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Wyniki wyszukiwania dla: FRACTIONAL ORDER CIRCUITS
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Boundary problems for fractional differential equations
PublikacjaIn this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.
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Numerical Investigation of Nuclear Reactor Kinetic and Heat Transfer Fractional Model with Temperature Feedback
PublikacjaAbstract—In the paper, the numerical results concerning the kinetics and proposed heat exchange models in nuclear reactor based on fractional calculus are presented for typical inputs. Two fractional models are proposed and compared with the model based on ordinary derivative. The first fractional model is based on one of the generalized Cattaneo equations. The second one is based on replacing the ordinary to fractional order of...
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On Applications of Elements Modelled by Fractional Derivatives in Circuit Theory
PublikacjaIn this paper, concepts of fractional-order (FO) derivatives are reviewed and discussed with regard to element models applied in the circuit theory. The properties of FO derivatives required for the circuit-level modeling are formulated. Potential problems related to the generalization of transmission-line equations with the use of FO derivatives are presented. It is demonstrated that some formulations of FO derivatives have limited...
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A complex variable fractional-delay FIR filter structure
PublikacjaW artykule wprowadzamy strukturę zespolonego filtru o skończonej odpowiedzi impulsowej (ang. finite impulse response - FIR) ze zmiennym opóźnieniem ułamkowym (ang. fractional delay - FD). Strukturę tę otrzymujemy na podstawie przestrajanego filtru FD FIR o współczynnikach rzeczywistych. Stanowi ona połączenie zbioru liniowo-fazowych filtrów FIR o współczynnikach stałych rzeczywistych i dwóch łańcuchów mnożąco-akumulujących, zawierających...
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Fractional differential equations with causal operators
PublikacjaWe study fractional differential equations with causal operators. The existence of solutions is obtained by applying the successive approximate method. Some applications are discussed including also the case when causal operator Q is a linear operator. Examples illustrate some results.
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Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector
PublikacjaIn this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their...
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Modelling and simulations in time-fractional electrodynamics based on control engineering methods
PublikacjaIn this paper, control engineering methods are presented with regard to modelling and simulations of signal propagation in time-fractional (TF) electrodynamics. That is, signal propagation is simulated in electromagnetic media described by Maxwell’s equations with fractional-order constitutive relations in the time domain. We demonstrate that such equations in TF electrodynamics can be considered as a continuous-time system of...
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Fault detection in electronic circuits using test buses
PublikacjaA survey of test buses designed for diagnostics of digital and analog electronic circuits is presented: the IEEE 1149.1 bus for digital circuits, the IEEE 1149.4 bus for mixed-signal and the IEEE 1149.6 bus for AC coupled complex digital circuits. Each bus is presented with its structure, solution of key elements, particularly boundary registers and a set of test instructions. Diagnosis with the use of the described buses is...
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On Sample Rate Conversion Based on Variable Fractional Delay Filters
PublikacjaThe sample rate conversion algorithm based on variable fractional delay filters is often used if the resampling ratio cannot be expressed as the ratio of small integer numbers or if it is not constant. The main advantage of such solution is that it allows for arbitrary resampling ratios which can even be changed during the resampling process. In this paper a discussion on influence of different approaches to fractional filter...
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Electric shock hazard in circuits with variable-speed drives
PublikacjaThe conventional approach to electrical safety under fault condition in typical power systems considers earth fault currents of sinusoidal waveform and frequency of 50/60 Hz. However, in circuits with variable-speed drives, there is earth fault current flow with harmonics, and these harmonics influence the threshold of ventricular fibrillation. The paper presents earth fault current waveforms in circuits with variable-speed drives...
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Positive solutions to advanced fractional differential equations with nonlocal boundary conditions
PublikacjaWe study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.
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Programmable Digital Circuits (2023/2024)
Kursy Online -
Square root RC Nyquist filter of fractional delay
PublikacjaIn this paper we propose a discrete-time FIR (finite impulse response) filter which couples the role of square root Nyquist filter with fractional delay filter. This filter enables to substitute for a cascade of square root RC (SRRC) Nyquist filter and fractional delay filter in one device/algorithm. The aim is to compensate for transmission delay in communication system. Statistically defined performances, e.g. BER (bit error...
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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
PublikacjaIn this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced....
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Numerical solution of fractional neutron point kinetics in nuclear reactor
PublikacjaThis paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme...
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Comments on various extensions of the Riemann–Liouville fractional derivatives : About the Leibniz and chain rule properties
PublikacjaStarting from the Riemann–Liouville derivative, many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation. Discussing in full generality the existence of such operator over continuous functions, we derive some obstruction Lemma which can be used to prove the triviality...
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System of protection against electric shock for circuits with power electronics converters
PublikacjaModern low voltage circuits are very often equipped with power electronics converters, therefore in these circuits non-sinusoidal earth currents (touch currents) may occur. For non-sinusoidal currents safety criteria should be modified. This paper presents these modified criteria and a computer system of protection against electric shock which can be implemented in circuits with power electronics converters. The system is based...
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efficient fractional delay hilbert transform filter in the farrow structure
PublikacjaIn this paper the design and application of a Fractional Delay Hilbert Transform Filter (FDHTF) into an adaptive sub-sample delay estimation between two separated sinusoidal signals is considered. The FDHTF incorporates the functions of Hilbertian and variable fractional delay filtering of the incoming signal simultaneously, in one stage. In traditional approach each of these operations was performed separately. Obtained value...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublikacjaIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Religion and the Social Order
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Fractional equations of Volterra type involving a Riemann Liouville derivative
PublikacjaIn this paper, we discuss the existence of solutions of fractional equations of Volterra type with the Riemann Liouville derivative. Existence results are obtained by using a Banach fixed point theorem with weighted norms and by a monotone iterative method too. An example illustrates the results.
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MEMORY EFFECT ANALYSIS USING PIECEWISE CUBIC B-SPLINE OF TIME FRACTIONAL DIFFUSION EQUATION
PublikacjaThe purpose of this work is to study the memory effect analysis of Caputo–Fabrizio time fractional diffusion equation by means of cubic B-spline functions. The Caputo–Fabrizio interpretation of fractional derivative involves a non-singular kernel that permits to describe some class of material heterogeneities and the effect of memory more effectively. The proposed numerical technique relies on finite difference approach and cubic...
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A new approach to a fast and accurate design of microwave circuits with complex topologies
PublikacjaA robust simulation-driven design methodology of microwave circuits with complex topologies has been presented. The general method elaborated is suitable for a wide class of N-port unconventional microwave circuits constructed as a deviation from classic design solutions. The key idea of the approach proposed lies in an iterative redesign of a conventional circuit by a sequential modification and optimisation of its atomic building...
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Immunity of residual current devices to the impulse leakage current in circuits with variable speed drives
PublikacjaThis paper concerns reliability of supply in variable speed drive circuits with residual current devices. During normal operation of these circuits high value of leakage current causes unwanted tripping of residual current devices. Immunity of residual current devices to the impulse leakage current should be evaluated. The system for testing of residual current devices and results of the test are presented
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Variable Ratio Sample Rate Conversion Based on Fractional Delay Filter
PublikacjaIn this paper a sample rate conversion algorithm which allows for continuously changing resampling ratio has been presented. The proposed implementation is based on a variable fractional delay filter which is implemented by means of a Farrow structure. Coefficients of this structure are computed on the basis of fractional delay filters which are designed using the offset window method. The proposed approach allows us to freely...
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Half-Order Modeling of Saturated Synchronous Machine
PublikacjaNoninteger order systems are used to model diffusion in conductive parts of electrical machines as they lead to more compact and knowledge models but also to improve their precision. In this paper a linear half-order impedance model of a ferromagnetic sheet deduced from the diffusion of magnetic field is briefly introduced. Then, from physical considerations and finite elements simulation, the nonlinear half-order impedance model...
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Fuzzy Multi-Regional Fractional PID controller for Pressurized Water nuclear Reactor
PublikacjaThe paper presents the methodology for the synthesis of a Fuzzy Multi-Regional Fractional Order PID controller (FMR-FOPID) used to control the average thermal power of a PWR nuclear reactor in the load following mode. The controller utilizes a set of FOPID controllers and the fuzzy logic Takagi-Sugeno reasoning system. The proposed methodology is based on two optimization parts. The first part is devoted to finding the optimal...
