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Supercapacitors have been rapidly adopted to replace batteries in many instances from power tools to automotive and aviation. Designing systems incorporating supercapacitors necessitate an accurate model of supercapacitor to maintain system efficiency. However, due to varying impedance property of supercapacitor, modeling becomes critical with likelihood of introducing errors. This work proposes an enhanced model to predict the system dynamics under various initial state of charge in supercapacitors. The proposed flexible model is suitable to represent actual supercapacitor impedance without prior assumption on the model structure. The use of one model to cover the other various impedance structures is simple and possible to estimate accurate supercapacitor's impedance. Selection of impedance structure is selfregulated to improve the accuracy with minimum variables. To illustrate the variable structure fractional model, experimental results are shown with three different values of supercapacitors from three different manufacturers.

In order to control or operate any system in a closed-loop, it is important to know its behavior in the form of mathematical models. In the last two decades, a fractional-order model has received more attention in system identification instead of classical integer-order model transfer function. Literature shows recently that some techniques on fractional calculus and fractional-order models have been presenting valuable contributions to real-world processes and achieved better results. Such new developments have impelled research into extensions of the classical identification techniques to advanced fields of science and engineering. This article surveys the recent methods in the field and other related challenges to implement the fractional-order derivatives and miss-matching with conventional science. The comprehensive discussion on available literature would help the readers to grasp the concept of fractional-order modeling and can facilitate future investigations. One can anticipate manifesting recent advances in fractional-order modeling in this paper and unlocking more opportunities for research.

In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios.