Search Results (3)

The tapping-mode atomic force microscope (TM-AFM) is widely used today; however, improper matching between the operating medium and the sampling time may lead to inaccurate measurement results. The relationship between the damping coefficient and the steady state of the TM-AFM microcantilever is investigated in this paper using multiple stability theory. Firstly, the effects of changes in dimensionless linear damping coefficients and dimensionless piezoelectric film damping coefficients on the motion stability of the system are examined using bifurcation diagrams, phase trajectories, and domains of attraction. Subsequently, the degrees of effect of the two damping coefficients on the stability of the system are compared. Finally, the bi-parametric bifurcation characteristics of the system under a specific number of iterative cycles are investigated using the bi-parametric bifurcation diagram in conjunction with the actual working conditions, and the boundary conditions for the transition of the system’s motion from an unstable state to a stable state are obtained. The results of the study show that to ensure the accuracy and reliability of the individual measurement data in 500 iteration cycles, the dimensionless linear damping coefficient must be greater than 0.01014. Our results will provide valuable references for TM-AFM measurement media selection, improving TM-AFM imaging quality, measurement accuracy and maneuverability, and TM-AFM troubleshooting. Full article

This paper presents an analysis and control of chaos in the boost converter controlled with zero average dynamics, fixed-point induced control, and time-delayed autosynchronization techniques. First, the existence of chaos is demonstrated numerically when positive Lyapunov exponents are found in the controlled system, for a range from $k_1=-0.26$ to $k_1=0.4387$, when $k_2=0.5$. Additionally, chaos is also found for a range from $k_1=-0.435$ to $k_1=0.26$, when $k_2=-0.5$. Subsequently, fixed-point-induced control and time-delayed autosynchronization techniques are used to control the chaos. The results show that both techniques are useful to control the chaos in the boost converter. Furthermore, the fixed-point-induced control technique allows better regulation than the time-delayed autosynchronization technique. Moreover, when only the fixed-point induced control technique is used on the boost converter with a time delay, the results were not good enough to stabilize orbits. The stability is validated by calculating the Lyapunov exponents. Full article

In high load conditions, the boost converter presents some phenomena, such as chattering, chaos, subharmonics, and $nT$-periodic orbits, which require studying them with the aim of reducing the effects and improving the performance of these electronic devices. In this paper, sufficient conditions for the existence of $nT$-periodic orbits are analytically obtained and the system stability is evaluated using eigenvalues of the Jacobian matrix of the Poincaré application. It is demonstrated numerically that $1T$-periodic orbits occur for a broad range of $\gamma$ parameters. The research obtains a particular class of $2T$-periodic orbits in the boost converter and a formula that provides sufficient conditions for the existence of $nT$-periodic orbits with and without saturation in the duty cycle. In addition, an analysis of $nT$-periodic orbits is performed with a biparametric diagram. The system stability is computed using a variational equation that allows perturbation of the $1T$-periodic orbits. Moreover, an analytical calculation of the Floquet exponents is performed to determine the stability limit of the $1T$-periodic orbit. Finally, the phenomena found in this research are described according to the behavior of real applications encountered in previous literature. Full article