Chaos control of an atomic force microscopy model in fractional-order

Tusset, Ângelo Marcelo; Balthazar, José Manoel; Ribeiro, Maurício A.; Lenz, Wagner B.; Rocha, Rodrigo Tumolin

doi:10.1140/epjs/s11734-021-00242-6

Cited by 8 publications

(3 citation statements)

References 44 publications

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“…Furthermore, the robustness of the proposed time-delayed feedback control was tested by a sensitivity analysis of parametric uncertainties. Recently [19] considering (AFM) that the system is operating in intermittent mode, the damping dynamics of the squeeze film damping can be represented by fractional calculus through numerical simulation and dynamic analysis to prove chaotic regimes. To suppress chaotic behavior, the authors used and analyzed two control strategies, the SDRE (Riccati equation dependent states) and OLFC (Linear Control for Optimum Feedback) controls.…”

Section: Atomic Force Microscopy: a State Of The Artmentioning

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

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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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Section: Atomic Force Microscopy: a State Of The Artmentioning

confidence: 99%

“…According to Ref. [19], an approximation of the solution of Eq. ( 5) is by using the linear modes and frequencies of the microcantilever around its electrostatic equilibrium that are different from those of a microcantilever located far from the surface.…”

Section: Andmentioning

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

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“…Tusset et al [21] address the nonlinear dynamics and control of atomic force microscopy (AFM) considering fractional-order derivatives. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space, the behavior of which is characterized by using the power spectral density and the 0-1 test.…”

Section: Contributed Papers In This Special Issuementioning

confidence: 99%

Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply

Balthazar

Gonçalves

Tusset

et al. 2021

Eur. Phys. J. Spec. Top.

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The special issue entitled "Mathematical modelling, nonlinear dynamics, bifurcation, synchronization and control of mechanisms driven by power supply," published by The European Physical Journal: Special Topics (EPJST), aims to bring into discussion works involving nonlinear and dynamic and chaotic behaviors, which are frequently found in mechanical and electromechanical systems, nonlinear circuits, and biologically inspired systems, stimulating the integration of findings on the nonlinear dynamics that can be observed in various systems in the physical sciences and engineering. This special issue presents 27 papers concerning the dynamics and control of flexible structure systems, nonideal systems, energy harvesting problems, and vibration absorbers. In addition, the papers address problems involving chaos control of nonlinear oscillations, phase-locked loops, synchronization of nonlinear oscillators, dynamics of bio-inspired and biostructural systems, nonlinear methods, and nonlinear circuits.

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