As fractional-order systems are becoming more widely accepted and their usage is increasing, it is important to understand their energy storage and loss properties. Fractional-order operators can be implemented using a distributed state representation, which has been shown to be equivalent to the Riemann–Liouville representation. In this paper, the distributed state for a fractional-order integrator is represented using an infinite resistor–capacitor network such that the energy storage and loss properties can be readily determined. This derivation is repeated for fractional-order derivatives using an infinite resistor–inductor network. An analytical example is included to verify the results for a half-order integrator. Approximation methods are included.
Energy Storage and Loss in Fractional-Order Systems
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 30, 2014; final manuscript received December 27, 2014; published online April 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.
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Hartley, T. T., Trigeassou, J., Lorenzo, C. F., and Maamri, N. (November 1, 2015). "Energy Storage and Loss in Fractional-Order Systems." ASME. J. Comput. Nonlinear Dynam. November 2015; 10(6): 061006. https://doi.org/10.1115/1.4029511
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