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Numerical solution analysis of fractional point kinetics and heat exchange in nuclear reactor
PublikacjaThe paper presents the neutron point kinetics and heat exchange models for the nuclear reactor. The models consist of a nonlinear system of fractional ordinary differential and algebraic equations. Two numerical algorithms are used to solve them. The first algorithm is application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. The second involves building an analog scheme in the FOMCON Toolbox...
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The effect of the motor filters on earth fault current waveform in circuits with variable speed drives
PublikacjaIn circuits with variable speed drives distorted earth fault current flows. Earth fault current distortion influences the threshold of ventricular fibrillation. This paper presents earth fault current distortion in circuits with variable speed drives when motor filter is used. Two types of motor filter are analyzed. For every type of filter the effect of earth fault current distortion on ventricular fibrillation is evaluated.
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The effect of the motor filters on earth fault current waveform in circuits with variable speed drives
PublikacjaIn circuits with variable speed drives distorted earth fault current flows. Earth fault current distortion influences the threshold of ventricular fibrillation. This paper presents earth fault current distortion in circuits with variable speed drives when motor filter is used. Two types of motor filter are analyzed. For every type of filter the effect of earth fault current distortion on ventricular fibrillation is evaluated.
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Fractional Differential Calculus
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Computer System for Evaluation of Shock Hazard in Circuits with Non-sinusoidal Earth Currents
PublikacjaEffects of current on people are mainly considered for 50/60 Hz sinusoidal current and smooth direct current. However, modern low voltage circuits are very often equipped with power electronics converters – rectifiers, frequency converters, therefore non-sinusoidal earth currents (touch currents) occur. For non-sinusoidal currents safety criteria should be modified. This paper presents a computer system, based on LabVIEW environment,...
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Effect of the let-through energy of overcurrent protective devices on the temperature of conductors during short-circuits
PublikacjaThe scope of the verification of low-voltage systems covers the earth fault loop impedance measurement. This measurement is usually performed with the use of low-value current meters, which force a current many times lower than the one occurring during a real short-circuit. Therefore, the international standard recommends consideration of the increase of resistance of conductors with the increase of temperature, which may occur...
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Identification and non-integer order modelling of synchronous machines operating as generator
PublikacjaThis paper presents an original mathematical model of a synchronous generator using derivatives of fractional order. In contrast to classical models composed of a large number of R-L ladders, it comprises half-order impedances, which enable the accurate description of the electromagnetic induction phenomena in a wide frequency range, while minimizing the order and number of model parameters. The proposed model takes into account...
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Two-Rate Based Low-Complexity Variable Fractional-Delay FIR Filter Structures
PublikacjaThis paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate structures but derived through a two-rate approach. The basic structure considered hitherto utilizes a regular half-band (HB) linear-phase filter and the Farrow structure with linear-phase subfilters. Especially for wide-band specifications, this structure is computationally efficient...
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Fault Loop Impedance Measurement in Circuits Fed by UPS and Principle of Safety Protection
PublikacjaThis paper indicates a significant problem of uncertainty of fault loop impedance (FLI) measurement in circuits powered from uninterruptible power supply (UPS) (double-conversion AC-DC-AC). The correctly determined value of this impedance, related to the short-circuit current disconnection time and to the reference value, is one of the most important elements that determines the approval of an electrical installation and its receivers...
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Comments on “Closed Form Variable Fractional Time Delay Using FFT”
PublikacjaIn this letter drawbacks of the aforementioned paper are pointed out. The proposed approach is improved with minor modifications of the discrete frequency response. This allows for design of fractional delay filters which are close to optimal and can be efficiently implemented in the frequency domain using the sliding DFT based structure. Alternatively, the derived equivalent closed form formulae for offset windows can be used...
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Fractional neutron point kinetics equations for nuclear reactor dynamics – Numerical solution investigations
PublikacjaThis paper presents results concerning numerical solutions to a fractional neutron point kinetics model for a nuclear reactor. The paper discusses and expands on results presented in (Espinosa-Paredes et al., 2011). The fractional neutron point kinetics model with six groups of delayed neutron precursors was developed and a numerical solution using the Edwards’ method was proposed (Edwards et al., 2002). The mathematical model...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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ORF Approximation in Numerical Analysis of Fractional Point Kinetics and Heat Exchange Model of Nuclear Reactor
PublikacjaThis paper presents results concerning numerical solutions of the fractional point kinetics (FPK) and heat exchange (HE) model for a nuclear reactor. The model consists of a nonlinear system of fractional and ordinary differential equations. Two methods to solve the model are compared. The first one applies Oustaloup Recursive Filter (ORF) and the second one applies Refined Oustaloup Recursive Filter (RORF). Simulation tests have...
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Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution
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Rapid multi-objective simulation-driven design of compact microwave circuits
PublikacjaA methodology for rapid multi-objective design of compact microwave circuits is proposed. Our approach exploits point-by-point Pareto set identification using surrogate-based optimization techniques, auxiliary equivalent circuit models, and space mapping as the major model correction method. The proposed technique is illustrated and validated through the design of a compact rat-race coupler. A set of ten designs being trade-offs...
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Selected problems of earth fault loop impedance testing in circuits fed from UPS
PublikacjaIn the paper a principle of earth fault loop impedance testing in low voltage systems has been presented. Selected factors, influencing accuracy of the testing, are indicated. A structure of UPS of VFI-type and the problem of impedance testing in circuits with such type of UPS are discussed.
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STANY NIEUSTALONE TOWARZYSZĄCE POMIAROWI IMPEDANCJI PĘTLI ZWARCIA W OBWODACH WYJŚCIOWYCH ZASILACZY BEZPRZERWOWYCH UPS
PublikacjaW pracy przedstawiono metodykę i wyniki pomiarów stanów nieustalonych w zasilaczu bezprzerwowym (UPS) typu on - line. Do rejestracji zdarzeń po stronie zasilania i na wyjściu UPS wykorzystano dwa przyrządy do pomiaru jakości energii elektrycznej zsynchronizowane czasowo. Rejestratory kompresują uzyskane dane pomiarowe, co może wprowadzać dodatkowe błędy pomiaru wielkości mierzonych – napięć i prądów. Dodatkowe rejestracje oscyloskopem...
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Atomistic Surrogate-Based Optimization for Simulation-Driven Design of Computationally Expensive Microwave Circuits with Compact Footprints
PublikacjaA robust simulation-driven design methodology for computationally expensive microwave circuits with compact footprints has been presented. The general method introduced in this chapter is suitable for a wide class of N-port un-conventional microwave circuits constructed as a deviation from classic design solutions. Conventional electromagnetic (EM) simulation-driven design routines are generally prohibitive when applied to numerically...
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Evaluation of applicability of classic methods of a fault loop impedance measurement to circuits with residual current devices
PublikacjaMeasurement of fault loop impedance in low voltage grids and systems is in most cases performed to verify the effectiveness of protection against electric shock by automatic disconnection of supply. For the sake of measurement accuracy, it is advisable to perform it using large current. Unfortunately, in circuits with residual current devices which are very widely used nowadays, a large measurement current may trigger those devices...
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A NUMERICAL STUDY ON THE DYNAMICS OF DENGUE DISEASE MODEL WITH FRACTIONAL PIECEWISE DERIVATIVE
PublikacjaThe aim of this paper is to study the dynamics of Dengue disease model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana–Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative are examined for the aforementioned problem. The suggested...
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Metal dusting phenomena of 501 AISI furnace tubes in refinery fractional distillation unit
PublikacjaThe purpose of this investigation was to conduct the failure analysis of 501 AISI furnace tubes places before distillation column in fractional distillation unit. The investigated furnace tubes were planned to work for ten years however after just two years of exploitation <30% of the material left. The observed corrosion process had the intense and complex character. The well-adhered shiny black deposits and deep, round pits were...
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Topological model of aptitude of the measurement circuits of main subassemblies of an internal combustion engine crankshaft-piston assembly
PublikacjaThe paper presents a topological model allowing to determine the probability of aptitude of the diagnosing system (SDG) individual measuring circuits and also to determine to what degree they influence the assessment of the technical condition of an arbitrary main subassembly of crankshaft-piston assemblies as a diagnosed system (SDN).
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Rapid EM-Driven Design of Compact RF Circuits By Means of Nested Space Mapping
PublikacjaA methodology for rapid design of RF circuits constituted by compact microstrip resonant-cells (CMRCs) is presented. Our approach exploits nested space mapping (NSM) technology, where the inner SM layer is used to correct the equivalent circuit model at the CMRC level, whereas the outer layer enhances the coarse model of the entire structure under design. We demonstrate that NSM dramatically improves performance of surrogate-based...