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'''Fractional-order control (FOC)''' is a field of [[control theory]] that uses the [[fractional-order integrator]] as part of the control system design toolkit.
 
The fundamental advantage of FOC is that the fractional-order integrator weights history using a function that decays with a power-law tail. The effect is that the effects of all time are computed for each iteration of the control algorithm. This creates a 'distribution of time constants,' the upshot of which is there is no particular time constant, or resonance frequency, for the system.
 
In fact, the fractional integral operator <math>\frac{1}{s^{\lambda}}</math> is different from any integer-order rational transfer function <math> {G_{I}} (s)</math>, in the sense that it is a non-local operator that possesses an infinite memory and takes into account the whole history of its input signal.<ref>M. S. Tavazoei, M. Haeri, S. Bolouki, and M. Siami, "Stability preservation analysis for frequency-based methods in numerical simulation of fractional-order systems," SIAM Journal on Numerical Analysis, vol. 47, pp. 321–338, 2008.</ref>
 
Fractional-order control shows promise in many controlled environments that suffer from the classical problems of overshoot and resonance, as well as time diffuse applications such as thermal dissipation and chemical mixing.
 
==See also==
*[[Differintegral]]
*[[Fractional calculus]]
* [[Fractional-order system]]
 
==External links==
* [http://sites.google.com/site/fractionalcalculus/ Dr. YangQuan Chen's page about fractional calculus on Google Sites]
* [http://web.tuke.sk/fda10/index.html 4th IFAC Workshop on Fractional Differentiation and Its Applications University of Extremadura, Badajoz, Spain, October 18–20, 2010]
* [http://fda08.cankaya.edu.tr/ 3rd IFAC Workshop on Fractional Differentiation and its Applications, Ankara, Turkey, 5–7 November, 2008]
* [http://www.gecad.isep.ipp.pt/FDA06/ 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, Portugal, 19–21 July, 2006]
* [http://extranet.ims-bordeaux.fr/LAPS/wlap/events/FDA04/home.html 1st IFAC Workshop on Fractional Differentiation and its Applications, Bordeaux, France, 19–21 July, 2004]
 
===References===
 
<references/>
 
[[Category:Control theory]]
[[Category:Cybernetics]]
 
 
{{Mathapplied-stub}}

Latest revision as of 18:44, 9 November 2014

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