Local Versus Global Dynamics and Control of an AFM Model in a Safety Perspective

Settimi, Valeria; Rega, Giuseppe

doi:10.1007/978-3-319-99710-0_5

Cited by 3 publications

(1 citation statement)

References 35 publications

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“…This analysis is conducted by following the seminal works of Thompson [51], and Rega and Lenci [52,53]. For a deep overview, we refer to Thompson [54] and Rega et al [55]; for applications on AFM we refer to Settimi and Rega [56], and for applications on MEMS to Ruzziconi et al [26].…”

Section: The Principal Resonance: Pres and Pnonresmentioning

confidence: 99%

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

et al. 2021

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This work investigates the dynamics of a microbeam-based MEMS device in the neighborhood of a 2:1 internal resonance between the third and fifth vibration modes. The saturation of the third mode and the concurrent activation of the fifth are observed. The main features are analyzed extensively, both experimentally and theoretically. We experimentally observe that the complexity induced by the 2:1 internal resonance covers a wide driving frequency range. Constantly comparing with the experimental data, the response is examined from a global perspective, by analyzing the attractor-basins scenario. This analysis is conducted both in the thirdmode and fifth-mode planes. We show several metamorphoses occurring as proceeding from the principal resonance to the 2:1 internal resonance, up to the final disappearance of the resonant and non-resonant attractors. The shape and wideness of all the basins are examined. Despite they are progressively eroded, an appreciable region is detected where the compact cores of the attractors involved in the 2:1 internal resonance remain substantial, which allows effectively operating them under realistic conditions. The dynamical integrity of each resonant branch is discussed, especially as approaching the bifurcation points where the system becomes more vulnerable to the dynamic pull-in instability.

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Section: The Principal Resonance: Pres and Pnonresmentioning

confidence: 99%

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

et al. 2021

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Global Nonlinear Dynamics: Challenges in the Analysis and Safety of Deterministic or Stochastic Systems

Rega

2024

Exploiting the Use of Strong Nonlinearity in Dynamics and Acoustics

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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

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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.

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Local Versus Global Dynamics and Control of an AFM Model in a Safety Perspective

Cited by 3 publications

References 35 publications

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

Global Nonlinear Dynamics: Challenges in the Analysis and Safety of Deterministic or Stochastic Systems

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

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