Fractional Dynamics in Mechanical Manipulation

Abstract

This paper analyzes the signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals, an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs offline and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system to be used in reducing or eliminating the effect of vibrations.

Dynamics of the Dow Jones and the NASDAQ stock indexes

“…The importance of fractional-order mathematical model is that it can be used to make a more accurate description and it can even give a deeper insight into the processes underlying long-range memory behavior [9,11,16]. It seems that there are many distinct analogies between the dynamics of complex physical and economical or even social systems.…”

Fractional dynamics in liquid manipulation

“…The position signals present identical characteristics, in terms of its spectrum, for the others cases (ii) container with a solid and (iii) container with a liquid. In fact the position signals maintain the same shape for the three cases [19]. Figure 8 shows the amplitude of the FFT of the axis 3 position signal (case i and case iii).…”

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

“…The importance of fractional order modeling is that it can be used to make a more accurate description and it can give a deeper insight into the processes underlying long range memory behavior [14,21,26]. It seems that there are many distinct analogies between the dynamics of complex physical and economical or even social systems.…”