Real-time sliding mode observer scheme for shear force estimation in a transverse dynamic force microscope

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.This paper describes a sliding mode observer scheme for estimation of the shear force affecting the cantilever in a Transverse Dynamic Force Microscope (TDFM). The vertically oriented cantilever is oscillated in proximity to the specimen under investigation. The amplitude of oscillation of the cantilever tip is affected by these shear forces. They are created by the ordered-water layer above the specimen. The oscillation amplitude is therefore a measure of distance between the tip and the surface of the specimen. Consequently, the estimation of the shear forces provides useful information about the specimen characteristics. For estimating the shear forces, an approximate finite dimensional model of the cantilever is created using the method of lines. This model is subsequently reduced for its model order. An unknown input sliding mode observer has been used to reconstruct the unknown shear forces using only tip position measurements and the cantilever excitation. This paper describes the development of the sliding mode scheme and presents experimental results from the TDFM set up at the Centre for Nanoscience and Quantum Information (NSQI) at Bristol University

Real-time force reconstruction in a transverse dynamic force microscope

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this recordOne major functionality of force microscopes is their ability to measure forces at a high sensitivity, thereby, allowing understanding of vital mechanisms: for instance, in bio-specimens. The investigation of a specimen’s viscoelasticity on nano-scale can have significant scientific impact, but has been inhibited by the lack of fast, comprehensive scanning instruments. In principle, transverse dynamic force microscopes (TDFMs) permit the measurement of interaction forces within delicate samples in a non-contact manner. The force measurements are reconstructed via complicated offline analysis in TDFMs, therefore, they can hardly be utilised as an online force measuring tool. This paper introduces a novel integrated robust design for practical scanning using the TDFM system. The digital design is implemented in fixed-point arithmetic using Field Programmable Gate Array (FPGA) devices, thereby, permitting measurement of the interaction force at a high sampling rate. The novel digital design tackles different implementation issues achieving fast and robust force measuring performance. This enables a new force-scan mode for the TDFM, realising for the first time, online force mapping of sample-surfaces in real-time.Engineering and Physical Sciences Research Council (EPSRC

A super-twisting observer for atomic-force reconstruction in a probe microscope

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordThis paper presents a new methodology employing a super-twisting sliding mode observer to reconstruct un-measureable atomic-forces at nano-Newton precision in a Vertically Oriented Probe Microscope (VOPM). The VOPM senses the deflection of a vertically oriented cantilever, caused by shear-force interaction with a confined water layer above the sample-substrate. The paper describes the development of a model and the subsequent experimental process for computing its parameters. This forms the basis for the design of a super-twisting observer to estimate the unknown shear-forces. The reconstructed force can be decomposed into elastic and viscous components ,which are important in biological research.Engineering and Physical Sciences Research Council (EPSRC

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Multi-Eigenmode Control for Improved Tracking Speed in Multifrequency Atomic Force Microscopy

