Identification of Complex Order-distributions

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Abstract
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.