. The article establishes connections to other existing methods such as zero-phase-error-tracking feedforward and robust feedforward. Additionally the article reviews the use of feedforward in emerging applications such as SPM-based nanoscale combinatorial-science studies, image-based control for subnanometer-scale studies, and imaging of large soft biosamples with SPMs.

Design and Modeling of a High-Speed AFM-Scanner

Abstract: A new mechanical scanner design for a high-speed atomic force microscope (AFM) is presented and discussed in terms of modeling and control. The positioning range of this scanner is 13 mum in the X- and Y-directions and 4.3 mum in the vertical direction. The lowest resonance frequency of this scanner is above 22 kHz. This paper is focused on the vertical direction of the scanner, being the crucial axis of motion with the highest precision and bandwidth requirements for gentle imaging with the AFM. A second- and a fourth-order mathematical model of the scanner are derived that allow new insights into important design parameters. Proportional-integral (Pl)-feedback control of the high-speed scanner is discussed and the performance of the new AFM is demonstrated by imaging a calibration grating and a biological sample at 8 frames/s.