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In the paper we extend the ultracapacitor modelling results onto the frequency domain and we concentrate on the ultracpacitor's parameters identification. For the completeness of presentation some basic notions in fractional order calculus are recalled. Then the issue of capacity for the ultracapacitors is shown and discussed. Further, the frequency domain identification of ultracapacitors' models...
In this paper the modelling of ultracapacitor system using continuous and discrete fractional order systems is presented. The discrete fractional order state-space model is obtained for the ultracapacitor basing on its original continuous time description. In order to make the state of the system accessibile for control purposes the Fractional-order Kalman Filter (FKF) and Extended Fractional-order...
Dynamic programming and discrete-time calculus of variations optimization problems for fractional discrete-time systems with quadratic performance index have been formulated and solved. A new methods for numerical computation of optimization problems have been presented. The efficiency of the methods have been demonstrated on numerical example and illustrated by graphs. Graphs also show the differences...
In this article a new approach of using the discrete time fractional order artificial neural network controller for control of charging and discharging process for system with ultracapacitor is proposed. First, the discrete fractional order neural network for incommensurate non-linear system modeling is presented. After successful modeling of the system with ultracapacitor the neural network inverse...
In the paper a novel method of analog modeling of fractional order integrators is presented. In particular, two special cases are discussed, i.e. integrators of order α = 0.25, and α = 0.5. The method proposed is based on the domino ladder approximation of irrational transfer function. It allows to obtain an analog model using only electric elements like resistors and capacitors of standard produced...
In the paper a comparison of different optimization methods to identification of fractional order dynamical systems is presented. The fractional models of the examples of physical systems — ultracapacitors — are established. Then different real frequency responses data from a laboratory setup of the processes are collected and the comparison of identification methods based on Least Squares and Total...
In this paper, the modeling of the ultracapacitor using fractional order model is shown. The derivation of time domain response of the ultracapacitor and system with the ultracapacitor is presented. The results of frequency domain identification were used to validate the response of the ultracapacitor in time domain. All theoretical results are compared with the response of the physical system with...
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