Die Sensoren von Rasterkraftmikroskopen sind mechanische Schwinger, die zur zeitgleichen Aufnahmevon Topographie und Materialeigenschaften genutzt werden können. Besonders wichtig sinddie Bildrastergeschwindigkeit und Kraftsensitivität, die oft einen Kompromiss benötigen. In dieserArbeit wird ein neuartiger Multi-Eigenmode Kompensator basierend auf einem Zustandsschätzervorgestellt, der die dynamischen Eigenschaften jeder Cantilever-Resonanz unabhängig voneinandermodifizieren kann. Dargelegt wird die Modellierung, Kompensator-Design und Implementierungsstrategiein ein digitales System. Als Erstes wird der Kompensator zur Modifikation desQ Faktors einzelner Eigenmoden genutzt. Somit kann die Abbildungsrate um das 20-fache erhöhtwerden. Die Modifikation der natürlichen Frequenz erlaubt die Abbildung von Proben mitvollständig verschobenen Resonanzen. Moderne Mehrfachfrequenz-Abbildungsverfahren nutzenhöheren Eigenmoden, um bessere Abbildungsraten und Materialsensitivitäten zu erreichen. Beieiner Methode werden die angeregten höheren Harmonischen extrahiert, die beim Rastern einerOberfläche im Fourier-Spektrum entstehen. Eine andere Methode regt die erste und höhere Eigenmodengleichzeitig an. In Experimenten wird der Kompensator in Kombination mit beiden Abbildungsverfahrengenutzt, um speziell den Q Faktor der ersten beiden transversalen Eigenmoden gleichzeitigzu beeinflussen. Experimente zeigen, dass beste Abbildungsraten und Materialkontrastemit geringen Q Faktoren in der ersten und hohen Q Faktoren in der zweiten Eigenmode erreichtwerden. Eine Erweiterung des Kompensators erlaubt die Hochgeschwindigkeits-Demodulationvon Cantilever-Amplituden ohne Einsatz eines Lock-in Verstärkers, was anhand von Abbildungenmit der ersten Eigenmode gezeigt wird. Eine weitere Möglichkeit zur Verbesserung des Materialkontrastesbasiert auf der strukturellen Modifikation des Cantilevers. Mit Hilfe einer Ionenfeinstrahlanlagewird Material an bestimmten Bereichen des Cantilevers entfernt, so dass die erste undhöheren Eigenmoden aufeinander abgestimmt werden. Die Bestimmung von Form und Ort derMaterialentfernung wird entweder durch Simulationen im Voraus oder mit einem in situ Ansatzerreicht. Die extrahierten höheren harmonischen Signale des harmonischen Cantilevers zeigen eindeutlich verstärktes Signal von bis zu 10 % im Vergleich zur ersten Resonanz.Atomic Force Microscope probes are mechanical beams that can be used to simultaneously maptopography and material properties. In particular the imaging speed and force sensitivity aremajor concerns that often require a trade-off approach. In this work, a novel estimator basedmulti-eigenmode compensator is introduced to modify the dynamics of each resonance independently.Modeling, compensator design, implementation strategy in a digital system and validationin experiments will be presented. A single-eigenmode version of the compensator is used to modifythe Q factor of the first three eigenmodes separately. Using higher eigenmodes in combinationwith a modified Q factor leads to a 20-fold increase in image acquisition rates. The modificationof the natural frequency (F control) allows imaging at resonance frequencies that are not naturalto the cantilever. The emerging multifrequency Atomic Force Microscopy utilizes higher eigenmodesto improve imaging speed and force sensitivity concurrently. One method actuates the firsteigenmode for topography imaging and records the excited higher harmonics to map a sample’snanomechanical properties. To enhance the higher frequencies’ response two or more eigenmodesare actuated simultaneously, where the higher eigenmodes are used to quantify the nanomechanics.In experiments, the compensator is used to specifically modify the Q factors of the cantilever’sfirst two transversal eigenmodes concurrently in both imaging schemes. The experiments indicatemost enhanced material contrast and imaging rate with low Q factors in the first eigenmode andhigh Q factors in the higher eigenmode. An extension of the compensator allows for a high speedLock-in amplifier free amplitude demodulation, which is used for topography imaging with the firstresonance. A different technique for improving material property sensitivity is presented basedon structural modifications of the cantilever. Focused Ion Beam milling is used to remove massfrom specific areas in the cantilever such that the first and higher eigenmodes are tuned towardseach other. The shape and location of mass removal is determined either by simulation beforehandor through an in-situ approach. Higher harmonics of the harmonic active cantilevers indicate asignificant response of up to 10% in respect to the first resonance/harmonic

Dynamic Characteristics of Biologically Inspired Hair Receptors for Unmanned Aerial Vehicles

