Rectification and phase locking of graphite

Abstract

Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction causes the appearance of dynamicalmode locking and the steps in the response function of the system. On the other hand, the presence of an ac force in the transverse direction causes the appearance of rectification,even though there is no net dc force in the transverse direction. It is found that whereas the longitudinal velocity increases in a series of steps, rectification in the transverse direction can occur only between two neighbor steps. The amplitude and phase of the external ac driving force affect the depinning force,rectification of the system and particles trajectories.

Command Filter AILC for Finite Time Accurate Tracking of Aircraft Track Angle System Based on Fuzzy Logic

“…Due to the parameter definition of fuzzy logic systems has a clear physical meaning, make it an effective method for selecting initial parameters. The determination of initial parameters in this paper is more appropriate, so compared with article [27], the error rate of convergence can be faster. In addition, compared with the study of Zhang et al [27], the controller in this article has a simpler structure due to the use of filters.…”

“…It can be seen from Figure 2 that the flight path inclination error of the designed controller tends to zero with the increase of the number of iterations gradually whether using the method of this article or the method of article [27]. Due to the parameter definition of fuzzy logic systems has a clear physical meaning, make it an effective method for selecting initial parameters.…”

“…The backstepping method is a powerful tool for dealing with high-order strict feedback systems. In the paper by Zhang et al [27], the authors proposed a new AILC method for the finite time tracking control problem of uncertain aircraft track angle system based on the neural network. However, the quasi controller and the desired output are derived continuously in the design process.…”

“…With the increase of the order of the system, the realization of the controller will become extremely complex, which will lead to the explosion problem of complexity. Based on this paper by Zhang et al [27], considering that the command filter [28,29] can estimate the derivative of the virtual controller to deal with the corresponding explosion problem of complexity. We introduce it to solve the explosion problem of complexity in the process of designing the controller of aircraft track angle system.…”

“…(3) Compared with the paper by Zhang et al [27], the command filter is introduced to estimate the derivative of the virtual controller and solve the explosion problem of complexity in the process of designing the controller of aircraft track angle system. The controller becomes simpler.…”