Abstract
The nonlinear dynamics control of a contact-mode atomic force microscopy (AFM) system with multi forces (harmonic and parametric excitation force) utilizing the time delay proportional derivative (PD) controller is investigated. The perturbation method is utilized to calculate the first-order approximate solutions for the AFM system. The stability of the AFM system is investigated at the worst resonance case by Lyapunov's first method. We also show the bifurcation diagrams of response curves using frequency response equations before and after control are performed. Furthermore, we focus on the effect of the time-delayed control and returns signals gain on the vibration amplitude and the stability analysis of the controlled system in primary, sub-harmonic resonance for different parameter variations. In addition, the numerical results are procured using MATLAB program. Eventually, validation curves are presented to estimate the nearness degree between the analytical predictions also numerical simulation. The obtained results exhibited that, the time-delayed PD control efficiency to put down the nonlinear oscillations of the system.
Highlights
The Atomic force microscopy (AFM) is a powerful method that can picture almost any kind of surface, inclusive glass, The associate editor coordinating the review of this manuscript and approving it for publication was Hui Xie
Berg and Briggs [2] investigated intermittent contact system AFM from the viewpoint that the nonlinearity inserted by the drastic increasing the hardness on impact from that of the cantilever to that of the tip sample connect is important to its dynamics
The control and feedback signals gain effects respecting the vibration amplitude stability behavior of the controlled system were studied with the case 1 ∼= ω1, 2∼=2ω1
Summary
The Atomic force microscopy (AFM) is a powerful method that can picture almost any kind of surface, inclusive glass, The associate editor coordinating the review of this manuscript and approving it for publication was Hui Xie. Hamed et al.: PD Controller for Suppression the Vibrations of a Contact-Mode AFM Model applicability of acoustic/ultrasonic AFM to public contact conditions They used multiple perturbation method to get approximating expressions of the response of the probe to one-half subharmonic resonance. The multiple scales technique is applied to obtain approximate solution to the probe response in the existence of 2:1 autoparametric resonance between the second and third modes They found that the effectiveness of the interaction extends over a considerable domain of the tip-sample model hardness. The hysteresis suppression and frequency response shift of contact mode AFM is illustrated by [10] applying parametric modification of the contact hardness They used multiple perturbation technique and direct partition of motion to get the corresponding slow flow and the slow dynamic of the model, respectively. Verification curves show a good agreement between numerical simulation and analytical solution
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