The highly optimized performance of nature’s creations and biological assemblies has inspired the development of their engineered counter parts that can potentially outperform conventional systems. In particular, bat wings are populated with air flow hair receptors which feedback the information about airflow over their surfaces for enhanced stability and maneuverability during their flight. The hairs in the bat wing membrane play a role in the maneuverability tasks, especially during low-speed flight. The developments of artificial hair sensors (AHS) are inspired by biological hair cells in aerodynamic feedback control designs. Current mathematical models for hair receptors are limited by strict simplifying assumptions of creeping flow hair Reynolds number on AHS fluid-structure interaction (FSI), which may be violated for hair structures integrated on small-scaled Unmanned Aerial Vehicles (UAVs). This study motivates by an outstanding need to understand the dynamic response of hair receptors in flow regimes relevant to bat-scaled UAVs. The dynamic response of the hair receptor within the creeping flow environment is investigated at distinct freestream velocities to extend the applicability of AHS to a wider range of low Reynolds number platforms. Therefore, a threedimensional FSI model coupled with a finite element model using the computational fluid dynamics (CFD) is developed for a hair-structure and multiple hair-structures in the airflow. The Navier-Stokes equations including continuity equation are solved numerically for the CFD model. The grid independence of the FSI solution is studied from the simulations of the hairstructure mesh and flow mesh around the hair sensor. To describe the dynamic response of the hair receptors, the natural frequencies and mode shapes of the hair receptors, computed from the finite element model, are compared with the excitation frequencies in vacuum. This model is described with both the boundary layer effects and effects of inertial forces due to fluid-structure xiv interaction of the hair receptors. For supporting the FSI model, the dynamic response of the hair receptor is also validated considering the Euler-Bernoulli beam theory including the steady and unsteady airflow

Vibration Analysis of Piezoelectric Microcantilever Sensors

The main objective of this dissertation is to comprehensively analyze vibration characteristics of microcantilever-based sensors with application to ultra small mass detection and low dimensional materials characterization. The first part of this work focuses on theoretical developments and experimental verification of piezoelectric microcantilevers, commercially named Active Probes, which are extensively used in most today\u27s advanced Atomic Force Microscopy (AFM) systems. Due to special geometry and configuration of Active Probes, especially multiple jump discontinuities in their cross-section, a general and comprehensive framework is introduced for forced vibration and modal analysis of discontinuous flexible beams. More specifically, a general formulation is obtained for the characteristics matrix using both boundary and continuity conditions. The formulation is then reduced to the special case of Active Probes with intentional geometrical discontinuities. Results obtained from experiment are compared with the commonly used uniform beam model as well as the proposed discontinuous beam model. It is demonstrated that a significant enhancement on sensing accuracy of Active Probes can be achieved using the proposed discontinuous beam model compared to a uniform model when a multiple-mode operation is desired. In the second part of this dissertation, a comprehensive dynamic model is proposed for vector Piezoforce Microscopy (PFM) system under applied electrical loading. In general, PFM is considered as a suspended microcantilever beam with a tip mass in contact with a piezoelectric material. The material properties are expressed in two forms; Kelvin-Voigt model for viscoelstic representation of the material and piezoelectric force acting on the tip as a result of response of material to applied electric field. Since the application of bias voltage to the tip results in the surface displacement in both normal and in-plane directions, the microcantilever is considered to vibrate in all three directions with coupled transversal/longitudinal and lateral/torsional motions. In this respect, it is demonstrated that the PFM system can be governed by a set of partial differential equations along with non-homogeneous and coupled boundary conditions. Using the method of assumed modes, the governing ordinary differential equations of the system and its state-space representation are derived under applied external voltage. The formulation is then reduced to vertical PFM, in which low dimensional viscoelestic and piezoelectric properties of periodically poled lithium niobate (PPLN) material can be detected. For this purpose, the experimental and theoretical frequency responses along with a minimization strategy for the percentage of modeling error are utilized to obtain optimal spring constant of PPLN. Finally, the step input responses of experiment and theory are used to estimate the piezoelectric and damping coefficients of PPLN. Overall in this dissertation, a precise dynamic model is developed for piezoelectric microcantilever for ultra small mass detection purpose. This model can also be utilized in AFM systems to replace laser-based detection mechanism with other alternative transductions. Moreover, a comprehensive model is proposed for PFM system to simultaneously detect low dimensional viscoelastic and piezoelectric properties of materials. This model can also be utilized for data storage purpose in ferroelectric materials