Where are We Going To?
- 2.1k Downloads
The non-integer order systems can describe dynamical behavior of materials and processes over vast time and frequency scales with very concise and computable models. Nowadays well known concepts are being extended to the development of fractional robust control systems, signal filtering, identification and modelling. Of particular interest is the fact that the fractional systems exhibit both short and long term memory (in some areas the designation “long range processes” is firmly established). While the short term memory corresponds to the “distribution of time constants” associated with the distribution of isolated poles and zeroes in the complex plane, the long term memory corresponds to infinitely many interlaced close to each other poles and zeros that in the limit originate a branch cut line as we saw in Chap. 3. This translates to a lack of specific time scale and, therefore, no new resonance or other instability effects appear and incorporates the power law behavior found in natural systems that show the greatest robustness to variation of environmental parameters. These characteristics have great influence on the development and application of fractional systems that is dependent on satisfactory solutions for the traditional tasks: modelling, identification, and implementation. In the fractional case, they are slightly more involved due to the fact of having, at least, one extra degree of freedom: the fractional order. However, this difficult increments the possibilities of obtaining more reliable and robust systems.
KeywordsFractional Order Fractional Derivative Fractional Calculus Fractional Brownian Motion Fractional System
- 4.Kolmogorov NA (1940) Wienersche Spiralen und Einige Andere Interessante Kurven im Hilbertschen Raum. Compte Rendus de l’Académie des Sciences de 1’Union des Républiques Soviétiques Socialistes 26(2):115–118Google Scholar