Local and global bifurcations in magnetic resonance force microscopy

Hacker, E.; Gottlieb, O.

doi:10.1007/s11071-019-05401-y

Cited by 4 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The role of local and global dynamics to assess system robustness and actual safety in operating conditions is investigated, by also studying the effect of different local and global control techniques on the nonlinear behavior of a noncontact AFM. First, the nonlinear dynamical behavior of a single-mode noncontact AFM model is analyzed in terms of stability of the main periodic solutions, as well as the robustness of the attractors and the integrity of the basins [10]. The focus of the paper by Ref.…”

Section: Atomic Force Microscopy: a State Of The Artmentioning

confidence: 99%

“…Both control techniques use two controllers called feedback (u f ) and feedforward (ũ), so the control signal of the nonlinear system is defined U=ũ+u?.Whileu f has the characteristic of correcting the difference between the real values and the stipulated values, taking the system to the stipulated orbit, ũ has the purpose of keeping the system in the desired orbit [24,25]. The SDRE controller design, like the OLFC, follows some steps to obtain the optimal solution to the dynamic control problem [10,31]:…”

Section: Control Designmentioning

confidence: 99%

See 1 more Smart Citation

MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control

Ribeiro¹,

Balthazar²,

Tusset³

et al. 2024

Chaos Monitoring in Dynamic Systems - Analysis and Applications

View full text Add to dashboard Cite

In this chapter, we explore a mathematical modelling that describes the nonlinear dynamic behavior of atomic force microscopy (AFM). We propose two control techniques for suppressing the chaotic motion of the system. The proposed model considers the interatomic interactions between the analyzed sample and the cantilever. These acting forces are van der Waals type, and we add a mathematical term that is a simple approximation to the viscoelasticity that possibly occurs in biological samples. We analyzed the behavior of the initial conditions of the proposed mathematical model, which showed a degree of complexity of the basins of attraction that were detected by entropy and uncertainty parameter, both detect if the basins have a fractal behavior. Numerical results showed that the nonlinear dynamic behavior has chaotic regions with the Lyapunov exponent, bifurcation diagram, and the Poincaré map. And, we propose two control techniques to suppress the chaotic movement of the AFM cantilever. First technique is the optimal linear feedback control (OLFC), which does not consider the nonlinearities of mathematical model. On the other hand, the control state dependent Riccati equation (SDRE) considers the nonlinearities of mathematical model. Both control techniques for a desired periodic orbit proved to be efficient.

show abstract

Section: Atomic Force Microscopy: a State Of The Artmentioning

confidence: 99%

Section: Control Designmentioning

confidence: 99%

MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control

Ribeiro¹,

Balthazar²,

Tusset³

et al. 2024

Chaos Monitoring in Dynamic Systems - Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Here, multidimensional microstages, applied for SPM measurement systems, require large strokes along multiple directions with nanometer-level positioning accuracy. Recently, a burgeoning magnetic resonance force microscopy (MRFM) technique, combined with atomic force microscopy detection mechanism, can non-invasively detect the densities of radicals by using a magnet-mounted cantilever [25][26][27][28]. Usually, a cryogenic environment for measuring the magnetic resonant force is required to reduce the thermomechanical noise and improve the cantilever-resonance sensitivity [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Demonstration of Heterogeneous Structure for Fabricating a Comb-Drive Actuator for Cryogenic Applications

Xue

Toda

et al. 2022

Micromachines

View full text Add to dashboard Cite

This study presents an experimental demonstration of the motion characteristics of a comb-drive actuator fabricated from heterogeneous structure and applied for cryogenic environments. Here, a silicon wafer is anodically bonded onto a glass substrate, which is considered to be a conventional heterogeneous structure and is commonly adopted for fabricating comb-drive actuators owing to the low-cost fabrication. The displacement sensor, also with comb-finger configuration, is utilized to monitor the motion characteristics in real time at low temperatures. The irregular motions, including displacement fluctuation and lateral sticking, are observed at specific low temperatures. This can be attributed to the different thermal expansion coefficients of two materials in the heterogeneous structure, further leading to structural deformation at low temperatures. The support spring in a comb-drive actuator is apt to be deformed because of suspended flexible structures, which affect the stiffness of the support spring and generate irregular yield behavior. The irregular yield behavior at low temperatures can be constrained by enhancing the stiffness of the support spring. Finally, we reveal that there are limited applications of the heterogeneous-structure-based comb-drive actuator in cryogenic environments, and simultaneously point out that the material substrate of silicon on the insulator is replaceable based on the homogeneous structure with a thin SiO2 layer.

show abstract

$${L}^{\varvec{p}}$$ optimal feedback control of homoclinic bifurcation in a forced Duffing oscillator

Piccirillo

2023

Nonlinear Dyn

View full text Add to dashboard Cite

Local and global bifurcations in magnetic resonance force microscopy

Cited by 4 publications

References 25 publications

MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control

MEMS-Based Atomic Force Microscope: Nonlinear Dynamics Analysis and Its Control

Demonstration of Heterogeneous Structure for Fabricating a Comb-Drive Actuator for Cryogenic Applications

$${L}^{\varvec{p}}$$ optimal feedback control of homoclinic bifurcation in a forced Duffing oscillator

Contact Info

Product

Resources

About