There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

* The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The book presents sound coverage of the fundamentals of lightwave technology, along with material on pulse compression techniques and rare-earth-doped fiber amplifiers and lasers. The extensively revised chapters include information on fiber-optic communication systems and the ultrafast signal processing techniques that make use of nonlinear phenomena in optical fibers.New material focuses on the applications of highly nonlinear fibers in areas ranging from wavelength laser tuning and nonlinear spectroscopy to biomedical imaging and frequency metrology. Technologies such as quantum cryptography, quantum computing, and quantum communications are also covered in a new chapter.This book will be an ideal reference for: RD scientists involved with research on fiber amplifiers and lasers; graduate students and researchers working in the fields of optical communications and quantum information. * The only book on how to develop nonlinear fiber optic applications* Two new chapters on the latest developments; Highly Nonlinear Fibers and Quantum Applications* Coverage of biomedical applications

Applications of nonlinear fiber optics

Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

Combined with backstepping techniques, an observer-based adaptive consensus tracking control strategy is developed for a class of high-order nonlinear multiagent systems, of which each follower agent is modeled in a semi-strict-feedback form By constructing the neural network-based state observer for each follower, the proposed consensus control method solves the unmeasurable state problem of high-order nonlinear multiagent systems The control algorithm can guarantee that all signals of the multiagent system are semi-globally uniformly ultimately bounded and all outputs can synchronously track a reference signal to a desired accuracy A simulation example is carried out to further demonstrate the effectiveness of the proposed consensus control method

Observer-Based Adaptive Backstepping Consensus Tracking Control for High-Order Nonlinear Semi-Strict-Feedback Multiagent Systems

Pull-in instability as an inherently nonlinear and crucial effect continues to become increasingly important for the design of electrostatic MEMS and NEMS devices and ever more interesting scientifically. This review reports not only the overview of the pull-in phenomenon in electrostatically actuated MEMS and NEMS devices, but also the physical principles that have enabled fundamental insights into the pull-in instability as well as pull-in induced failures. Pull-in governing equations and conditions to characterize and predict the static, dynamic and resonant pull-in behaviors are summarized. Specifically, we have described and discussed on various state-of-the-art approaches for extending the travel range, controlling the pull-in instability and further enhancing the performance of MEMS and NEMS devices with electrostatic actuation and sensing. A number of recent activities and achievements methods for control of torsional electrostatic micromirrors are introduced. The on-going development in pull-in applications that are being used to develop a fundamental understanding of pull-in instability from negative to positive influences is included and highlighted. Future research trends and challenges are further outlined.

Electrostatic pull-in instability in MEMS/NEMS: A review

The design, identification, and control of a novel, flexure-based, piezoelectric stack-actuated XY nanopositioning stage are presented in this paper. The main goal of the design is to combine the ability to scan over a relatively large range (25times25 mum) with high scanning speed. Consequently, the stage is designed to have its first dominant mode at 2.7 kHz. Cross-coupling between the two axes is kept to -35 dB, low enough to utilize single-input--single-output control strategies for tracking. Finite-element analysis (FEA) is used during the design process to analyze the mechanical resonance frequencies, travel range, and cross-coupling between the X- and Y-axes of the stage. Nonlinearities such as hysteresis are present in such stages. These effects, which exist due to the use of piezoelectric stacks for actuation, are minimized using charge actuation. The integral resonant control method is applied in conjunction with feedforward inversion technique to achieve high-speed and accurate scanning performances, up to 400 Hz.

Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning

This paper introduces integral resonant control, IRC, a simple, robust and well-performing technique for vibration control in smart structures with collocated sensors and actuators. By adding a direct feed-through to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. It is shown that this modification permits the direct application of integral feedback and results in good performance and stability margins. By slightly increasing the controller complexity from first to second order, low-frequency gain can be curtailed, alleviating problems due to unnecessarily high controller gain below the first mode. Experimental application to a piezoelectric laminate cantilever beam demonstrates up to 24 dB modal amplitude reduction over the first eight modes.

http://iopscience.iop.org/article/10.1088/0964-1726/16/2/023/pdf

Integral resonant control of collocated smart structures

This paper demonstrates a simple second-order controller that eliminates scan-induced oscillation and provides integral tracking action. The controller can be retrofitted to any scanning probe microscope with position sensors by implementing a simple digital controller or operational amplifier circuit. The controller is demonstrated to improve the tracking bandwidth of an NT-MDT scanning probe microscope from 15 Hz (with an integral controller) to 490 Hz while simultaneously improving gain-margin from 2 to 7 dB. The penalty on sensor induced positioning noise is minimal. A unique benefit of the proposed control scheme is the performance and stability robustness with respect to variations in resonance frequency. This is demonstrated experimentally by a change in resonance frequency from 934 to 140 Hz. This change does not compromise stability or significantly degrade performance. For the scanning probe microscope considered in this paper, the noise is marginally increased from 0.30 to 0.39 nm rms. Open and closed-loop experimental images of a calibration standard are reported at speeds of 1, 10, and 31 lines per second (with a scanner resonance frequency of 290 Hz). Compared with traditional integral controllers, the proposed controller provides a bandwidth improvement of greater than 10 times. This allows faster imaging and less tracking lag at low speeds.

A New Method for Robust Damping and Tracking Control of Scanning Probe Microscope Positioning Stages

In this paper, we propose a control design method for single-link flexible manipulators. The proposed technique is based on the integral resonant control (IRC) scheme. The controller consists of two nested feedback loops. The inner loop controls the joint angle and makes the system robust to joint friction. The outer loop, which is based on the IRC technique, damps the vibration and makes the system robust to the unmodeled dynamics (spill-over) and resonance frequency variations due to changes in the payload. The objectives of this work are: 1) to demonstrate the advantages of IRC, which is a high-performance controller design methodology for flexible structures with collocated actuator-sensor pairs and 2) to illustrate its capability of achieving precise end-point (tip) positioning with effective vibration suppression when applied to a typical flexible manipulator. The theoretical formulation of the proposed control scheme, a detailed stability analysis and experimental results obtained on a flexible manipulator are presented.

/pdf/integral-resonant-control-for-vibration-damping-and-precise-2wl8beop4i.pdf

Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator

Piezoelectric stack-actuated parallel-kinematic nanopositioning platforms are widely used in nanopositioning applications. These platforms have a dominant first resonant mode at relatively low frequencies, typically in the hundreds of hertz. Furthermore, piezoelectric stacks used for actuation have inherent nonlinearities such as hysteresis and creep. These problems result in a typically low-grade positioning performance. Closed-loop control algorithms have shown the potential to eliminate these problems and achieve robust, repeatable nanopositioning. Using closed-loop noise profile as a performance criterion, three commonly used damping controllers, positive position feedback, polynomial-based pole placement, and resonant control are compared for their suitability in nanopositioning applications. The polynomial-based pole placement controller is chosen as the most suitable of the three. Consequently, the polynomial-based control design to damp the resonant mode of the platform is combined with an integrator to produce raster scans of large areas. A scanning resolution of approximately 8 nm, over a 100 mum times 100 mum area is achieved.

/pdf/minimizing-scanning-errors-in-piezoelectric-stack-actuated-2ulql4url7.pdf

Sumeet S. Aphale

Papers

Design, Identification, and Control of a Flexure-Based XY Stage for Fast Nanoscale Positioning

Integral resonant control of collocated smart structures

A New Method for Robust Damping and Tracking Control of Scanning Probe Microscope Positioning Stages

Integral Resonant Control for Vibration Damping and Precise Tip-Positioning of a Single-Link Flexible Manipulator

Minimizing Scanning Errors in Piezoelectric Stack-Actuated Nanopositioning Platforms