TY - CHAP

T1 - Where are we going to?

AU - Ortigueira, Manuel Duarte

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79959725151&partnerID=8YFLogxK

U2 - 10.1007/978-94-007-0747-4_7

DO - 10.1007/978-94-007-0747-4_7

M3 - Chapter

AN - SCOPUS:79959725151

SN - 9789400707467

T3 - Lecture Notes in Electrical Engineering

SP - 145

EP - 152

BT - Fractional Calculus for Scientists and Engineers

ER -