Two state of charge estimation methods using fractional order extended and unscented Kalman filter and a nonlinear variable fractional order battery model are implemented. Both, battery model and Kalman filters are evaluated and compared using measurements of an actual lithium-ion polymer battery cell. The observability of the battery model and the influence of an initialization function on the estimation algorithms is investigated.

This paper considers a fractional modelbased identification method with the objective to determine the aging of a battery cell. The method avoids lumped approximations of the fractional operator. Moreover with this approach it is possible to identify physically motivated battery cell parameters. The basic idea is to transfer the derivatives from the measurements to the so called modulating functions. With the help of simulations a robust behavior against measurement noise is shown. It is possible to use the method for online battery identification. Zusammenfassung:In diesem Artikel wird eine fraktionale modellbasierte Identifikationsmethode vorgestellt. Diese liefert einen Beitrag zur Altersdiagnose von Batteriezellen. Vorteilhaft ist, dass die sonst frühe Approximation des fraktionalen Operators entfällt und dass mit ihr physikalisch motivierte Parameter identifiziert werden können. Die Kernidee des Verfahrens ist, Ableitungen der Messgröẞen auf sogenannte Modulationsfunktionen zu über-tragen. Anhand von Simulationen konnte gezeigt werden, dass das Verfahren robust gegenüber Messrauschen ist. Die Methode ist aus den genannten Gründen für eine online Identifikation einer Batteriezelle geeignet.

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Thin, porous films of WO3 were fabricated by solution-based synthesis via spin-coating using polyethylene glycol (PEG), a block copolymer (PIB50-b-PEO45), or a combination of PEG and PIB50-b-PEO45 as structure-directing agents. The influence of the polymers on the composition and porosity of WO3 was investigated by microwave plasma atomic emission spectroscopy, energy-dispersive X-ray spectroscopy, scanning electron microscopy, X-ray diffraction, and gas sorption analysis. The electrochromic performance of the WO3 thin films was characterized with LiClO4 in propylene carbonate as electrolyte. To analyze the intercalation of the Li+ ions, time-of-flight secondary ion mass spectrometry, and X-ray photoelectron spectroscopy were performed on films in a pristine or reduced state. The use of PEG led to networks of micropores allowing fast reversible electrochromic switching with a high modulation of the optical transmittance and a high coloration efficiency. The use of PIB50-b-PEO45 provided isolated spherical mesopores leading to an electrochromic performance similar to compact WO3, only. Optimum characteristics were obtained in films which had been prepared in the presence of both, PEG and PIB50-b-PEO45, since WO3 films with mesopores were obtained that were interconnected by a microporous network and showed a clear progress in electrochromic switching beyond compact or microporous WO3.

This paper presents a new method for parameter identification based on the modulating function method for commensurable fractional-order models. The novelty of the method lies in the automatic determination of a specific modulating function by controlling a model-based auxiliary system, instead of applying and parameterizing a generic modulating function. The input signal of the model-based auxiliary system used to determine the modulating function is designed such that a separate identification of each individual parameter of the fractional-order model is enabled. This eliminates the shortcomings of the common modulating function method in which a modulating function must be adapted to the investigated system heuristically.

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