Application of input — State of the system transformation for linearization of some nonlinear generators

Zawadzki, Andrzej; Różowicz, Sebastian

doi:10.1007/s12555-014-0026-3

Cited by 13 publications

(11 citation statements)

References 17 publications

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“…The second method used to approximate the s α factor is the expansion into the Oustaloup series, where for frequency range (ω l ,ω h ), it is shown as transfer function H(s) [31][32][33][34]:…”

Section: Selected Approximation Methods In the Analysis Of Fractionalmentioning

confidence: 99%

Properties of Fractional-Order Magnetic Coupling

et al. 2020

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This paper presents the properties of fractional-order magnetic coupling. The difficulties connected with the analysis of two coils in dynamic states, resulting from the classical approach, provided motivation for studying the properties of fractional-order magnetic coupling. These difficulties arise from failure to comply with the commutation laws, i.e., a sudden power disappearance in the primary winding caused by a switch-mode power supply. Theoretically, under ideal conditions, a sudden power disappearance in the coil is, according to the classical method, manifested by a sudden voltage surge in the form of the Dirac delta function. As is well-known, it is difficult to obtain such ideal conditions in practice; the time of current disappearance does not equal zero due to the circuit breaker’s imperfection (even when electronic circuit breakers are used, the time equals several hundred nanoseconds). Furthermore, it is necessary to take into account phenomena occurring in real inductances, such as the skin effect, the influence of the ferromagnetic core and many other factors. It would be very difficult to model all these phenomena using classical differential calculus. The application of fractional-order differential calculus makes it possible to model them in a simple way by appropriate selection of coefficients and fractional-order derivatives. It should be mentioned that the analysis could be used, for example, in the case of high-voltage generation systems, including spark ignition systems of internal combustion engines. The use of fractional-order differential calculus will allow for more accurate modeling of phenomena occurring in such systems.

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Section: Selected Approximation Methods In the Analysis Of Fractionalmentioning

confidence: 99%

Properties of Fractional-Order Magnetic Coupling

et al. 2020

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“…in the theory of electrical circuits. Such attempts have already been made (for example [26][27][28][29][30]), but they were too few and not exhaustive enough. It appears that geometrical methods can easily find other applications.…”

Section: Introductionmentioning

confidence: 99%

The use of differential geometry methods for linearization of nonlinear electrical circuits with multiple inputs and multiple outputs (MIMOs)

Różowicz

Zawadzki

2018

Electr Eng

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The paper presents a transformation of nonlinear MIMO electrical circuit into linear one by a change in coordinates (local diffeomorphism) with the use of a closed feedback loop. The necessary conditions that must be fulfilled by a nonlinear system to make linearizing procedures possible are presented. Numerical solutions of state equations for the nonlinear system and equivalent linearized system are included.

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“…The main difference lies in the small size and low thermal capacity of parts to be welded; they are responsible for an escalation in weld discontinuities due to overheating [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

An Analysis of the Microstructure, Macrostructure and Microhardness of Nicr-Ir Joints Produced by Laser Welding with and without Preheat

Różowicz

Tofil

Zrak

2016

Archives of Metallurgy and Materials

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This paper discusses some of the basic problems involved in laser welding of dissimilar materials with significant differences in melting points. It focuses on the micro and macrostructure of laser welded NiCr-Ir microjoints used in central spark plug electrodes. The joints were produced by welding with and without preheat using an Nd,YAG laser. The structure and composition of the welded joints were analyzed by means of a light microscope (LM) and a scanning electron microscope (SEM) equipped with an energy dispersive X-ray (EDX) spectrometer. The microhardness of the weld area was also studied.

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Application of input — State of the system transformation for linearization of some nonlinear generators

Cited by 13 publications

References 17 publications

Properties of Fractional-Order Magnetic Coupling

Properties of Fractional-Order Magnetic Coupling

The use of differential geometry methods for linearization of nonlinear electrical circuits with multiple inputs and multiple outputs (MIMOs)

An Analysis of the Microstructure, Macrostructure and Microhardness of Nicr-Ir Joints Produced by Laser Welding with and without Preheat

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