Experimental Studies of a Fractional Order Universal Adaptive Stabilizer

Abstract

This work performs experimental verification of the asymptotic stability of two different types of fractional scalar systems by using universal adaptive stabilization as in. The types of systems verified experimentally are: (I) Fractional dynamics with integer order control strategy (II) Fractional dynamics with fractional order control strategy. The Mittag-Leffler function E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sub> (-lambdat <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">alpha</sup> ), forallalphaisin (2, 3] and lambda > 0 is used as a Nussbaum function as per [1]. Extensive hardware in the loop simulation of the mathematically developed results have been included in the paper. The results of the experiment serve not only to improve the understanding of fractional order universal adaptive stabilization but also proves that the methodology works well on real world systems.