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Identification of Complex Order-distributions

Department of Electrical and Computer Engineering, The University of Akron, Akron OH 44325 USA, jla36{at}uakron.edu

T.T. Hartley

Department of Electrical and Computer Engineering, The University of Akron, Akron OH 44325 USA

C.F. Lorenzo

NASA Glenn Research Center, Cleveland, OH 44135 USA

This article discusses the identification of fractional systems using the concepts of complex order distribution. Based on the ability to define systems using complex order-distributions, it is shown that system identification in the frequency domain using a least-squares approach can be performed. A mesh is created to cover an area in the complex-order plane. The weighting of each block in the order-plane is selected to minimize the square-error between the frequency response of the system and the identified system. The identified systems have real time responses. Four examples, including both pure real-order systems and pure complex-order systems, are presented to demonstrate the utility of the identification method.

Key Words: Fractional calculus • fractional-order systems • complex order-distributions • system identification

Journal of Vibration and Control, Vol. 14, No. 9-10, 1375-1388 (2008)
DOI: 10.1177/1077546307087443


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