This paper discusses the research and analysis of the dynamics of high-voltage generating systems. The test subject is an ignition system modelled by a set of two induction coils with an open ferromagnetic core that constitutes an ignition coil. The essence of the tests involved the application of magnetic coupling of the fractional order that enabled taking into account the non-idealities of the coils and the connector that implements the ignition point. The paper contains the results of a theoretical analysis, supported by digital simulations. The conducted experiments confirm the purposefulness of the conducted analyses and the possibility of modeling real objects based on circuits with fractional-order elements.
Abstract. In the paper, the analytical forms of fractional order derivatives of sinusoidal function according to definitions of RiemannLiouville and Caputo are presented. To determine the analytical form of the integrals appearing in definitions of derivatives of fractional order the Lommel functions from hypergeometrical functions family were applied. With the use of properties of the derivatives of fractional order -differential-integral there were presented the conception of generalized element of a single equation, which depending on the value of the derivative order, can be inductor, resistor, capacitor, or a hypothetical element of a fractional order differential equation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.